Steering torque analysis and robust control method for steer-by-wire road feel simulation

Abstract

The present application relates to a kind of for steer-by-wire road feel simulation steering torque analysis and robust control method, comprising the following steps: obtaining the relevant parameters of steering torque controlled object;Based on the relevant parameters, the dynamics model of steering torque controlled object is established;Based on the dynamics model, by considering the expected steering torque, steering torque closed-loop control, steering torque feedforward control and friction feedforward compensation control are designed to solve steering torque control quantity.Compared with prior art, the present application has the advantages of improving steering torque robustness, anti-interference, etc.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of automobile chassis control, in particular to a steering torque analysis and robust control method for steer-by-wire road feel simulation. BACKGROUND

[0002] Steer-by-wire system cancels the mechanical connection between the upper and lower steering, which can realize flexible adjustment of hand feeling, variable transmission ratio, active steering and other functions, and is a representative technology of automobile intelligence. Since the road feel cannot be directly transmitted to the steering wheel through the mechanical structure, it is necessary to design a road feel simulation algorithm to control the motor of the hand wheel actuator (HWA) to generate appropriate steering hand feeling. The existing road feel simulation algorithm generally includes two parts: the first part is to design a desired steering torque algorithm; the second part is to design a steering torque control strategy to control the actual steering torque to track the desired steering torque.

[0003] The method used to design the desired steering torque can be divided into two categories: function fitting method and dynamics model estimation method. The former regards the desired steering torque as a two-dimensional function of vehicle speed and steering angle, which can be constructed by designing a Map or establishing a vehicle dynamics model. The latter first estimates the rack force based on disturbance observation method or (extended) Kalman filter method, and then designs the desired steering torque according to the idea of superimposing several torque, and provides a design method for different hand feeling modes (sporty, comfortable).

[0004] The steering torque control method used includes open-loop control, PID control, active disturbance rejection control, robust control, closed-loop + friction force feedforward compensation control, etc., to realize the tracking control of the steering torque on the desired steering torque. However, most of the existing torque control has the following two shortcomings: (1) The influence of the design characteristics of the desired steering torque on the stability of the torque closed loop is ignored, which easily leads to the problem of high-frequency jitter during the parameter calibration of the desired steering torque, i.e. the robustness problem of the torque closed loop mentioned below. (2) Only a few performance indicators such as tracking accuracy and bandwidth are considered, and few studies can comprehensively consider other performance indicators such as robustness, anti-interference and stability margin of the torque closed loop. Ultimately, it leads to the problems of poor steering torque smoothness of steer-by-wire road feel simulation and inconvenient parameter calibration of the desired steering torque. SUMMARY

[0005] The purpose of the present application is to provide a steering torque analysis and robust control method for steer-by-wire road feel simulation that improves the robustness of the steering torque.

[0006] The purpose of the present application can be achieved by the following technical solutions:

[0007] A steering torque analysis and robust control method for steer-by-wire road feel simulation, comprising the following steps:

[0008] Obtaining relevant parameters of a steering torque controlled object;

[0009] Establishing a dynamic model of the steering torque controlled object based on the relevant parameters;

[0010] Based on the dynamic model, the steering torque control amount is solved by considering the steering torque closed-loop control, steering torque feedforward control and friction feedforward compensation control of the expected steering torque, so as to control the controlled object to perform steer-by-wire road feel simulation.

[0011] Further, the expression of the dynamic model is:

[0012]

[0013]

[0014]

[0015] In the formula, J sw , C se are the inertia and damping of the upper end of the column, θ sw , and are the rotation angle, rotation speed and rotation acceleration of the upper end of the column, T h is the input torque of the driver, k TB is the stiffness of the torsion bar, Δθ is the deformation of the torsion bar, J eq , C eq are the inertia and damping of the lower end of the column, θ m , and are the rotation angle, rotation speed and rotation acceleration of the lower end of the column, T m is the torque of the motor output equivalent to the lower end of the column, T f is the nonlinear friction of the motor friction equivalent to the lower end of the column, T s is the torsion bar torque.

