电控动力转向系统的的控制原理和补偿策略的设计

Design of Control Logic and Compensation Strategy for Electric Power Steering Systems Tsung-Hsien Hu, Chih-Jung Yeh, Shih-Rung Ho, Tsung-Hua Hsu, and Ming-Chih Lin Automotive Research and Testing Center (ARTC). Email: elvishu@.twAbstract—The purpose of this research is to develop an electric power steering (EPS) control logic which integrates base-assist, damping, return, and inertia control logic. This research also introduces a special method which employs the steering angle signal and the vehicle speed signal into the control logic to tune the compensation gain immediately. It can optimize the steering response and improve the steering feel. In addition, a new control logic, impact compensation, has been proposed. It reduces the oscillatory effect of the steering system when the vehicle passes through an uneven road. For verifying the ideas mentioned above, this research integrates Matlab/Simulink with CarSim. Co-simulation technique is used to validate the proposed ideas for the high accurate description of vehicle dynamics and model of the steering behavior. The results show that the designed control logic and compensation strategy can satisfy various driving conditions. The impact control logic can alleviate the unwanted vibration of the steering wheel effectively. Keywords—Electric power steering; Impact control logic; Co-simulation.I.I NTRODUCTIONA steering system is a significant subsystem for a vehicle operation. Since considerable steering effort is required with the increase of vehicle weight increasing and parking convenience for maneuvers, a power steering system was introduced to assist the drivers in turning the steering wheel in such driving conditions. Most power steering systems are hydraulic, which use a pump to supply hydraulic pressure and is driven by an engine all the time. The EPS system has a compact structure compared with conventional one, and it is an on-demand system that operates only when the steering wheel is turned. In other words, substituting an EPS for a hydraulic one improves both space and engine efficiency and is more environmentally friendly. Besides, the EPS has more flexibility by the advantage of electronic control of the motor. It is easy to adjust the steering system characteristic just by modifying the program of the EPS controller. This is also the reason why there are many features developed for the EPS system.The magnitude, the direction, and the timing of torque output control of the assist motor are especially important. Hence, in order to develop the control logic for the EPS system, it needs to build the steering system model previously. Chen and Chen [1] applied Newton’s Law to build the dynamic model of every parts of the EPS system. Parmar and Hung [2] utilized the Lagrange’s Equations to construct the dynamic equation of the EPS system. Liao and Du [3] tried to combine the Matlab/Simulink and Adams to simulate the behavior of the vehicle and used the co-simulation technique to understand the effect of the EPS system on the vehicle motion. Choi et al. [4] associated SimPowerSystems with Matlab/Simulink to describe the effect of power electronics on the EPS system.Furthermore, the assist power is provided by an electric motor and affects the steering feel directly. Kurishige et al.[5] and Pang et al. [6] introduced motor control methods for avoiding the fluctuation, from the rotation motor, to influence the steering wheel and prevent to the driver from unfavorable steering feel.For control logic design, references [7~11] specified some methods that can improve the steering dynamics in some special situations while driving. They aimed to research and develop various control logics such as return compensation logic, and damping compensation logic.The major purpose of this research is to develop an EPS control logic which is composed of base assist, damping, return, inertia, and impact compensation logic with the aid of Matlab/Simulink and CarSim. In addition, this research proposes a new method to improve the compensation performance. It employs the steering angle signal and the vehicle speed signal into the control logic to tune the compensation gain immediately.II.M ODELINGThis research utilizes the co-simulation technique to develop the suitable control logic for the EPS system application. This needs to build up the mathematic model to describe the system dynamics and take this mathematic model to verify the accuracy and reliability of the control logic. But the degree of freedom of a full car model is too large and the control logic of the EPS system is too complex to model the overall system using a single code.Figure 1. Simulation block diagram of the EPS system with full carmodel.978-1-4244-1849-7/08/$25.00○C2008 IEEE.Thus the overall mathematic model can be divided intotwo parts. One is the full car model developed byMSC/CarSim. The other is the EPS system modeled byMatlab/Simulink. Integrating Matlab/Simulink withCarSim is helpful to design control logic accurately and make it easy to realize the influence of the EPS system on the vehicle motion. Fig. 1 shows the simulation block of the steering system and the full car model of CarSim in Matlab/Simulink environment.A. Steering Mechanism ModelThe schematic diagram of the EPS system is shown in Fig. 2. It is a typical column-type EPS system that consists of a torque sensor, an electric motor, a reduction gear, a column and a rack–pinion mechanism. In order to model the steering system behavior for the control logic design, it can obtain the equations of motion of the EPS system according to the Newton’s Law. The equations are shown below,sw sw sw sw sc sw t h J B K T θθθθ =−−−)(.