DEPARTMENT OF MECHANICS AND MARITIME SCIENCES DIVISION OF VEHICLE ENGINEERING AND AUTONOMOUS SYSTEMS CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2023 www.chalmers.se Development and Implement- ation of Torque Feedback for Steer-by-wire systems Master’s thesis in Systems, Control & Mechatronics OSSIAN BERGSTRÖM JOHAN JANSSON http://www.chalmers.se/ MASTER’S THESIS IN SYSTEMS, CONTROL & MECHATRONICS Development and Implementation of Torque Feedback for Steer-by-wire systems OSSIAN BERGSTRÖM JOHAN JANSSON Department of Mechanics and Maritime Sciences Division of Vehicle Engineering and Autonomous Systems CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2023 Development and Implementation of Torque Feedback for Steer-by-wire systems OSSIAN BERGSTRÖM JOHAN JANSSON © OSSIAN BERGSTRÖM, JOHAN JANSSON, 2023 Department of Mechanics and Maritime Sciences Division of Vehicle Engineering and Autonomous Systems Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone: +46 (0)31-772 1000 Cover: The vehicle used for real-time testing of steering feel model. Chalmers Reproservice Göteborg, Sweden 2023 Development and Implementation of Torque Feedback for Steer-by-wire systems Master’s thesis in SYSTEMS, CONTROL & MECHATRONICS OSSIAN BERGSTRÖM JOHAN JANSSON Department of Mechanics and Maritime Sciences Division of Vehicle Engineering and Autonomous Systems Chalmers University of Technology Abstract Steer-by-wire (SbW) has gained significant attention in recent years, revolutionizing vehicle steering by eliminating the mechanical connection between the steering wheel and steering rack. However, by eliminating the connection, the external forces acting on the steering rack are lost and no informative torque feedback will be given to the driver. A solution to this problem is to simulate the corresponding forces by implementing torque feedback using a Force Feedback (FFb) actuator. The focus of this master’s thesis was to develop and implement torque feedback for an SbW system. The objective was to create a steering feel model that simulated a base torque profile and incorporate a set of fundamental features such that the steering feel resembled a conventional steering system with a mechanical connection. Throughout the thesis, a hardware setup was available, integrated as a testing rig and in a testing vehicle for implementation, testing, and evaluation purposes. The system consisted of a steering wheel, a planetary gearbox, an FFb actuator, an Electronic control unit (ECU), and a steering rack. A closed-loop model was utilized to simulate the hardware setup in Simulink. The model incorporated the torque input from the driver, FFb actuator, and a reference generator i.e. the steering feel model, and was used for both implementation and testing purposes. After acceptable simulation results, the steering feel model was implemented in the ECU for real-life testing and evaluation of the torque feedback in the testing rig and vehicle. The initial step of designing the torque profile was by designing the base torque behavior. This was accomplished by deriving a set of system equations based on torque feedback measurements obtained from tests performed on a vehicle equipped with a conventional steering system. The equations contained a set of tunable parameters that were fine-tuned to accurately emulate the measured base torque. Some torque feedback features, such as End-stop were subjectively tuned as they were not based on the reference measurements. The development and implementation resulted in a steering feel model that closely resembled the behavior of the reference steering system, particularly for mid-range vehicle speeds. The steering feel for steering directions away from the center position was found to be satisfactory for all vehicle speeds for real-life testing on the testing rig and in the testing car. However, future work is required to refine the model and achieve hysteresis that fully emulates a conventional steering system for all vehicle speeds. Although, in order to improve the hysteresis, the implementation of a more efficient FFb actuator could minimize the significant influence of the cogging torque in the system. Future work on the features emulating understeer and oversteer is also required. Overall, this thesis contributed to advancing the understanding and implementation of torque feedback in SbW systems, providing insights for improving the steering feel and driving experience for such systems. Keywords: Steer-by-wire, Force Feedback, Electric Power Assisted Steering i Acknowledgements We extend our heartfelt gratitude to Volvo Cars for providing us with an extraordinary opportunity and project that allowed us to showcase and enhance our engineering abilities. It has been an absolute honor to be part of this work. First and foremost, we would like to express our sincere appreciation to our supervisor, Matthijs Klomp, for his in- valuable guidance and support throughout the entire duration of this thesis. His deep interest and passion for the subject matter, combined with his expert guidance, contributed significantly to the quality of our master’s thesis. Our gratitude also extends to our examiner, Fredrick Bruzelius, whose expertise in signal processing and various other subjects greatly enriched our research. We deeply appreciate the insightful conversations and discussions we had with him along the way. Lastly, we would like to express our thanks to Filip Brink and Linnea Wennberg for their companionship and lighthearted conversations, which brought joy and levity to our days in the office. We are immensely grateful to everyone mentioned above and to all others who have supported us directly or indirectly during this journey. Without their contributions, this thesis would not have been possible. Their unwavering support, guidance, and camaraderie have been a huge contribution to our success. Thank you all from the bottom of our hearts. ii Nomenclature Parameters: τsw - Torque acting on steering wheel by driver τfricGrd - Torque acting on Steer-by-wire system by tire-ground friction τfricSys - Torque acting on Steer-by-wire system by steering system friction τFFb - Torque applied by Force Feedback actuator JFFb - Moment of inertia of Force Feedback system bFFb - Damping coefficient of Force Feedback system δ̈sw - Angular acceleration of steering wheel δ̇sw - Angular velocity of steering wheel Fyf - Lateral force on front tires Fzf - Normal force on front tires l - Lever dependent on the contact surface between the tire and the size of the road τa - Aligning torque tp - Pneumatic trail tm - Mechanical trail Cf - Front tire cornering stiffness coefficient αf - Front tire slip angle δ - Front wheel steering angle δ̇ - Front wheel steering angle velocity δmax - Maximum steering angle before grip starts to decrease L - Wheel base R - Turning radius ay - Lateral acceleration v - Vehicle velocity g - Gravitational acceleration constant µtireGrd - Frictional constant between tire and road µsys - Frictional constant for the steering system ksys - Constant varying the total friction in the steering system∑ F - Sum of all forces k - Spring constant b - Damping constant Fexternal - External forces acting upon a spring-damper m - Mass x - Position ẋ - Velocity ẍ - Acceleration τSD - Torque from spring-damper y2 - Base torque second-degree polynomial max torque x2 - Base torque second-degree polynomial max torque position k2 - Base torque first-degree polynomial slope constant and Base torque second-degree polynomial slope at x2 m2 - Base torque first-degree polynomial constant term velvehicle km - Vehicle speed in km/h vehiclevel - Vehicle speed in m/s pos - Current position of the steering wheel TfricDamp - Friction damping torque xslipStart - Position at which loss of grip starts xslipEnd - Position at which grip has been lost yslipStart - Amount of torque when loss of grip starts yslipEnd - Amount of torque when grip has been lost xmax - Position at which maximum amount of torque at End-stop has been reached xend - Position at which End-stop starts ymax - Maximum amount of torque at xmax yend - Amount of torque at which End-stop starts bbaseTrq - Damping variable for On-center damping bendStop - Damping variable for End-stop iii bendMax - Maximum number for bendStop posshifted - Position shifted from the Displacement of zero torque position TfricComp - Constant amount of torque used as friction compensation Tintegrator - Torque generated by the Return to center integrator error - Integrator error for the Return to center integrator Ki - Integrator constant TintegratorMax - Maximum torque that can be generated by the Return to center integrator Units: rpm - Revolutions per minute N - Newton mNm - Millinewton meter Acronyms CAN - Controller Area Network DC - Direct Current CAPL - Communication Access Programming Language RTU - Remote Terminal Unit ECU - Electronic Control Unit SbW - Steer-by-wire FFb - Force Feedback EPAS - Electronic Powers Assistance System ECM - Engine Control Module EBCM - Electronic Brake Control Module PCM - Powertrain Control Module VCM - Vehicle Control Module BCM - Body Control Module PC - Personal Computer USB - Universal Serial Bus LED - Light Emitting Diode BLDC - Brushless Direct Current iv Contents Abstract i Acknowledgements ii Nomenclature iii Acronyms iv Contents v 1 Introduction 1 1.1 Steering feel background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Hardware and software used in Project 5 2.1 Force feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Gearbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Electronic Control Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Vector VN8911 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 CANoe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.3 Communication Access Programming Language (CAPL) . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Steering rack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Testing rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Developing and Implementation software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5.1 Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5.2 Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5.3 CANoe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Modelling of Steering system 11 3.1 Steer-by-wire system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Aligning torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 Friction torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Spring-damper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.5 Loss of grip from understeer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4 Development and Implementation of Torque Feedback 15 4.1 Base torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.1.1 Zero velocity torque feature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.2 Loss of traction (Understeer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3 End-stop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.3.1 Obstacle detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.4 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.4.1 On-center damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.4.2 End-stop damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.5 Displacement of zero torque position (Oversteer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.6 Return to center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.7 Angular velocity limiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5 Vehicle handling tests 26 v 6 Experimental results 28 6.1 Base torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 6.2 Base torque with On-center damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 6.3 Base torque with additional Return to zero features . . . . . . . . . . . . . . . . . . . . . . . . . . 35 6.3.1 Return to center assistance by friction compensation . . . . . . . . . . . . . . . . . . . . . . . . . 