[0016] Further, the specific steps of solving the steering torque control amount include:

[0017] Based on the dynamic model, the expected steering torque is considered to obtain the steering torque closed-loop control with the optimal robust performance by using the robust control theory;

[0018] The steering torque feedforward control method is used to calculate the steering torque feedforward control;

[0019] Adopting friction force feedforward compensation method, the friction force feedforward compensation control is calculated;

[0020] Based on the steering torque closed loop control, steering torque feedforward control and friction force feedforward compensation control, the steering torque control quantity is obtained.

[0021] Further, the obtaining step of the steering torque closed loop control specifically comprises:

[0022] By introducing weight function, evaluation input and evaluation output, the dynamic model of the controlled object is converted into the dynamic model of the generalized controlled object;

[0023] Based on robust control theory, the H ∞ norm constraint of the generalized controlled object is established.

[0024] The weight function in the generalized dynamic model is determined;

[0025] Based on the determined weight function and the H ∞ norm constraint, the steering torque closed loop control with optimal robust performance is obtained.

[0026] Further, the expression of the dynamic model of the generalized controlled object is:

[0027]

[0028] Wherein

[0029]

[0030] In the formula, Z r =[z1 z2] T is all evaluation outputs of the generalized controlled object, d r =[r d1 d2 d3] T is all evaluation inputs of the generalized controlled object, W1, W2, W3, W4 and W5 are weight functions, P is the transfer function matrix of the generalized controlled object, u fb is the output of the closed loop controller, A and G are respectively the response characteristic transfer function of the road feeling motor and the dynamic transfer function of the controlled object.

[0031] Further, the weight function W3 is the product of two parts, and the expression is:

[0032]

[0033] In the formula, is the weight function corresponding to the suppression of nonlinear friction force disturbance; is the weight function corresponding to the suppression of driver load disturbance.

[0034] Further, the H∞ The norm constraint is:

[0035] ||G dtoZ (s)|| ∞ <γ r

[0036]

[0037] where G dtoZ (s) is a closed-loop transfer function from evaluation input d r to evaluation output Z r , γ r is an optimal value of robust performance, Z r is all evaluation outputs of the generalized controlled object, and d r is all evaluation inputs of the generalized controlled object.

[0038] Further, the calculation expression of the manipulation torque feedforward control is:

[0039] u ffd = C ffd (s) · T cmd

[0040] where u ffd is a manipulation torque feedforward control amount, C ffd (s) is a feedforward controller transfer function, and T cmd is a desired manipulation torque.

[0041] Further, the calculation expression of the desired manipulation torque is:

[0042]

[0043] where T cmd (s) is a desired manipulation torque, G all (s) is a response characteristic, θ m (s) and θ sw (s) are a lower end rotation angle of the pipe column and an upper end rotation angle of the pipe column, respectively, T s (s) is a torsion bar torque, and k TB is a stiffness of the torsion bar.

[0044] Further, the calculation expression of the friction force feedforward compensation control is:

[0045]

[0046] where u fricCompFFd is a friction force feedforward compensation amount, f fricModel is a nonlinear friction force model, and ω is a lower end rotation speed of the pipe column.

[0047] Compared with the prior art, the present application has the following beneficial effects:

[0048] (1) The present application considers the influence of the expected steering torque design characteristics on the stability of the torque closed loop, i.e. the robustness problem, and significantly improves the robustness of the steering torque control method through the linearization analysis of the steering torque closed loop, the steering torque closed loop control, the feedforward control and the friction feedforward compensation control.

[0049] (2) In addition to considering the torque tracking accuracy, bandwidth performance index and other performance indexes, the present application also considers the nonlinear friction disturbance and the driver load disturbance, and conveniently achieves a better torque control effect through the weight function design and the feedforward control amount design in the steering torque closed loop control, so that the steering torque control has good robust stability, smoothness, noise resistance, tracking accuracy and bandwidth. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 The method flowchart of the embodiment of the present application is shown in the figure;

[0051] Figure 2 The HWA schematic diagram of the embodiment of the present application is shown in the figure;

[0052] Figure 3 The principle overall block diagram of the embodiment of the present application is shown in the figure;

[0053] Figure 4 The G all (s) influence caused torque fluctuation schematic diagram is shown in the figure;