(1)sc sc r sc r sc sw t sc sc f mnJ rx k K B T T θθθθθ =−−−+−+()( (2)r r r r r rsc r xm x b F rx r k =−−−(θ. (3) where T h is the instructional torque on the steering wheel from the driver; K t is the stiffness of the torsion bar; J sw and B sw are the inertia and the damping constants of the steering wheel; θsw and θsc are the steering wheel angle and the steering column angle respectively. T mn and T f are the electromagnetic drive and the friction torque on the steering column; J sc and B sc are the inertia and damping constants of the steering column. k r is the stiffness between the rack and pinion; x r is the dispacement of the rack; r is the stroke ratio. The angle of the pinion is equal to the column angle. F r is the alignment force on the rack from the road wheel; m r and b r are the mass and the damping constant of the rack.B. Motor ModelFor better assistance performance, this paper utilizes a 3-phase permanent magnetic synchronous machine (PMSM) to supply a torque that helps the driver turningthe steering wheel easily while cornering. In order to model the dynamics of PMSM, it can be described in the well-know d-q frame through the rotation reference frame transformation. [12][13] This modeling method cancontrol the motor torque by directly controlling the current in q-axis, because the torque is proportional to the product of the current in q-axis and a constant. Fig. 3 shows the schematic diagram of PMSM and the rotor reference frame.The differential equation is stated as: mL mn T n T ⋅=. (4)t q m k I T ⋅=. (5)⎥⎦⎤⎢⎣⎡+⎥⎦⎤⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡+−+=⎥⎦⎤⎢⎣⎡b e q d q a d e q e d a q d k I I L dt dR L L L dt d R V V θθθ 0. (6) m m m m mL m J B T T θθ =−−. (7)m e Pθθ2=. (8) Equation (6) and (7) are the electrical and themechanical equation of PMSM. T m and T mL are the electromagnetic drive and the counter balance torque on the motor shaft, respectively; n is the gear ratio. V d and V qare the d, q axis voltages, I d and I q are the d, q axis stator currents, L d and L q are the d, q axis inductances, while R a and θe are the stator resistance and the rotor electrical position, respectively. J m and B m are the inertia and damping constants of the motor; θm is the mechanical position of the rotor. P is the number of the magent poles on the rotor.Figure 4. Simulation block diagram of the PMSM with the spacevector control.swsw B θ,,mθ,r r r r rFigure 2. Schematic diagram of the EPS system.m ,T qL d L axisq −axisd −qV dVFigure 3. Schematic diagram of the PMSM.About the motor control, this paper adopts the space vector control mehtod to achieve the current control objective. The realization of pulse-width modulation takes the advantage of unified voltage modulation technique which is described clearly in reference [14]. Fig. 4 shows the simulation block diagram of the PMSM with space vector control in Matlab/Simulink environment. Combining the PMSM model with the EPS model is helpful to find problems caused by the motor before the implementation.C. Full Car ModelMatlab/Simulink is an equation-domain modeling tool. It is very complex to model the full car dynamics in this environment. This paper, therefore, adopts the CarSim to simulate the behavior of the vehicle motion. CarSim can show how vehicles respond dynamically to inputs from the driver and the immediate environment. It produces the same kinds of outputs that might be measured with physical tests involving instrumented vehicles. For this reason, it is a fine tool to simulate the full car behavior while cornering. CarSim environment is shown in Fig. 5. III. C ONTROL STRATEGYThe primary goals of the EPS system are to reduce the steering torque exerted by the driver and to better the steering performance. It not only improves the steering feel but also increases the driving pleasure. This research integrates the base assist, return, damping, inertia, and impact compensation logic into the EPS control loop. The overall structure of the control logic is shown in Fig. 6. A. Base assist logicThe major object of the EPS system is to providw a proper amount of assist torque by the electric motor to reduce the effort of the driver when the vehicle is cornering. For generating a suitable torque output from the motor to assist the driver, a base assist map shown in Fig. 7 is needed. According to the map, the core controller of the EPS system receives signals from the torque sensor and the vehicle speed sensor and calculates a suitable amount of assist gain to output to the motor controller. Therefore, the motor can provide a proper torque to assist the driver to turn the steering wheel.B. Return, Damping, and Inertia Control logicThe EPS system can overcome drawbacks associated with conventional one. One of the advantages is that the EPS could improve the return-to-center performance, called returnability, which is an important feature while driving. When the front wheels are steered, some energy would store in the