35 6.3.2 Return to center assistance by integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6.4 Torque at zero velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 6.5 Displacement of zero torque position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 6.6 Test track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.7 Cogging Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 7 Discussion 53 8 Conclusion 56 9 Future work 57 References 58 vi 1 Introduction Steer-by-Wire (SbW) is a popular topic that is increasing in the automotive industry. A SbW system is a replacement for the mechanical steering system used in most vehicles today. Whereas mechanical steering systems are usually Electric Power Assisted Steering (EPAS) systems. For a SbW system, the mechanical connection between the steering rack and the steering wheel is replaced with an electrical connection. The electrical connection consists of an actuator mounted on the steering rack, a Force Feedback (FFb) actuator mounted on the steering wheel axle, and an Electronic Control Unit (ECU). The actuators include angular sensors to keep track of the position of each actuator. Removing the mechanical connection results in zero feedback in the steering wheel from all forces acting upon the steering system and disturbances caused by the environment. Hence is the investigation of torque feedback for SbW systems critical to ensure a satisfactory human driving experience. There are different possible methods to achieve satisfactory torque feedback i.e. a satisfactory steering feel. In this project, the torque feedback generation was primarily based on steering wheel torque measurements from a vehicle with an EPAS system. Since no physical constraints are affecting the connection between the steering wheel and the road wheels, caused by erasing the mechanical connection, the natural safety aspect of having that connection is lost. The overall driving experience might be improved so that the driver can maneuver the vehicle more efficiently over different road conditions and obstacles with a higher probability of preventing driver-inflicted accidents. But it instead exposes the driver to a higher probability of software-inflicted accidents. Therefore, emphasis on safety is essential if the development of Sbw systems is to continue. One of the advantages of using a Sbw system is that it enables to unconditionally adjust and specify the torque feedback in the steering wheel and the steering ratio between the steering wheel and road wheels. This makes it possible to specifically choose which disturbances should be felt in the steering wheel but also enhance those more important. It also makes it possible to have a steering ratio dependent on the vehicle’s speed which is its own topic in itself. Another advantage of Sbw systems is the possibility of designing a new innovative interface that facilitates people with disabilities to make it easier for them to drive vehicles. People who have problems with turning a steering while e.g. parking because of the many degrees a steering wheel might have to be turned might benefit from the possibility of a variable steering ratio that makes it possible to turn the wheels with a smaller steering wheel angle. 1.1 Steering feel background Steering feel is a complex subject including both subjective and objective components. There are a number of mechanical parts and physicalities playing a role in the composition of a good steering feel. The authors of the paper [14] say that there are two concepts of steering reaction force control i.e. steering feel. Where the first concept is to achieve a steering feel equivalent to an EPAS system where all information from the road and vehicle is transmitted to the driver. The other concept is to make use of the missing mechanical linkage between the steering wheel and the steering rack. This allows for only necessary information to be transmitted to the driver. According to [14] some of the necessary information includes the grip limit of the tires, steering vibrations caused by road surface roughness, contact with obstacles, and full stroke of the steering unit. Some information that could be deemed as unnecessary includes steering wheel movement on a rutted road and steering vibration caused by brake judder. This is all fed back to the driver using an EPAS system. It can thus be concluded that the steering feel expectations of a SbW system at least includes information regarding the grip limit of tires, steering vibrations caused by road surface roughness, contact with obstacles, and full stroke of the steering unit. Additionally, some information can be filtered out if the missing linkage between the steering wheel and the steering rack is taken advantage of instead of replicating the steering feel of an EPAS system. In this project, the steering feel from an EPAS system during ideal conditions was used as the base feeling i.e. no additional vibrations were taken into consideration. Then in addition to this EPAS based base steering feel features such as contact with obstacles, full stroke of the steering unit, and grip limit of the tires were developed. 1 1.2 Problem description The purpose of this project is to develop a steering feel model for a SbW system that generates a steering feel resembling the feeling of driving with an EPAS system. It is important to note that only the forces acting upon the steering system generated during normal driving conditions with a conventional steering system are to be considered. To accomplish this, a set of features needed to be created to obtain a torque feedback in the steering wheel to imitate the physical forces reacting on the steering rack. The necessary features to be developed and implemented are Base torque, Loss of grip (understeer), End-stop, Displacement of zero torque position (oversteer), and Angular velocity limiter, see section 4 for details on how the features where developed. • Base torque The base torque should be the torque felt in the steering wheel created by the forces striving for the steering wheel to be centered. In cars using EPAS the base torque mainly comes from the aligning torque from the tire to road interaction and torque generated from the lateral tire force acting through the caster offset. Therefore should the base torque be inspired by the behavior of the aligning friction torque to generate a steering feel similar to the cars on the road today. This could be done by using the mathematical models for the aligning torque, see section 3. For this project measurement data from an EPAS system was used to develop the base torque. • Zero velocity torque The torque profile when the vehicle is stationary should imitate the steering feel of an EPAS system. While stationary, the key distinction is the absence of active return acting on the steering wheel, leading to a displacement of the zero torque position while turning. The zero velocity torque feature should generate a steering feel that closely resembles the steering feel of a vehicle integrated with an EPAS system. This could be achieved by implementing a spring-damper model to generate the torque profile. To serve as a reference, a test was performed to measure the steering wheel torque on a test car, providing a reference torque profile for comparison. • Return to center The implementation of an active return feature is a solution to improve the steering feel model. The feature should automatically return the steering wheel to the center position when unhanded. It provides additional torque to assist the base torque, compensating for the combined effects of system friction and the cogging torque generated by the FFb actuator. • Loss of traction (understeer) When the grip between the tires and the road starts to decrease the steering wheel torque also starts to decrease. Therefore a feature that decreases the torque when the grip decreases has been implemented. It will be assumed that the friction between the tires and the road is constant while driving. The angle at which the grip starts to decrease is calculated using mathematical correspondences between steering angle and lateral acceleration, see section 3 for details. • End-stop For vehicles with a mechanical steering system when turning to the maximal steering angle the steering wheel will stop as well because of the mechanical limitations of the system. It is possible to implement a mechanical end-stop for SbW systems as well but for this project, an electrical end-stop was chosen. • Obstacle detection Similarly as for the end-stop for mechanical steering systems, when the tires encounter an obstacle such as a road curb while attempting to turn, the steering wheel will be prevented from turning. Hence, an obstacle detection feature should be implemented to notify the driver when such an event occurs. • Displacement of zero torque position (oversteer) If the vehicle starts to skid because of oversteer instead of understeer the zero torque position of the steering system is moved such that it matches the direction of travel of the skidding vehicle. Thus a feature that simulates this behavior is to be implemented. An application of the Displacement of zero torque position could be lane keep assistance. • Angular velocity limiter Because of the limitations of the steering rack actuator the steering rack has a maximal traveling speed. 2 This means that if the steering wheel is turned faster than the steering rack’s traveling speed a dynamic mismatch in angle between the steering wheel and road wheels will arise. A feature to retain the synchronization has therefore been attempted to be implemented. 1.3 Limitations Some limitations have been set for the project to ensure that the focus remains on the project scope. • External forces not generated during normal driving conditions with a conventional steering system that might affect the general steering feel, will not be considered during the project. • No other hardware will be used other than the ones implemented on the test rig. • The software tools used in the project will be limited to CANoe, Simplex Motion Tool, and Matlab. • Variable steering ratio will not be investigated and is assumed to be implemented. • A constant road surface will be considered when designing the features. • The hardware performance of the used prototypes will not be part of the study. 