[0054] Figure 5 The Bode diagram of different working points G all (s) of the embodiment of the present application is shown in the figure;

[0055] Figure 6 The steering torque closed loop Bode diagram of different working points G all (s) of the embodiment of the present application is shown in the figure;

[0056] Figure 7 The steering torque closed loop control schematic diagram based on the H ∞ robust control of the embodiment of the present application is shown in the figure;

[0057] Figure 8 The Bode diagram of the weight function W3(s) and the components thereof of the embodiment of the present application is shown in the figure

[0058] Figure 9 The Bode diagram of the weight function W5(s) of the embodiment of the present application is shown in the figure;

[0059] ​Figure 10 A schematic diagram of HWA hardware-in-the-loop test for an embodiment of the present application;

[0060] Figure 11 A physical diagram of HWA hardware-in-the-loop test for an embodiment of the present application;

[0061] Figure 12 Test results of HWA hardware-in-the-loop test in slow steering working condition for an embodiment of the present application;

[0062] Figure 13 Test results of HWA hardware-in-the-loop test in slow steering working condition for an embodiment of the present application;

[0063] Figure 14 Test results of HWA hardware-in-the-loop test in small angle fast steering working condition for an embodiment of the present application;

[0064] Figure 15 FFT analysis results of steering torque in simulation of bumpy road working condition test for an embodiment of the present application;

[0065] Figure 16 Test results of real vehicle test in slow steering working condition for an embodiment of the present application;

[0066] Figure 17 Test results of real vehicle test in small angle fast steering working condition for an embodiment of the present application. DETAILED DESCRIPTION

[0067] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present application, and detailed implementation and specific operation process are given, but the protection scope of the present application is not limited to the following embodiments.

[0068] The present embodiment provides a steering torque analysis and robust control method for steer-by-wire road feel simulation, as shown in FIG. 1, which comprises the following steps: Figure 1

[0069] S1, obtaining relevant parameters of a steering torque controlled object.

[0070] The controlled object of steering torque control is a steering torque simulation actuator (HWA) in a steer-by-wire system, as shown in FIG. 2. The HWA is simplified as a double mass system to obtain relevant parameters, including inertia, damping, rotation angle of the upper and lower ends of the column, and stiffness of the torsion bar, etc. Figure 2

[0071] S2, establishing a dynamics model of the steering torque controlled object based on the relevant parameters.

[0072] ​​The dynamics equation of the steering torque simulator includes the dynamics equation of the upper end of the pipe column and the dynamics equation of the lower end of the pipe column, as shown below.

[0073] The dynamics equation of the upper end of the pipe column is:

[0074]

[0075] The dynamics equation of the lower end of the pipe column is:

[0076]

[0077] Wherein, the torsion rod deformation is:

[0078]

[0079] In the formula, J sw , C sw are the inertia and damping of the upper end of the pipe column, θ sw , and are the rotation angle, rotation speed and rotation acceleration of the upper end of the pipe column, T h is the input torque of the driver, k TB is the stiffness of the torsion rod, Δθ is the torsion rod deformation, J eq , C eq are the inertia and damping of the lower end of the pipe column, which are unified to the worm gear reducer, motor and the like of the lower end of the pipe column, θ m , and are the rotation angle, rotation speed and rotation acceleration of the lower end of the pipe column, T m is the torque of the motor output end equivalent to the lower end of the pipe column, T f is the nonlinear friction of the motor friction equivalent to the lower end of the pipe column, T s is the torsion rod torque.

[0080] The dynamics equation of the lower end of the pipe column can be further rewritten as:

[0081]

[0082] In the formula: J eq , C eq are the inertia and damping of the lower end of the pipe column, which are unified to the worm gear reducer, motor and the like of the lower end of the pipe column, Δθ, and are the torsion rod deformation, first order and second order derivatives, k TB is the stiffness of the torsion rod, T m is the torque of the motor output end equivalent to the lower end of the pipe column, T f is the nonlinear friction of the motor friction equivalent to the lower end of the pipe column, T dis caused by the steering wheel rotation speed and rotation acceleration caused by the driver steering the steering wheel, expressed as:

[0083]

[0084] The Laplace transform of the dynamic equation of the lower end of the column gives the controlled object of the mechanical part of the HWA:

[0085]

[0086] wherein T s (s) is the torque of the torsion bar, T m (s) is the torque of the lower end of the column, k TB is the stiffness of the torsion bar.