mechanical structure of the steering system. The energy would produce a torque which tends to return the steering wheel to the center. In some driving cases, such as low speed driving, the steering wheel may not be able to return to center because of the friction in the road wheel and the steering system. For this reason, the return control logic has been introduced in the EPS system. It takes the advantage of controllable torque of the electric motor to improve the return-to-center performance and the vehicle dynamics. In this paper, the steering angle has been adopted as a major signal to control the assist motor to rotate the steering wheel to the near center position when the driver has his/her hands off the steering wheel. Besides, this paper attempts to take the steering wheel angular acceleration and the vehicle speed as compensation signals to enhance the performance of steering returnability. The compensation maps areestablished to tune the control gain according to theFigure 5. Full car model of MSC/CarSim.Figure 6. Block diagram of EPS control system.Steering torque (Nm)Vehicle speed (km/hr)A s s i s t g a i nFigure 7. Base assist map.steering wheel angular acceleration signal and vehicle speed signal as shown in Fig. 8. The steering wheel angular acceleration gain is in nonlinearly inverse proportion to the absolute value of the steering wheel angular acceleration, and the vehicle speed compensation gain decreases with the increase of the vehicle speed. The return performance will be better based this method. During the high speed operation, the aligning torque is significant large, which might make the steering wheel have an overshoot response. This characteristic leads to generate an unexpected yaw motion of the vehicle. As a result, the damping compensation logic has been applied in the EPS system to absorb the overshoot and alleviate the unexpected yaw motion. This paper tries to take the steering wheel angular velocity as a main control objective by means of the closed-loop technique. Thelogic generates a gain, which is opposite to the direction of the steering wheel angular velocity, as a reference of the motor current control loop. The motor torque resists the aligning torque from road wheel against the direction of the steering wheel motion. In this situation, the motor seems to be a buffer to mitigate the severe return action. Adding the steering wheel angle signal and the vehicle speed signal as the reference of compensation strategy can help tune the control gain to make the performance preferable. The steering wheel angle gain increases with the increase of the steering wheel angle, and the vehicle speed gain increases with the increase of the vehicle speed. For most of driving conditions, the base assist logic is almost able to cover all of assistance requirements according to the vehicle speed and the diver’s torque input. But when the driver turns the steering wheel rapidly, the heavy steering feel is produced by the inertia of the steering mechanism. It is an uncomfortable steering feel. In this situation, the base assist logic may be no longer enough to satisfy the steering demands. It is the major reason why the EPS control system needs the inertia control logic. The heavy handling feel is caused by the large steering wheel angular acceleration, so this approach utilizes the steering wheel angular acceleration as the main command, and takes the vehicle speed and the steering wheel angle as the auxiliary signals. This method can produce more assist torque to eliminate the heavy handling feel when the driver turns the steering wheel quickly. In addition, the steering wheel angle and vehicle speed have been used to compensate the inertia control performance. The steering wheel angle gain is in nonlinear proportion to the steering wheel angle, and the vehicle speed compensation gain increases with the increase of the vehicle speed. Fig. 8 shows the schematic diagram of the control logics of return, damping, and inertia.C.Impact Control logicWhen a vehicle passes through an uneven road surface, an oscillation may be occurs on the steering wheel. The oscillation normally takes place at low speed stage. In fact, it is an uncomfortable feeling of handling and may make the driver nervous during oscillation period. To reduce the effect from the road surface, this paper proposes a new method to achieve this function by means of estimating the reaction torque on the steering shaft (RTSS). The RTSS estimation method had been specified in reference [7] clearly. In this research, it takes the advantage of the RTSS estimation method and calculating the variation of the RTSS value. If the variation value increases more than the threshold, the control logic would generate a command to enable the impact compensation loop. The impact compensation loop will feed back the steering wheel angular velocity signal to control the assist motor. The motor control loop will calculate a suitable current command to motor and then the motor produces a suitable torque output to the steering system. The motor, in this case, alleviates the oscillation of steering wheel like a damper. Fig. 9 depicts the schematic diagram of the impact compensation logic.IV.S IMULATION R ESULTSTo satisfy the various conditions while cornering, the control logic of the EPS system