1.4 Related work Steer-by-wire is a popular subject that has been investigated for a long time for example in the fields of aircrafts and Formula 1 cars. It has only recently reached the production of passenger vehicles with the car company Lexus. There is also previous work regarding the topic of torque feedback for Sbw systems where there have been different methods for generating a satisfying steering feel. For example the research article [8] proposes a control algorithm to create the force feedback for Sbw systems. The authors use a direct current measurement approach to estimate the torque at the steering wheel and at the front axle motor. The authors use this as elements of the feedback torque together with a compensation torque to obtain a realistic feedback torque. To control the feedback torque and vary a steering feel gain the authors use gain scheduling and a Linear Quadratic Regulator (LQR). Other work related to torque feedback that has taken a different approach is the research article [6] where the authors focus on obtaining driver-environment transparency. Here the authors use a rack force observer to obtain a rack force estimate. This paper does not only investigate transparency for Sbw systems but also EPAS systems where the focus of validation lies on the EPAS system. The authors investigate two different rack-force estimation schemes to find the most reasonable observer that not only gives the best driver-environment transparency but also the best driver-coupled stability. This is due to the closed-loop interconnection that is formed. The advantage of using a rack force estimator is the transparency towards all disturbances affecting the steering rack which means that all forces affecting the steering rack can be felt in the steering wheel. Previous work related to this project made by the same author as [6] includes the Design of Haptic Feedback Control for Steer-by-Wire [5] and Comparison of Steering Feel Control Strategies in Electric Power Assisted Steering [4]. The paper [5] discusses a comparison of different haptic feedback control strategies where they primarily focus on closed and open-loop methods for FFb SbW systems. It is concluded in this paper that the open loop architecture lacks tracking performance at higher steering excitation frequencies due to feedback motor impedance. However, by using the closed-loop method this impedance is compensated for. Two different control schemes were used with the closed-loop architecture namely position and torque control. By using torque control a higher controller bandwidth was achieved in comparison to position control. By using torque control the closed-loop stability and performance are less sensitive to the driver arm inertia. However, torque control requires filtering of the reference generator which subsequently limits the reference tracking performance. But filtering required on the position controller limits the controller’s performance and stability. The paper [4] instead discusses a comparison between two closed-loop steering feel control concepts i.e. torque control and position control, for EPAS systems. The closed-loop methods aim to compensate the EPAS motor inertia effectively in comparison to an open-loop control scheme. The comparison resulted in the torque control scheme achieving a higher haptic controller bandwidth for reference tracking and stability margin. While the position controller stability and performance are limited due to feedback control filtering 3 and high system inertia from the EPAS actuator and driver’s arms. The torque control scheme offers better road disturbance attenuation for low and high-frequency spectra, while the position control scheme is better in the mid-frequency spectrum. 4 2 Hardware and software used in Project The setup of hardware that was available for this project consisted of an ECU from Vector henceforth called the VN module, an integrated servo motor used as a FFb-actuator, a steering rack with an actuator attached, and a steering wheel connected to a planetary gearbox and the FFb-actuator. The VN module was connected through Controller Area Network (CAN) buses with the FFb actuator and the steering rack actuator. All these components together with the necessary power supplies were built into a testing rig that was used as a developing and evaluation tool for the Sbw system. 2.1 Force feedback The FFb actuator is a servomotor used as a FFb actuator. It is connected to a gearbox which is further connected to the steering wheel. 2.1.1 Actuator The actuator is an integrated servo motor with a brushless DC outer rotor motor. The actuator has a position and speed encoder utilizing a position sensor measuring 4096 positions for each revolution to estimate the position and speed and an integrated torque estimator that estimated the torque applied. The actuator has two different control modes that were taken into consideration for this project, position control, and torque control. The integrated control electronics make it possible to choose a control mode and a setpoint for that mode through an external source. Position control The position control mode for the actuator utilizes an internal tunable PID controller to regulate the position of the motor unit with respect to a setpoint in a closed-loop system, using feedback by increasing the torque of the motor unit. The error of the position is actively calculated as the difference between the setpoint and the process value, i.e. the desired position and the actual position. The control signal is then transformed to the correct voltage and current to increase the torque to reach zero error, where the maximum torque that can be applied is limited by a configurable value. Torque control The torque control mode utilizes no internal tunable PID controller, like the position control mode, to regulate the process value. The torque control mode instead uses an unknown controller that cannot be tuned. A torque is assigned as a setpoint and that torque is achieved at the output end of the actuator. The torque control mode can instead be seen as an open loop system where the torque is assigned without any feedback and transformed to the correct voltage and current to achieve such torque. Cogging torque A problem with the actuator motor is something called cogging torque. Cogging torque is a phenomenon that is produced by the magnetic attraction between the rotor-mounted permanent magnets and the stator teeth. Cogging torque is generally seen as a disturbance in the motion of a motor and can cause vibrations and acoustic noise in the motor [13]. There are some techniques to compensate for the cogging torque where one of these techniques, is implemented in the motors electronic control unit as a calibration option. The calibration drastically improves the cogging torque but does not remove it entirely. There are multiple methods of reducing cogging torque for a BLDC motor and according to [15], three different methods for doing so are possible. The three methods are the following. • Optimize the air-gap length • Optimize the rotor structure • Optimize the stator structure 5 By increasing the air gap length between the rotor and stator the cogging torque will decrease, the downside is an increase in reluctance torque. Thus, the air gap length must be optimized taking both the cogging torque and the reluctance into consideration. There are multiple approaches to decreasing the cogging torque by modifying the rotor structure some of them are Magnet pole shaping, Skewing, and lowering the magnet flux density. The more common method is by skewing, either by skewing the magnets or the rotor slots, both have their advantages and disadvantages. According to [15], the cogging torque can in theory be eliminated entirely by optimizing the hardware design. For a real-life implementation, it might not be possible to be erased entirely but reduced significantly. The structure of the stator can also be optimized and there are 4 different approaches for doing so. Optimizing the thickness of stator tooth tips, the width of the slot opening, the number of slots, and adding an appropriate number of dummy slots. These 4 methods are further described in [15]. In addition, according to [12], the skewing method makes for a complicated production process and therefore increases the construction price significantly. 2.1.2 Gearbox The gearbox used is a planetary gearbox with a maximum input of 8000rpm and a static gear ratio of 1:9, one rotation of the gearbox shaft is nine rotations of the rotor in the servomotor. The gearbox has a maximum radial load of 265N and a maximum axial load of 220N. Apart from the planetary gearbox, there are other gearboxes that could possibly be utilized for implementation in an SbW system, such as worm gear and belt drive. The worm gear is a gearbox containing a worm and a worm wheel with their axes perpendicular to one another. There are in general two kinds of worm gears, namely cylindrical and drum-shaped worm gears. According to [17], the advantages of utilizing a worm gear are low noise and low vibration. However, since there is a sliding contact between the worm and the worm wheel they tend to retain heat and has low power transmission efficiency. Belt drives are constructed of rotating pulleys and a moving belt with corresponding sliding contacts, but there are multiple designs such as V-belt, V-ribbed belts, cog belts, and more. The advantage of using belt drives according to [18], are their cost efficiency and high safety among others. The setback is the endurance of the belt material which over time can lead to fatigue failure and cause a belt to loosen its shape, causing heat to build up from friction due to slippage and bringing damage to the belt. A gearbox is not a requirement for a SbW system, it was chosen for this particular setup that it was necessary to achieve the correct amount of torque. 2.2 Electronic Control Unit An Electronic Control Unit (ECU) is in the automotive industry an embedded electronic as described in [7]. Where the ECU basically is a digital computer that reads signals from sensors placed around the vehicle and in certain components in the vehicle. The ECU, then depending on the signals, controls certain units of the vehicle, e.g. the engine, power assistance actuator, and other actuators. There are different types of ECUs in a vehicle depending on which area of the vehicle the controls are actuated. For this particular project, controls, and monitoring of units that would be under the categorization of VCM are to be considered. Where the ECU to be used for this project is the VN8911 from VECTOR. 2.2.1 Vector VN8911 The VN8911 is one of the base modules of the 8900 interface family and the base module used for the steer-by- wire system used in this project. VN8911 is an ECU specifically designed for high-performance applications using CANoe and CANalyzer [16]. An important characteristic of the VN8911 is the modularity of the network interface i.e. the communication ports. The complete system composes of one base module (the processor unit) and one plug-in module, which represents the network interface. For this particular system setup, the VN8970 is used as the plug-in module. To configure the VN8911 the software tool CANoe, see section 2.2.3 for details on CANoe, is used. The module is configured through a Personal Computer (PC) connected via Universal Serial Bus (USB) to the module and the configuration is executed inside the module itself. See figure 2.1 for the module used in the project. 6 Figure 2.1: Image of the VN8911 with VN8970 plug-in module 2.2.2 CANoe CANoe is a flexible software tool from VECTOR for the development, analysis, and testing of individual ECUs and complete ECU networks [1]. This tool is used to be able to implement torque feedback solutions in the ECU for real-world testing. It is needed to set up simulated ECUs, system variables, write code, analyze measurements, and operate the system. 2.2.3 Communication Access Programming Language (CAPL) Communication Access Programming Language (CAPL) is a procedural programming language developed by VECTOR that is similar to C [3]. The programming language is event-based and CAPL programs are developed and compiled in a dedicated browser. Because of this, it is possible to access all objects contained in the dataset e.g. messages, signals, environment variables, and system variables. 2.3 Steering rack The steering rack used for this project was a steering rack mounted in a Volvo V60 2019. The internals of a steering rack that moves consist of a gear rack that moves from side to side when turning the steering wheel which turns the road wheels. The gear rack is moved by a gear called a pinion which rotates with the steering wheel which in turn moves the gear rack, see figure 2.2. For a conventional mechanical steering system e.g. EPAS the steering wheel is mechanically connected to the pinion by the steering column but for Sbw systems the pinion is connected to the steering rack actuator, see figure 2.3 for a mechanical steering system. Figure 2.2: An image of the steering rack used in the project 7 Figure 2.3: Visualization of the complete mechanical steering system used in the testing vehicle. 