[0087] S3, based on the dynamic model, the steering torque control amount is solved by considering the expected steering torque design, steering torque feedforward control and friction feedforward compensation control.

[0088] The conventional steering torque closed loop, as shown in the outer dashed box in Figure 3 , ignores the coupling relationship between the expected steering torque and the torque closed loop, and the reference input is the expected steering torque T cmd , and the torque error T e is calculated according to the measurement feedback of the torsion bar torque T s (representing the actual steering torque), the closed loop controller C fb (s) calculates the corresponding closed loop control amount u fb according to the error T e , and realizes the closed loop tracking control of the torsion bar torque T s to the expected steering torque T cmd .

[0089] The steering torque closed loop analysis method in this embodiment considers the steering torque closed loop system with expected steering torque design characteristics, as shown in the outer dashed box in Figure 3 . In actual situations, the design of the expected steering torque T cmd and the steering torque control closed loop is not a completely decoupled relationship. Since the principle of steering torque design is to calculate the expected steering torque T cmd according to the real-time acquisition of the lower end of the HWA column angle sensor signal θ m and the column lower end rotation speed signal calculated by the motor controller, the expected steering torque T cmd at each working point can be regarded as the response characteristic G all (s) with θ m as the input, which is expressed as:

[0090]

[0091] where T cmd (s) is the desired control torque, G all (s) is the response characteristic, θ m (s), θ sw (s) are the rotation angle of the lower end of the column and the rotation angle of the upper end of the column, respectively, T s (s) is the torque of the torsion bar, k TB is the stiffness of the torsion bar; G all (s) θ sw (s) is regarded as the reference input of the control torque closed loop system, (s) is regarded as the additional negative feedback of the control torque closed loop system.

[0092] In the above formula, T cmd (s) is composed of two parts, the former G all (s) θ sw (s) is regarded as the reference input of the torque closed loop and does not affect the stability of the closed loop; the latter G is equivalent to the additional negative feedback in the conventional torque closed loop and directly affects the stability of the torque closed loop. If the effect of the additional negative feedback G all (s) is not considered, the high-frequency stability of the control torque closed loop is insufficient when the desired control torque is parameterized, and the control torque fluctuation above 20 Hz as shown in FIG. 2 is caused. Figure 4

[0093] The present embodiment improves the robustness of the control torque control method by controlling the robustness of the control torque closed loop control, the control torque feedforward control, and the friction feedforward compensation control.

[0094] The robustness of the control torque closed loop control refers to the problem that the characteristics of the desired control torque G all (s) are different at different operating points, resulting in high-frequency uncertainty of the control torque closed loop. The characteristics of G all (s) are completely determined by the design parameters of the desired control torque. Whether the desired control torque is designed based on function fitting or based on dynamic model estimation, the characteristics of G cmd (s) can be derived through system identification or the design mechanism of the desired control torque T Figure 5 (s) at two operating points G all (s) are the Bode diagrams corresponding to the two operating points, and G all ​(s) exhibits high-pass filter characteristics, which is determined by the fact that the desired control torque includes components such as damping and simulated friction torque, and the desired control torque VS the rotation angle exhibits hysteresis characteristics. Since the design torque gradient and torque hysteresis differ at different operating points, the control torque design characteristic G... all The high-pass characteristics exhibited by (s) are also different. This G all The varying degrees of high-pass characteristics of (s) lead to high-frequency uncertainties in the control torque closed loop, such as Figure 6 As shown, this places high demands on the robustness of the torque closed-loop controller.

[0095] This embodiment also considers the anti-interference problem of the closed-loop control of the operating torque. The system disturbance input includes a nonlinear frictional disturbance T. f and driver load disturbance T d .

[0096] For a closed-loop controller C fb For the closed-loop system of the control torque (s), the transfer function The nonlinear frictional force T represents the closed loop of the control torque. f Its anti-interference performance is expressed as:

[0097]

[0098] In the formula, A(s) and G(s) are the transfer function of the road sensor motor response characteristics and the transfer function of the controlled object dynamics, respectively.