has been developed. This paper integrates the Matlab/Simulink with CarSim to research and analyse the interaction between the vehicle behavior and the characteristic of the EPS system, and then to develop and design the control logic by means of co-simulation technique.The simulation results of the control logic mentioned above are shown below. For simulating on-center handling characteristic, it can follow the ISO 13674-1 [15] which specifies a weave test schedule that addresses a particular aspect of the on-center handing characteristic of a vehicle. The weave test procedure requires the steering wheel to be subjected to an oscillatory input. The preferred steering input waveform is normally sinusoidal. The frequency of the steering input shall be 0.2Hz±10%. The amplitude of the steering input shall be sufficient toVehicleReturnFigure 8. Control logics of return, damper, and inertia.Figure 9. Schematic diagram of impact control logic.Steering wheel angle (deg)S t e e r i n g t o r q u e (N m )Figure 11. Torque-angle plots of various vehicle speeds.Steering wheel angle (deg)S t e e r i n g t o r q u e (N m )Figure 12. Torque-angle plots of various steering wheel angles.let the vehicle lateral acceleration reach 0.2g. The standard test velocity is 100km/hr. Fig. 10 shows the results of the simulation with and without EPS assistance following the ISO 13674-1 procedure. Fig. 11 and Fig 12 show the steering torque-angle plot of the simulation at various vehicle speeds and various input amplitudes respectively. The returnability is an important property of the EPS system. It associates with the good behavior of vehicle when the driver has his/her hands off the steering wheel.Fig. 13 shows the simulation result of return control at two different vehicle speeds. It simulates that the driver applies a torque, like an impulse, on the steering wheel and then has his/her hands off the steering wheel. From Fig. 14, without the return control, the steady state of the steering angle is far away from the center position. On the contrary, the EPS system with the return control has a better return-to-center performance. It also means that it is possible to improve the subjective feel of driving.For the verification of the damping compensation logic, the steering torque is subjected to an impulse input. The test speeds of the vehicle are 80km/hr and 50km/hr. the simulation results are shown in Fig. 14. According to the simulation, it is easy to find the EPS system that has damping compensation function can alleviate the effect of oscillation and improve the vehicle dynamics obviously. The purpose of the inertia compensation simulation is to verify the steering torque and good feeling when turning the steering wheel quickly. The preferred steering input is usually sinusoidal. Fig. 15 shows the simulation result. On the center position, the steering wheel has the minimum angular acceleration. The maximum angular acceleration occurs at two ends. From the figure, the steering wheel torque is reduced gradually when angular velocity increase. For this reason, the function of inertia control logic has been proved here.The impact control logic is designed to mitigate the oscillatory effect of the steering wheel while a vehicle passing through an uneven road surface shown in Fig. 16.Time (sec)S t e e r i n g w h e e l a n g l e (d e g )Figure 13. The simulation result of return control logic.Time (sec)S t e e r i n g w h e e l a n g l e (d e g )Figure 14. The simulation result of damping control logic.Steering wheel angle (deg)S t e e r i n g t o r q u e (N m )Figure 10. Torque-angle plots of on-center handling test.Steering wheel angle (deg)S t e e r i n g t o r q u e (N m )Figure 15. The simulation result of inertia control logic.Figure 16. The impact simulation in CarSim environment.Time (sec)S t e e r i n g w h e e l a n g l e (d e g )Figure 17. The simulation result of impact control logic.The test speed is 15km/hr. The height of the bump is 0.1m. Fig. 17 shows the behavior of the steering wheel of this simulation. It demonstrates that the EPS system with the impact control logic has better response. V. C ONCLUSIONSThe control logic that integrates the base assist, return, damping, and inertia control can satisfy various driving conditions and have been shown in the simulation results. The special compensation strategy can optimize the steering response and improve the steering feel. The impact control logic has effectively alleviated the unwanted vibration from the uneven road. The co-simulation technique has high accuracy to verify the ideas that have been proposed in this paper. In the future, thecontrol logic will be carried out on the test bench to confirm its feasibility for EPS-equipped vehicles. A CKNOWLEDGMENTThis work is funded by the Department of Industial Technology of MOEA (Ministry of Economic Affair, Taiwan, R. O. C.) under the contract no. 97-EC-17-A-16-R7-0792.R EFERENCES[1] Xiang Chen and Xiaoqun Chen, “Control-Oriented Model forPower Steering System,” SAE TECHNICAL PAPER SERIES , 2006-01-0938.[2] Manu Parmar and John Y. Hung, “Modeling and SensorlessOptimal Controller Design for an Electric Power Assist Steeing System,” Industrial Electronics , Volume 3, Nov 2002, pp.1784-1789.[3] Y. Gene Liao and H. 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