2.4 Testing rig The complete testing rig used in the project consisted of a steering wheel connected to the gearbox with an assumed to be rigid axle which is coupled with the FFb actuator. The FFb actuator is connected via a CAN-bus to the ECU and is powered by a power supply. The steering rack actuator was connected via CAN-bus to the ECU as well. The ECU was also connected to a control box with some switches and Light Emitting Diodes (LEDs) that were used as a simple communication interface with the operator to e.g. start the torque feedback, let the operator know that the feedback is active or change steering ratio. The ECU was also connected with USB to a PC to be able to operate and modify the software of the testing rig. 8 Figure 2.4: The testing rig with the steering wheel, FFb actuator, ECU, and steering rack. 2.5 Developing and Implementation software For the developing phase and early evaluation of the features, mainly Matlab and Simulink were used. While for the implementation phase and final evaluation of the steering feel model, CANoe was used. 2.5.1 Matlab Matlab is a powerful programming platform allowing for an effective way of solving computational mathematics e.g. matrix-based multiplication and design systems. It was utilized to derive the torque feedback algorithms and to evaluate the results by analyzing corresponding plots. Matlab was the primary platform used in the development and simulation phase of the project before the real-life implementation of the model was realized. Doing so prevented unnecessary wear and tear on the testing rig hardware and provided a safe testing environment if unintended torque values were to be generated. Matlab was used to design all individual torque curves for each feature composing the steering feel model except the zero velocity torque feature and the damping around the center position and End-stop. The torque curves developed in Matlab were generated by defining each curve with an equation system consisting of tunable parameters and then solving the equations system giving the solution to each curve parameter as functions of tunable parameters. 2.5.2 Simulink Simulink is a powerful tool often utilized to simulate, analyze, and verify model-based systems. During this project, it was used as a tool to build a simple mathematical model of the real-life testing rig available and run simulations of the functions developed in Matlab before real-time implementation. Since the FFb actuator 9 has the ability to generate high torque values, implementing and verifying the results in Simulink beforehand prevented possible unnecessary damage to the hardware as well as the driver. The following figure illustrates the simulation setup in Simulink and the different components. Figure 2.5: Image illustrating the simulation setup in Simulink, The main components of the simulation setup are the Reference Generator, Force Feedback Actuator, and torque input from the steering wheel. The setup is a closed-loop direct feedback model that represents the testing rig and communication between the VN-module, steering rack, and FFb actuator. The reference generator represents the torque feedback model taking the FFb motor position and angular velocity for each loop as well as the vehicle speed as inputs. The reference generator generates a torque feedback set-point which is directly transmitted to the FFb actuator block. The steering wheel torque input is symbolizing the driver steering torque input. The steering wheel torque input and the set-point act as the inputs to the FFb actuator. The FFb actuator computes the torque difference between the reference torque and the driver steering torque and transmits the current FFb motor position and angular velocity back to the reference generator, forming a closed-loop model. 2.5.3 CANoe CANoe is the software used in the VN-module for implementation and evaluation as described in section 2.2.2. During the development phase, parts of the steering feel model were implemented using CANoe. This was to ensure that the features performed correctly before the whole steering feel model was to be implemented and evaluated. The complete features required to be converted from Matlab syntax to CAPL for it to work in CANoe. During the evaluation of the features, a number of variables such as estimated FFb actuator torque, FFb actuator position, FFb actuator angle speed, pinion angle, pinion angle speed, and reference torque were logged and analyzed. 10 3 Modelling of Steering system Before starting the implementation on the physical system some simulations in Simulink need to be performed to ensure that e.g. the correct torque is generated at the correct position and speed. This requires a simple model of the physical system which is discussed in this section. It is also important to note that the torque feedback that occurs in the steering wheel in a vehicle with a mechanical steering connection, e.g. EPAS, comes from actual physicalities in the system. How these occur and can be modeled are also briefly discussed in this section to clarify where the torque feedback in the steering wheel comes from. 3.1 Steer-by-wire system The SbW system consists of two smaller systems, the FFb system, and the steering rack system. The FFb system consists of a steering wheel connected to the planetary gearbox by a, assumed to be rigid, solid axle. The planetary gearbox is directly connected with the FFb actuator with a short rigid axle, see figure 3.1. Figure 3.1: Force feedback system The FFb system can be simplified to be described as the following model τsw = τFFb + τf + JFFbδ̈sw + bFFbδ̇sw (3.1) where τsw is the torque acting on the steering wheel given by the driver, τFFb is the torque from the FFb actuator, τf is the torque created by the friction in the system (assumed to be constant), JFFb is the moment of inertia of the system, bFFb is the damping coefficient of the system, δ̈sw is the angular acceleration of the steering wheel and δ̇sw is the angular velocity of the steering wheel. The steering rack system consists of a steering rack rigidly connected to an actuator via a pinion, see figure 3.2. 11 Figure 3.2: Steering rack system It is known that the maximum angle of the pinion is 9rad and the maximum pinion angle speed by the steering rack actuator is 6rad/s. 3.2 Aligning torque One of the largest components of the steering feel is the aligning torque τa generated while cornering i.e. turning the steering wheel. When the velocity of the tire is not in the same direction as the tire is pointing, i.e. slipping is occurring, a lateral force Fyf , a pneumatic trail tp, and a mechanical trail tm are generated. The aligning torque can be modeled as the following equation τa = Fyf (tp + tm) (3.2) where the pneumatic trail is the distance between the center of the tire contact patch and the point where the lateral force is acting and the mechanical trail is the distance between the center of the tire and the point where the steering axis intersects the ground, see figure 3.3. The lateral force can be modeled as the following equation Fyf = 2Cfαf (3.3) where Cf is the front tire cornering stiffness coefficient and αf is the slip angle of the front tires. The cornering stiffness is a constant depending on the tire and the slip angle is the angle between the direction of travel and the direction of the tires that is e.g. dependent on the grip between the tires and the road, and the velocity of the vehicle [9]. 12 Figure 3.3: Visualization of pneumatic trail and mechanical trail. 3.3 Friction torque Another significant contribution to the steering feel is the frictional torque generated by the mechanical friction affecting the system. One component of the mechanical friction is the friction between the road and tires τfricGrd. Where the frictional torque can be modeled as τfricGrd = FzfµtireGrdsign(δ̇)l (3.4) where Fzf is the normal force generated by the front tires, µtireGrd is the friction coefficient, δ̇ is the angular velocity of the front tires, and l is a lever dependent on the contact surface between the tire and the size of the road. The friction torque affected by the friction between the tires and the road is only significant when the vehicle is stationary or operating at very low speeds. Another component of the total mechanical friction is the friction within the steering system τfricSys. This can be modeled as τfricSys = ksysµsyssign(δ̇) (3.5) where µsys is the frictional constant of the steering system and ksys is a constant that scales the total frictional torque within the steering system. The steering system friction affects the steering feel independent of the vehicle speed. However, when the vehicle is stationary or operating at very low speeds the frictional torque between the tires and the road is the dominant part of the total mechanical friction. 3.4 Spring-damper The mass-spring-damper model is a common model used as a simplification to model different physicalities e.g. tires, in this project different interpretations of the mass-spring-damper model have been used to generate the force feedback torque. Where the typical linear mass-spring-damper model can be derived as the sum of all forces acting upon the system as ∑ F = −kx− bẋ+ Fexternal = mẍ (3.6) 13 where ∑ F is the sum of all forces, k is the spring constant, b is the damping constant, Fexternal are the external forces acting upon the system, m is the mass, x is the position of the spring, ẋ is the velocity of the spring and ẍ is the acceleration of the spring. In this project, the linear spring-damper model looks like τSD = −kx− bẋ (3.7) where τSD is the torque that will be applied because of the spring-damper model. A nonlinear spring-damper model used in this project looks like τSD = −kx2 − bẋ2. (3.8) In some cases, the damping constant might also be dependent on the position, i.e. the value of b changes with x. 3.5 Loss of grip from understeer Understeer is what happens when the vehicle steers less than the steering angle. This happens when the slip angle gets to large i.e the lateral force gets to large. For there to be a lateral force on a point mass a lateral acceleration ay has to exist and the acceleration of the point mass can be estimated as ay = v2 R (3.9) where v is the velocity of the vehicle and R is the turning radius. The steering angle δ can be estimated as δ = L R (3.10) where L is the wheelbase of the vehicle. Inserting equation 3.9 into equation 3.10 then gives δ = ayL v2 (3.11) where the maximum lateral acceleration that can be reached before losing grip can be approximated to µg. This gives a maximum steering angle for when the vehicle starts losing grip as δmax = µgL v2 (3.12) where µ is the frictional constant between the tire and the road, and g is the gravitational acceleration constant. If the aligning torque is then plotted against the slip angle, see e.g [2], it can be seen that the slip angle for when the maximum aligning torque has been reached is approximately 40% of the slip angle when all grip has been lost i.e the aligning torque has decreased to zero. It is thus also assumed that for all vehicle velocities, the aligning torque is zero at 1.5δmax. 14 4 Development and Implementation of Torque Feedback This chapter presents the implementation of the developed solutions of the steering feel model. The first section describes the software tools used for the development and implementation of the solution and the rest of the chapter describes each feature composing the steering feel model. The hardware presented in section 2 was used throughout the project, hence, the model is designed and tuned thereafter. The torque profile generated by the steering feel model is based on the reference pinion angle, where the reference pinion angle is computed from the steering wheel angle and the steering ratio such that the torque profile always remains identical independent of the steering ratio. The steering ratio used during this project was 1:1 such that the steering wheel angle is equivalent to the reference pinion angle at all times. 4.1 Base torque The base torque feature provides a multivariable nonlinear base torque curve dependent on the vehicle speed, pinion angle, and pinion angular velocity where the active range of the base torque feature generates an output for all vehicle speeds greater than 0m/s. The complete base torque profile is designed as a spline containing a first-degree polynomial y = k2x + m2 that is a continuation of a second-degree polynomial y = a1x 2+b1x+c1 added together with a hyperbolic tangent function (Tanh) to replicate a similar torque curve based on measurements from an EPAS system instead of physical models. To attain the desired characteristics of the base torque slope, an equation system was defined for the second-degree polynomial to be symbolically solved to obtain the functions for the polynomial parameters. The equation system was defined as y2 = a1x 2 2 + b1x2 + c1 (4.1a) k2 = 2a1x2 + b1 (4.1b) 0 = c1 (4.1c) where it is defined that the second-degree polynomial intersects the origin, the torque at x2 is y2 and the gradient at x2 is k2 where x2 is the angle at which the base torque curve transforms from the second-degree to the first-degree polynomial. Solving the equation system gave the following functions for the second-degree polynomial parameters a1 = −y2 − k2x2 x2 2 (4.2a) b1 = 2y2 − k2x2 x2 (4.2b) c1 = 0. (4.2c) The first-degree polynomial continues with the gradient k2 and the parameter m2 is calculated as m2 = a1x 2 2 + b1x2 + c1 − k2x2. (4.3) The tuning parameters y2 and k2 are then calculated as the following y2 = −0.0633vel2vehicle km + 44.1664velvehicle km + 400.0816 (4.4a) k2 = 0.0680vel2vehicle km + 18.1468velvehicle km (4.4b) where velvehicle km is the driving speed of the vehicle in km/h. Equations 4.4 were found from curve-fitting data from the EPAS measurements for different vehicle speeds at the same pinion angle using second-degree polynomials. The torque values at 0.5 rad pinion angle for the vehicle speeds 30km/h, 45km/h, 60km/h, 80km/h, and 100km/h were used together with the Matlab function Polyfit() to find and approximating second-degree polynomial function describing the torque at 0.5rad pinion angle for all vehicle speeds i.e. equation 4.4a. The same torque values were also subtracted to a torque value for one larger pinion angle for each vehicle speed and divided by the difference between the two pinion angles to get a function that approximately describes the gradient of the first-degree polynomial torque curve for all vehicle speeds i.e. equation 4.4b. By utilizing these 15 polynomial equations, a base torque profile is generated that always intersects the origin while steering passed the center position. Additionally, the torque curves of the base torque profile are designed to be combined with a Tanh function that can be seen as a frictional damping of the physical system [11]. By observing e.g. the EPAS measurements in figure 6.2, a hysteresis can clearly be noted which was considered to be a frictional damping of the physical system. This hysteresis was replicated using the Tanh function as a function of pinion angular velocity since the hysteresis seemed to have a maximum limit of approximately 1Nm. The Tanh function affects the base torque profile by smoothly adding an additional 1000mNm of torque to the base torque profile when the pinion angular velocity is non-zero. However, if the pinion angular velocity is zero, the Tanh function smoothly transitions to adding 0mNm to the base torque profile. The following equation defines the Tanh function used to replicate the hysteresis TfricDamp = ea·x − 1 ea·x + 1 · 1000 (4.5a) where TfricDamp is the additional torque generated by the Tanh function, a is the gradient of the Tanh function at origin and x in this case represents the pinion angular velocity. The characteristic of a Tanh function can be seen in figure 4.1 below. -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Angular velocity [rad/s] -1000 -800 -600 -400 -200 0 200 400 600 800 1000 T o rq u e [ m N m ] Tanh Figure 4.1: An illustration of the Tanh function i.e. the hysteresis added to the torque curves generating the complete base torque profile. The complete base torque profile can be visualized as figure 4.2 if the steering wheel would start as stationary at 0rad and linearly increase the pinion angular velocity to 3rad/s at a vehicle speed of 10km/h. 16 0 1 2 3 4 5 6 7 8 9 Pinion angle [rad] 0 2000 4000 6000 8000 10000 12000 T o rq u e [ m N m ] Torque profile 10km/h Figure 4.2: A visualization of the complete base torque profile at 10km/h. If the steering wheel would instead be turned such that the movement emulates a sinusoidal wave at a vehicle speed of 10km/h, the base torque curve can be visualized as figure 4.3. -10 -8 -6 -4 -2 0 2 4 6 8 10 Pinion angle [rad] -3000 -2000 -1000 0 1000 2000 3000 T o rq u e [ m N m ] Torque profile 10km/h Figure 4.3: A visualization of the complete base torque profile at 10km/h for a sinusoidal change of steering angle. However, there is a problem with the torque profile where it drops at the point of change in turning direction because of how the implementation of the Tanh is done. 4.1.1 Zero velocity torque feature While stationary, the steering feel of a vehicle is evidently distinguishable compared to a scenario where the vehicle is non-stationary. The largest difference is that if the speed is non-zero an active return will be acting on the steering wheel continually forcing the steering wheel back to the center position. If the velocity is zero, the same forces are not acting upon the steering rack and the steering wheel will not actively return to the center position. Due to the dynamics of the tires, the center position of the active return will move with the change of pinion position. A separate function is therefore created for zero vehicle speed, which was based on a 17 linear spring-damper model to resemble the forces acting upon the steering rack by the tires to create a torque profile for when stationary. From EPAS measurements of a stationary vehicle, it was seen that a maximum steering wheel torque of approximately 2000mNm can be achieved if damping is not taken into consideration. It could also be seen that when turning more than approximately 0.5rad the center of the active return is moved the same distance as the new pinion angle subtracted with 0.5rad, see figure 6.17. Thus was the zero velocity torque profile first designed as a spring with a linearly increasing torque to a maximum value of 2000mNm at 0.5rad and the position of zero torque for the spring is moved with x− 0.5rad where x is a position larger than 0.5rad from the center. On top of this, a linear damping was added. The damping was subjectively tuned in a vehicle for the torque profile to match the EPAS system. 4.2 Loss of traction (Understeer) When understeer occurs i.e. when the grip between the front tires and the road starts to decrease the steering wheel torque also starts to decrease. It was decided at the beginning of the project that the accuracy of the torque loss from loss of traction was not to be in focus. The torque profile of the loss of traction should be considered more as a part of a trial of concept since the calculations of the angle when the torque loss starts is also heavily simplified. The torque profile for the loss of traction feature is designed as a second-degree polynomial with a number of tunable parameters for easy adaptability to any previous torque profile and possible succeeding torque profile. The second-degree polynomial was found by setting up an equation system of symbolic variables and solving it to find the equations solving each polynomial parameter. The equation system was defined by the following equations 0 = 2a2x 2 slipStart + b2 (4.6a) yslipEnd = a2x 2 slipEnd + b2xslipEnd + c2 (4.6b) yslipStart = a2x 2 slipStart + b2xslipStart + c2 (4.6c) where a2, b2 and c2 are the unknown polynomial parameters. The parameter xslipStart is the angle at which the loss of traction torque curve is initiated and the torque should start to decrease, xslipEnd is the angle at which the torque profile should reach its minimum amount of torque, yslipStart is the amount of torque that the torque profile should start with i.e. the amount of torque the was just before the loss of traction torque profile should initiate, and yslipEnd is the minimum amount of torque that can be reached by the loss of traction torque profile. For this project, it was set such that yslipEnd = 0 i.e. zero torque will be applied to the steering wheel when all grip has been lost. The parameter xslipStart is continuously calculated from equations 3.9-3.12 and xslipEnd is continuously updated as 1.5xslipStart. The parameter yslipStart was lastly continuously updated to the same torque value the base torque curve would give at xslipStart. Equation 4.14 defines the condition that the derivative of the torque curve at xslipStart should be 0 such that the torque always directly starts to decrease when the loss of traction feature is initiated. Equation 4.6b defines the condition that the torque should be yslipEnd at xslipEnd which is zero at the angle where all grip has been lost. Equation 4.6c defines the condition that the torque should be yslipStart at xslipStart where yslipStart is the amount of torque just before the loss of traction feature should be initiated such that the starting torque of the torque curve can be ensured to start the same torque as the base torque feature ended. Solving the equation system gives the following equations for the polynomial parameters a2 = yslipEnd − yslipStart (xslipEnd − xslipStart)2 (4.7a) b2 = −(2xslipStart(yslipEnd − yslipStart)) (xslipEnd − xslipStart)2 (4.7b) c2 = x2 slipEndyslipStart + x2 slipStartyslipEnd − 2xslipEndxslipStartyslipStart (xslipEnd − xslipStart)2 (4.7c) where equations 4.7a, 4.7b and 4.7c all define the torque profile for the loss of traction feature. See figure 4.4 for examples of the loss torque curve for loss of traction for the two vehicle speeds 30km/h and 60km/h. 18 0 1 2 3 4 5 6 7 8 9 Pinion angle [rad] 0 5000 10000 T o rq u e [ m N m ] Torque profile 30km/h 0 1 2 3 4 5 6 7 8 9 Pinion angle [rad] 0 5000 10000 T o rq u e [ m N m ] Torque profile 60km/h Figure 4.4: A visualization of the torque loss when grip has been lost for the two vehicle speeds 30km/h and 60km/h. 4.3 End-stop All passenger vehicles have steering racks with a maximum travel length i.e. all vehicles have a maximum steering angle. For the general vehicle with an EPAS steering system where the steering wheel is mechanically coupled with the steering rack when the maximum travel length of the steering rack is reached the steering wheel can not be moved further either. Thus for an SbW system, either a mechanical or electrical end-stop has to be additionally implemented. For this particular project with the hardware setup available, an electrical end-stop was chosen to be developed. To make the torque increase smooth and fast to alert the driver that the maximum steering angle has been reached it was chosen to use a second decree polynomial y = a3x 2 + b3x+ c3 to generate the torque as a function of the pinion angle which can be seen as non-linear spring. To be able to efficiently tune the end-stop an equation system of symbolic values was set up and solved to find the equations solving the second-degree polynomial parameters. The equation system used to find the polynomial parameters was the following ymax = a3x 2 max + b3xmax + c3 (4.8a) 0 = 2a3xend + b3 (4.8b) yend = a3x 2 endb3xend + c3 (4.8c) where xend is the angle at which the end-stop should initiate i.e. the maximum travel length of the steering rack. The parameter xmax is the position at which the end-stop should reach the maximum wanted torque since the FFb actuator can only output a maximum amount of torque. The parameter yend is the amount of torque at which the end-stop should initiate. This parameter is necessary because of the varying base torque profile depending on the vehicle speed since the end-stop should be able to initiate at any current torque. The parameter ymax specifies the amount of torque wanted at xmax i.e. the maximum amount of torque. The parameters a3, b3, and c3 are the polynomial constants that are of interest to find. 19 Equation 4.8a specifies that the torque should be ymax at xmax, equation 4.8b specifies that the slope of the torque at xend should be 0 and equation 4.8c specifies that the torque should be yend and xend. The solution to the equation system was the following equations for the polynomial constants a3 = −(yend − ymax) (xend − xmax)2 (4.9a) b3 = 2xend(yend − ymax) (xend − xmax)2 (4.9b) c3 = x2 endymax + x2 maxyend − 2xendxmaxyend (xend − xmax)2 (4.9c) where xend, xmax, yend, and ymax all are tunable parameters to find the correct end-stop function during vehicle operation. If the steering wheel would be rotated further than xmax a constant torque with the amount of ymax will be generated. This torque should be high enough for the driver to acknowledge that the steering wheel should not be rotated further but at the same time not be so high that it requires a large FFb actuator. It was decided that 8000mNm was enough for both conditions to be satisfied. See figure 4.5 below for a visualization of the end-stop torque curve joined with the base torque curves for the vehicle speeds 10km/h, 30km/h, and 60km/h. 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 Pinion angle [rad] 0 5000 10000 T o rq u e [ m N m ] Torque profile 10km/h 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 Pinion angle [rad] 0 5000 10000 T o rq u e [ m N m ] Torque profile 30km/h 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 Pinion angle [rad] 0 5000 10000 T o rq u e [ m N m ] Torque profile 60km/h Figure 4.5: Illustration of the end-stop torque curve initiating at 9rad pinion angle for the vehicle speeds 10km/h, 30km/h, and 60km/h. 20 4.3.1 Obstacle detection Just as the steering wheel should not be further rotated when the steering rack has reached its maximum traveling length for a SbW system without torque feedback, can the steering wheel further be rotated if the wheels happen to be in a locked case e.g. get stuck against a curb or something else inhibiting the wheels to keep turning. The same end-stop torque profile is thus also used for this feature to effectively give feedback to the driver that the wheels can not be further turned called obstacle detection. For the system to acknowledge that there is an obstacle hindering the wheels from turning the difference between the pinion angle of the steering rack and the steering wheel is constantly checked. If the difference between the angles starts to differ too much the end-stop torque profile is initiated. 4.4 Damping To achieve pleasant and smooth steering feel similar to that of EPAS while maneuvering a vehicle different types of damping are required. The steering feel model developed and implemented utilizes two kinds of damping, namely On-center and End-stop damping. All types of damping are always added as an additional torque in the opposite direction of the turn of the steering wheel. 4.4.1 On-center damping The On-center damper was designed for neutralizing steering wheel overshoot achieved at high vehicle speeds when letting the steering wheel return to its zero position when the driver releases the steering wheel. The On-center damper was designed as a Gaussian function with an additional constant term, y = a5e −b5x 2 + c5. The reason behind choosing a Gaussian function is that if the x-axis is dependent on the position of the steering wheel damping will only exist around the origin i.e the center position of the pinion, see figure 4.6 for visualization. The additional constant term added to the Gaussian function is due to the possibility of adding standard linear damping to the system independent of the pinion angle. Since if a constant is added to a curve the curves y-values increase with the same amount for all x-values. Because of unwanted irregular resistance in the system, the constant c5 was set to zero disregarding any linear damping to the steering feel model. The amount of damping needed to efficiently neutralize the steering wheel from overshooting needed to be larger for higher vehicle speeds. Thus needed the parameter a5 is dependent on the vehicle speed because this parameter decides the maximum value of the Gaussian function. A simple equation system was thus set up to find a linear function for a5 dependent on the vehicle speed as follows α = 80a6 + b6 (4.10a) β = 40a6 + b6 (4.10b) where α and β are tuning parameters, α is the amount of damping at the vehicle speed 80km/h, and β is the amount of damping at the vehicle speed 40km/h. The parameters a6 and b6 are the function parameters for the linear function. The vehicle speed 40km/h was chosen because it is at a speed higher than that that the steering wheel starts to overshoot. The vehicle speed 80km/h was not chosen for any particular reason, any vehicle speed higher than 40km/h had worked. By solving the equation system 4.10 the following solution for the linear function parameters was found a6 = α 40 − β 40 (4.11a) b6 = 2β − α (4.11b) where these functions then can be used to define the Gaussian function parameter a5 as follows a5 = a6 · velvehicle km + b6 = ( α 40 − β 40 ) · velvehicle km + 2β − α (4.12) where velvehicle km is the current vehicle speed in km/h. The complete Gaussian function can now be defined as bbaseTrq = a5e −b5x 2 + c5 (4.13) 21 where α = 500, β = 0, c5 = 0, and b5 = 0.2. The parameter α was tuned from real-life tests where the goal was to find the least amount of damping to neutralize the steering wheel from overshooting. The parameter β was set to zero because at 40km/h zero on-center damping is needed. The active range of the Gaussian function is decided by the value of b5 and using b5 = 0.2 attains a non-zero value within the interval of approximately [-4:4]rad, see figure 4.6 below. The computed damping constant bbaseTrq is then multiplied by the angular velocity of the steering wheel and subtracted from the total reference torque. Additionally, the value of bbaseTrq was designed to never attain a value below c5 to ensure that damping would not change sign if the vehicle speed is less than 40km/h i.e. the on-center damping remained zero for the vehicle speed below 40km/h. -8 -6 -4 -2 0 2 4 6 8 Pinion angle [rad] 0 500 1000 D a m p in g c o n s ta n t Gaussian function of damping constant 40km/h -8 -6 -4 -2 0 2 4 6 8 Pinion angle [rad] 0 500 1000 D a m p in g c o n s ta n t Gaussian function of damping constant 80km/h -8 -6 -4 -2 0 2 4 6 8 Pinion angle [rad] 0 500 1000 D a m p in g c o n s ta n t Gaussian function of damping constant 120km/h Figure 4.6: A visualization of three curves for the On-center damping constant for the three vehicle speeds 40km/h, 80km/h, and 120km/h. 4.4.2 End-stop damping The End-stop damper was designed to suppress the steering feel of feeling too much as an ideal spring when turning into the End-stop. It was decided that a hyperbolic Tanh function dependent on the pinion angle would be sufficient to define the damping constant. The Tanh function was chosen because the pure Tanh curve starts at zero at the origin and then increases to one when the x-axis goes to infinity. This can be utilized such that the damping constant for the End-stop is initialized as zero at the moment the End-stop is initiated and then smoothly increases to a desired maximum value with a desired speed. The End-stop damping feature was constructed as follows bendStop = e4x − 1 e4x + 1 · bend (4.14) where the constant bend = 700 determines the maximum value of the damping constant, x = pos− xend where pos is the current position of the steering wheel and xend is, as mentioned in section 4.3 when the End-stop torque profile is initiated and the number four in the exponent determines the gradient of Tanh at the origin and causes the function to almost fully converge at 1rad. Compared to previous use cases of the Tanh function, x is the difference between the current pinion angle and the initial end-stop position. The damping constant is multiplied by vehicle2vel to get the amount of torque for the damping, which gives non-linear damping to the system for the End-stop feature. 22 4.5 Displacement of zero torque position (Oversteer) In the early stages of the project, it was decided that a feature that simply allows the possibility of simulating what happens with the torque at an oversteer scenario. Oversteer occurs when a vehicle is affected by a loss of traction of the back wheels and the actual turning trajectory is greater than the reference trajectory, see figure 4.7 for a visualization. When this happens the position where the steering wheel has zero torque is moved such that the new zero torque position is centered with the actual trajectory of the vehicle. The position where the torque is zero will always be in the center of the trajectory of the vehicle. Adding a variable that can be used to add a displacement of the zero torque position of the steering wheel, makes it possible to simulate what happens with the torque profile when oversteering. Figure 4.7: An illustration of an oversteer scenario. A variable was added for inserting a displacement of the zero torque position as a track bar that could be adjusted during real-time testing and evaluation. When a displacement is added, the base torque profile and damping are adjusted to the current zero torque position but the end-stop and loss of traction during understeer positions remain fixed. No additional algorithms were developed or implemented for how the displacement of the zero torque position should alter the base torque profile or the understeer profile. The variable for the displacement of the zero torque position was named posshifted and was calculated as posshifted = pos− shift (4.15) where pos is the current pinion angle and shift is the shift made by the displacement. 4.6 Return to center Due to mechanical friction and the cogging torque affecting the system, the steering wheel does not always return to its center position with base torque alone. Therefore, two methods for compensating these forces have been implemented. In reality, the steering wheel does not return to the center position for all vehicle speeds but for this project, it is assumed that the steering wheel always should return to its center position regardless of the vehicle speed. Unless the vehicle is stationary. The first method is called friction compensation where the sum of the mechanical friction and the cogging torque is assumed to be constant for simplicity. The friction compensation is designed such that the value of y2 23 for the base torque is adjusted by adding a constant torque TfricComp in the turning direction. If the steering wheel is rotated away from the center position y2 is subtracted with a constant torque and if the steering wheel is rotated to the center position a constant torque is added to y2. By doing so, the slope and amount of torque for the entire torque profile are adjusted to the new value of y2 at x2 i.e. the complete base torque profile has been adjusted from the friction compensation accordingly with the rotation direction of the steering wheel. For the steering wheel to always return to the center position, independent of the vehicle speed, the constant TfricComp was set to a value of 1000mNm to overcome both the mechanical friction and the cogging torque. The constant value was found from real-time testing of the system in the testing rig. The second method is to add an integrating part Tintegrator = ∑ Kierror to the steering feel model with the zero torque position as the reference value of the error. Due to the hysteresis of the overall torque profile, a fast-acting integral part is required for small angles to compensate for when the mechanical friction and cogging torque are greater than the base torque. For angles within the interval of abs(steering wheel angle) < 1rad the error equals error = 1 x (4.16) where x is the pinion angle. For abs(steering wheel angle) ≥ 1rad the error equals error = x. (4.17) The integral part is updated with a frequency of 100Hz with a maximum step value for each iteration. An integral gain of Ki = 1.5, a maximum step size of 10mNm, and a maximal value of the integral generated torque equal to Tintegrator max = 750mNm were chosen to achieve satisfactory results where the steering wheel returns to its center position for all vehicle speeds. 4.7 Angular velocity limiter Because the steering rack actuator has a maximum angular speed of 6rad/s the steering wheel and the steering rack might end up unsynchronized if the steering wheel is rotated faster than 6rad/s. This would mean that the difference between the steering rack actuator pinion angle and the pinion angle would be nonzero which would mean that the obstacle detection could be initiated, see section 4.3.1. This would give feedback to the driver that the wheels are stuck to something rather than the steering wheel has been rotated too fast. To prevent this from happening an Angular velocity limiter could be used to impede the driver from actually being able to turn the steering wheel faster than 6rad/s. Two different velocity limiters were briefly developed and tested because of it not being a priority and not enough time was available to fully develop and evaluate this feature. The first velocity limiter was developed as a PI controller where the goal was to generate an additional torque as feedback to prevent the driver from rotating the steering wheel too fast. The control scheme was constructed such that the PI-controller only was active if the pinion angular velocity was over 5.5 rad/s. The number 5.5 was chosen to give the controller some margin in case the controller was too slow to directly apply the correct amount of torque as soon as the steering gets unsynchronized without overshoot and instability. The control algorithm was based on the acceleration of the steering wheel in such a way that the control algorithm uses the acceleration as its reference signal with a setpoint of zero to generate a control signal i.e. a torque in the opposite direction of the acceleration with the goal to keep the acceleration of the pinion at zero. The second velocity limiter was developed as a nonlinear damper to hinder the driver from turning the steering wheel too fast. The disadvantage with the damping instead of the PI-controller is that the pinion velocity can not be controlled using acceleration with the goal to make it impossible for the driver to rotate the steering wheel too fast. The damper instead generates a torque depending on the pinion velocity which does not depend on the torque the driver turns the steering wheel with. This means that the driver could turn with a higher torque than the angular velocity limiter generates and the speed of the steering wheel could then in theory be faster than the maximum allowed speed. But just as the End-stop feature the goal is just to give the driver enough information that something is wrong, and in this particular case informing the driver that the steering wheel is being rotated too fast. The nonlinear damper was designed as T = bx2 where T is the damping torque, b is the damping constant, and x is the angular velocity of the pinion. A damping constant of 5000 was found to give the desired amount of damping. Due to the fact that the damping is a feature to prevent the driver from turning the steering wheel 24 too fast and not affect the overall steering feel by adding unnecessary damping, the damping only affects the steering feel if the steering wheel is rotated faster than 4rad/s. Due to the limitations of the FFb actuator, a maximum amount of damping torque was set to 20000mNm if the steering wheel is to be rotated faster than 6rad/s. 25 5 Vehicle handling tests There are multiple tests for evaluating the steering feel of a vehicle. For the passenger vehicle industry, a number of internationally standardized tests have been developed to evaluate the steering feel of any passenger vehicle. For this project, one standardized test and two unstandardized tests have been used. The following tests were utilized for evaluating the relation between pinion torque and position for SbW systems. The Weave test is a standardized test developed to evaluate the handling characteristics of a passenger vehicle during maneuvers performed at higher vehicle speeds [10]. A low-frequency sinusoidal steering maneuvering is performed during the test that allows for measurements accurately describing the relation between the steering wheel angle and steering wheel torque but in this case the pinion angle and steering wheel torque. The output data provides a steering hysteresis describing the on and off-center torque slope behavior difference between turning away from the center position at a certain degree and back. See figure 5.1 below for an example of the motion of the pinion during a weave test. 0 2 4 6 8 10 12 Time [s] -0.5 0 0.5 P in io n A n g le [ ra d ] Pinion angle against time 0 2 4 6 8 10 12 Time [s] -1 -0.5 0 0.5 1 P in io n a n g u la r v e lo c it y [ ra d /s ] Pinion angular speed against time Figure 5.1: Image illustrating pinion angle and pinion angular velocity for a Weave test The Ramp steer test is a test that was used to evaluate the handling characteristics while conducting steering maneuvers consisting of linearly increasing the steering wheel angle position at a slow and fixed angular velocity. The test is performed within a fixed position interval from the center position to a predetermined final value. This allows for accurate measurements describing the relation between pinion torque and position at slow pinion velocities at different vehicle speeds. See figure 5.2 below for an example of the motion of the pinion during a Ramp steer test. 26 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Time [s] -0.2 0 0.2 0.4 0.6 P in io n A n g le [ ra d ] Pinion angle against time -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Time [s] -0.1 0 0.1 0.2 0.3 P in io n a n g u la r v e lo c it y [ ra d /s ] Pinion angular speed against time Figure 5.2: Image illustrating pinion angle and pinion angular velocity for a Ramp steer test Return to Center test is a test that was used to evaluate and demonstrated the ability of the steering wheel to return to the center if let go. The test was conducted by turning the steering wheel to the maximum torque peak at a certain vehicle speed before arriving at the end-stop and then releasing the steering wheel such that the steering wheel could return to its center position without any external forces acting upon it. 0 0.5 1 1.5 2 2.5 3 Time [s] 0 2 4 P in io n A n g le [ ra d ] Pinion angle against time 0 0.5 1 1.5 2 2.5 3 Time [s] -4 -3 -2 -1 0 P in io n a n g u la r v e lo c it y [ ra d /s ] Pinion angular speed against time Figure 5.3: Image illustrating pinion angle and pinion angular velocity for a Return to Center test 27 6 Experimental results The results of performing a set of different handling tests on the steering feel model, combined with different assisting features for returning to the center, are shown in this chapter in comparison with the EPAS measurements used to develop the steering feel model. All combinations of features for the steering feel model include the Base torque, the End-stop feature, and the Loss of traction feature. The set of tests performed was Ramp steer, Weave, and Return-to-center which have been described in chapter 5. The tests were performed on different variants of the steering feel model. The chapter is divided into the following sections. • Base torque: Illustrates the results of performed Ramp steer tests, Weave tests, and Return to center tests of solely the base torque, the understeer feature, and the end-stop. The results are then compared to those of an EPAS system to show the resemblance of the torque generation between the SbW system and an EPAS system. • Base torque with On-center damping: Illustrates the results of performed Ramp steer tests, Weave tests, and Return to center tests of the base torque with On-center damping, the understeer feature, and the end-stop. The results are then compared to those of an EPAS system to show the resemblance of the torque generation between the SbW system and an EPAS system. • Base torque with additional Return to zero features: Illustrates the results of performed Ramp steer tests, Weave tests, and Return to center tests of the base torque with additional return to center assistance, the understeer feature, and the end-stop. The results are then compared to those of an EPAS system to show the resemblance of the torque generation between the SbW system and an EPAS system. • Torque at zero velocity: Illustrates the results of the torque generation for a stationary vehicle as a comparison between the SbW system and an EPAS system. • Displacement of zero torque position: Illustrates the results of performed Ramp steer tests for both steering directions, Weave tests, and return to center tests for both steering directions. The torque is generated as solely the base torque, the understeer feature, and the end-stop combined with an additional displacement of the zero torque position. • Test track: Illustrates the results of performing a driving test conducted on a short and long test track by displaying the measured torque curve of the steering wheel and the measured pinion angle for the SbW system. The results are then compared to the corresponding measurements performed by an EPAS system on the same test tracks. • Cogging torque: Illustrates the results of the cogging torque affecting the system by performing a test showing the torque curve of the steering wheel from standstill to moving while continuously increasing the motor torque. The tests illustrate the difference between the FFb actuator utilizing and not utilizing cogging compensation. For all figures of the Ramp steer test follow that the dotted lines represent data taken from measurement on an EPAS system, the solid lines represent the reference torque generated by the steering feel model, and the dashed lines represent the torque estimated by the FFb actuator currently applied to the steering wheel. For all figures of the Weave test, the yellow lines represent the EPAS measurements, the orange lines represent the FFb actuator estimated torque and the blue lines represent the reference torque. All tests except the EPAS measurements were performed by human hands, hence human error might concur. 6.1 Base torque The following figure 6.1 illustrates a Ramp steer test performed on the steering feel model for the base torque without any return to center assisting features. For all vehicle speeds, namely 3.6km/h, 30km/h, 45km/h, 60km/h, 80km/h, and 100km/h, the reference torque profile resembles the profile generated from the EPAS measurements accurately with low deviation for the data that was available. The differences in the torque profile while increasing the vehicle speed are the initial slope gradients before the pinion angle x2 = 0.5 hence increasing the value of y2, as well as a quadratic increase of the slope gradient of the linear function beyond the pinion angle x2 = 0.5. Additionally, the pinion angle at which loss of traction occurs for an understeer scenario 28 is quadratically decreasing. For 3.6km/h, there are no EPAS measurements and the torque profile is linearly increasing beyond x2 = 0.5 until the End-stop. The irregularities of the estimated torque are the result caused by the cogging torque with fluctuating values between a range of [-400:400]mNm from the reference torque. However, its mean still follows the reference torque accurately. 0 1 2 3 4 5 6 7 8 9 Pinion angle [rad] -2000 0 2000 4000 6000 8000 10000 T o rq u e [ m N m ] Ramp steer test 3.6km/h 30km/h 45km/h 60km/h 80km/h 100km/h Figure 6.1: Resulting base torque as a function of pinion angle after performed Ramp steer test. The solid lines are the reference torque generated by the reference generator, the dashed lines are the estimated torque acting on the steering wheel, and the dotted lines are the torque taken from measurement in an EPAS vehicle. The Weave test results are illustrated in figure 6.2 for a scenario with the same steering feel model, performed on the same set of vehicle speeds. The reference torque closely follows the EPAS measurements for low vehicle speeds when turning away from the center position, but the distance between the initial slope gradients in the x-axis decreases as the vehicle speed increases. Hence, for higher vehicle speeds, the reference torque profile differs from the EPAS measurements for small pinion angles. In the instance when changing the steering direction toward the center position, the difference in the resulting torque from the SbW system and the EPAS measurements is noticeable but adjusts immediately. The zero torque position of the steering rack with a specific angular velocity profile deviates from the measurements resulting in an incremented position when zero torque occurs. This is the result of the torque profile having a steeper slope gradient with in general a lower mean torque value while turning towards the center position. This behavior holds true for all vehicle speeds. No definitive effects of the cogging torque can be seen for the Weave test because of the very limited range of motion of the steering wheel. 29 -0.6 -0.4 -0.2 0 0.2 0.4 Pinion angle [rad] -1500 -1000 -500 0 500 1000 1500 T o rq u e [ m N m ] Weave test - 3.6km/h -0.5 0 0.5 Pinion angle [rad] -3000 -2000 -1000 0 1000 2000 T o rq u e [ m N m ] Weave test - 30km/h -0.5 0 0.5 Pinion angle [rad] -3000 -2000 -1000 0 1000 2000 3000 T o rq u e [ m N m ] Weave test - 45km/h -0.4 -0.2 0 0.2 0.4 Pinion angle [rad] -3000 -2000 -1000 0 1000 2000 3000 T o rq u e [ m N m ] Weave test - 60km/h -0.4 -0.2 0 0.2 0.4 Pinion angle [rad] -4000 -2000 0 2000 4000 T o rq u e [ m N m ] Weave test - 80km/h -0.2 0 0.2 0.4 Pinion angle [rad] -3000 -2000 -1000 0 1000 2000 3000 T o rq u e [ m N m ] Weave test - 100km/h Figure 6.2: Resulting base torque as a function of pinion angle after performed Weave test. The solid lines are the reference torque generated by the reference generator, the dashed lines are the estimated torque acting on the steering wheel, and the dotted lines are the torque taken from measurement in an EPAS vehicle. 30 By performing a Return to center test on the steering feel model with no additional assisting features, the following results were found and are illustrated in figure 6.3. 0 10 20 30 40 50 60 70 Sample -2 0 2 4 6 8 10 P in io n a n g le [ ra d ] Return to center test 3.6km/h 30km/h 45km/h 60km/h 80km/h 100km/h Figure 6.3: An illustration of how the pinion angle changes during a Return to center test with solely base torque. The test was performed at five different vehicle speeds, 3.6km/h, 30km/h, 45km/h, 60km/h, 80km/h, and 100km/h. Figure 6.3 shows that the steering wheel returns to the center position for all vehicle speeds except 3.6km/h. When performing the test at 30km/h the steering wheel does return to center with a discontinuity due to getting stuck at a cogging torque peak. For all remaining vehicle speeds larger than 30km/h, the steering wheel returns to the center position without any discontinuities but is instead affected by an overshoot which grows larger for higher vehicle speeds. 6.2 Base torque with On-center damping To measure the impact of adding on center damping to the steering feel model, a Ramp steer test was performed at six different vehicle speeds, namely 3.6 km/h, 30 km/h, 45 km/h, 60 km/h, 80 km/h, and 100 km/h. The resulting torque profiles can be observed in figure 6.4. The reference torque profiles closely follow the EPAS measurements with no large deviation. There are no EPAS measurements for 3.6 km/h. For 30 km/h, the reference torque profile has a brief increase in torque for pinion angles beyond 2rad. The torque profile for different vehicle speeds does not follow a consistent behavior of reaching zero torque following the same second-degree loss of traction slope. Instead, for angles approaching zero torque, the profile shows non-linear behavior resulting in a slowly decreasing torque profile until reaching zero. This behavior is true if the pinion angle is below 5 rad. The estimated FFb torque profile is affected by the cogging torque resulting in fluctuations in the torque profile as can be seen by how the dashed lines fluctuate around the solid lines, illustrated in figure 31 6.4. 0 1 2 3 4 5 6 7 8 9 Pinion angle [rad] -2000 0 2000 4000 6000 8000 10000 T o rq u e [ m N m ] Ramp steer test 3.6km/h 30km/h 45km/h 60km/h 80km/h 100km/h Figure 6.4: Resulting base torque combined with on-center damping as a function of pinion angle after performed Ramp steer test. The solid lines are the reference torque generated by the reference generator, the dashed lines are the estimated torque acting on the steering wheel, and the dotted lines are the torque taken from measurement in an EPAS vehicle. Figure 6.5 illustrates the results after the Weave test for the vehicle speeds 3.6 km/h, 30 km/h, 45 km/h, 60 km/h, 80 km/h, and 100 km/h. The Weave test is performed with base torque combined with the On-center damping feature active. By observing the different torque profiles, the reference torque profile closely follows the EPAS measurements when turning away from the center position. However, for vehicle speeds above 45 km/h, the initial torque gradients of the reference torque profile increase faster than that of the EPAS measurements. Resulting in a steeper slope with higher torque for all small pinion angles. When changing steering direction towards the center position, the reference torque profile generally for all vehicle speeds tends to reach zero torque for a larger pinion angle, with a bigger difference for an increase in vehicle speed. Hence, the characteristics of the hysteresis have changed with a peak torque difference between turning away and turning towards the center position. The torque also drops in value during the instance of changing steering direction but quickly adjusts to the EPAS measurements. Compared to figure 6.2 where no On-center damping is active, the Weave tests show great similarity with minor discrepancies. 32 -0.5 0 0.5 Pinion angle [rad] -2000 -1000 0 1000 2000 T o rq u e [ m N m ] Weave test - 3.6km/h -0.5 0 0.5 Pinion angle [rad] -3000 -2000 -1000 0 1000 2000 T o rq u e [ m N m ] Weave test - 30km/h -0.5 0 0.5 Pinion angle [rad] -3000 -2000 -1000 0 1000 2000 3000 T o rq u e [ m N m ] Weave test - 45km/h -0.2 0 0.2 0.4 Pinion angle [rad] -3000 -2000 -1000 0 1000 2000 3000 T o rq u e [ m N m ] Weave test - 60km/h -0.2 0 0.2 0.4 Pinion angle [rad] -4000 -2000 0 2000 4000 T o rq u e [ m N m ] Weave test - 80km/h -0.2 -0.1 0 0.1 0.2 Pinion angle [rad] -3000 -2000 -1000 0 1000 2000 3000 T o rq u e [ m N m ] Weave test - 100km/h Figure 6.5: Resulting base torque combined with on-center damping as a function of pinion angle after performed Weave test. The solid lines are the reference torque generated by the reference generator, the dashed lines are the estimated torque acting on the steering wheel, and the dotted lines are the torque taken from measurement in an EPAS vehicle. 33 To measure the effectiveness of adding on center damping to the steering feel model, a return to center test was performed for six different vehicle speeds, namely 3.6 km/h, 30 km/h, 45 km/h, 60 km/h, 80 km/h, and 100 km/h which is illustrated in figure 6.6. For all vehicle speeds except 3.6 km/h, the steering wheel returns to the center position. For 30 km/h, the steering wheel stops for a short period of time before reaching the center position. The test results for the remaining vehicle speeds resulted in a smooth transition to the center position with next to no overshoot. 0 5 10 15 20 25 30 35 40 Sample -2 0 2 4 6 8 10 P in io n a n g le [ ra d ] Return to center test 3.6km/h 30km/h 45km/h 60km/h 80km/h 100km/h Figure 6.6: An illustration of how the pinion angle changes during a Return to center test with base torque combined with on-center damping active. 34 6.3 Base torque with additional Return to zero features This section shows the results of the steering feel model with the additional Return to center features Friction compensation and integration. 6.3.1 Return to center assistance by friction compensation By performing a Ramp steer test on the steering feel model with an additional friction compensation the following results were found, see figures 6.7 and 6.8. Figure 6.7 shows the results of the Ramp steer test on the steering feel model with friction compensation in comparison to the EPAS measurements for the vehicle speeds 30km/h, 45km/h, and 60km/h. Figure 6.8 shows the Ramp steer test on the steering feel model with friction compensation in comparison with the steering feel model without return to center assistance for the vehicle speed 3.6km/h. 0 1 2 3 4 5 6 7 8 9 Pinion angle [rad] -1000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 T o rq u e [ m N m ] Ramp steer test 30km/h 45km/h 60km/h Figure 6.7: Resulting base torque combined with a return to center assisting friction compensation as a function of pinion angle after performed Ramp steer test. The solid lines are the reference torque generated by the reference generator, the dashed lines are the estimated torque acting on the steering wheel, and the dotted lines are the torque taken from measurement in an EPAS vehicle. Figure 6.7 shows the torque measurements taken from an EPAS system on which the base torque is based, the reference torque generated by the reference generator, and the estimated torque acting on the steering wheel. It can be clearly seen that the reference torque and the estimated torque for all vehicle speeds rapidly increase to approximately 1000mNm but then dips such that the torque has an approximate 1000mNm offset from the EPAS measurements for all pinion angles larger than 0.5. The results show that due to the friction compensation necessary to assure the steering wheel returns to center the overall steering feel is negatively 35 affected since the reference torque nor the estimated torque follows the EPAS measurements for none of the vehicle speeds. In addition, the friction compensation also gives the undesired characteristic at the beginning of the turn at 30km/h, where the torque quickly increases to 1000mNm but then decreases before it starts to increase with the pinion angle at the same rate as the EPAS measurements. If figure 6.7 is compared with figure 6.1 it can clearly be seen that the resulting torque profile is worse with friction compensation if compared to the EPAS measurements. Figure 6.8 below shows the reference torque and the estimated torque at 3.6km/h where no EPAS torque measurements were available. 0 1 2 3 4 5 6 7 8 9 Pinion angle [rad] -2000 0 2000 4000 6000 8000 10000 T o rq u e [ m N m ] Ramp steer test Reference Torque Estimated Torque Reference Torque (no friction compensation) Estimated Torque (no friction compensation) Figure 6.8: Resulting base torque combined with a return to center assisting friction compensation as a function of pinion angle after performed Ramp steer test. The solid lines are the reference torque generated by the reference generator, and the dashed lines are the estimated torque acting on the steering wheel. Figure 6.8 shows how the torque very slightly increases with the pinion angle when friction compensation is applied in comparison to no friction compensation. It can also be seen how the torque slightly increases at the beginning of the turn but then decreases and even becomes negative before it starts to increase with the pinion angle. Figure 6.9 and 6.10 instead shows the torque profile of the steering feel model with additional friction compensation after a Weave test where figure 6.9 is for vehicle speeds of 30km/h, 45km/h and 60km/h and figure 6.10 is for 3.6km/h. 36 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Pinion angle [rad] -2000 -1000 0 1000 2000 T o rq u e [ m N m ] Weave test - 30km/h -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Pinion angle [rad] -2000 0 2000 4000 T o rq u e [ m N m ] Weave test - 45km/h -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Pinion angle [rad] -2000 -1000 0 1000 2000 T o rq u e [ m N m ] Weave test - 60km/h Figure 6.9: Resulting base torque combined with a return to center assisting friction compensation as a function of pinion angle after performed Weave test. The solid lines are the reference torque generated by the reference generator, the dashed lines are the estimated torque acting on the steering wheel, and the dotted lines are the torque taken from measuremen