[0099] Driver load disturbance T d The impact is reflected in the following indicators:

[0100]

[0101] This indicator describes the steering wheel angle θ when the driver operates the steering wheel. sw Corresponding control torque T s The frequency response characteristics. When the operating frequency is high (e.g., small corrections during straight-line driving, small corrections around a circle, etc.), The response amplitude decreases, the control torque amplitude decreases, and the subjective feeling is "a hollow feel".

[0102] Therefore, this embodiment adopts H ∞ The robust torque closed-loop control design method first introduces a weight function, evaluation input, and evaluation output, transforming the original controlled object into a generalized controlled object, such as... Figure 7 As shown, its expression is:

[0103]

[0104] in,

[0105]

[0106] where Z r = [z1 z2] T is the evaluation output of the generalized controlled object, d r = [r d1 d2 d3] T is the evaluation input of the generalized controlled object, W1, W2, W3, W4 and W5 are weight functions, P is the transfer matrix of the generalized controlled object, u fb is the output of the closed loop controller, A and G are the response characteristic transfer function of the road feel motor and the dynamic transfer function of the controlled object respectively.

[0107] The standard is based on H ∞ The performance robust control objective is to determine the optimal value of γ r by determining the constraint condition of the generalized controlled object, so as to achieve better robust performance and stability of the generalized controlled object.

[0108] ||G dtoZ (s)| ∞ <γ r

[0109] where,

[0110]

[0111] where G dtoZ (s) is the closed loop transfer function from the evaluation input d r to the evaluation output Z r , γ r is the optimal value of the robust performance, Z r is the evaluation output of the generalized controlled object, d r is the evaluation input of the generalized controlled object.

[0112] The design of the closed loop controller of the steering torque finally falls on the design of each weight function W1, W2, W3, W4 and W5:

[0113] (1) z1 is the evaluation output of the torque error T e . In order to control its low frequency band to have a lower level, W1 is designed as a low pass filter.

[0114] (2) z2 is the evaluation output of the control variable u. There is no specific constraint on it, and W2 is simply set as a constant.

[0115] (3) d1 is the evaluation input to measure the influence of the disturbance d. Since the disturbance contains the nonlinear friction force T f of the system and the driver load disturbance T dTwo parts, so W3(s) is set as the product of two parts:

[0116]

[0117] where, corresponding to the suppression of T f disturbance; corresponding to the suppression of T d disturbance. Due to the friction disturbance T f causes the inherent frequency of the HWA to fluctuate, is set as a peak filter with a large gain near the inherent frequency (10 Hz). While the driver load disturbance T d caused by "empty" is in the frequency range of about 2 Hz, is set as a peak filter with a large gain near 2 Hz. The final W3(s) weight function is set as shown in Figure 8 .

[0118] (4) d2 is an evaluation input that measures the influence of noise n. In order to suppress the influence of high-frequency noise, W4 is set as a high-pass filter.

[0119] (5) d3 is an evaluation input that measures the influence of system high-frequency uncertainty. In order to solve the robustness problem caused by the uncertainty of G all (s) in the control moment closed loop, W5 should be set as a high-pass filter as shown in Figure 9 .

[0120] By solving the corresponding linear matrix inequality (LMI), the corresponding H ∞ performance optimal control moment controller C fb (s) can be solved.

[0121] The control moment feedforward control design method is used to suppress the influence of the driver load disturbance T d and solve the "empty" problem during small-angle fast steering. The feedforward control amount is represented as:

[0122] u ffd = C ffd (s) · T cmd

[0123] where, the feedforward controller C ffd (s) is designed as a peak filter of 2 Hz.

[0124] Friction feedforward compensation design is used to reduce the nonlinear friction disturbance T fThe effect is based on a friction model, directly controlling the road feel feedback motor to generate a certain torque to counteract the frictional disturbance T. f Its control quantity is expressed as:

[0125]

[0126] In the formula: f fricModel It is a nonlinear friction force model.

[0127] The control torque closed-loop control, control torque feedforward control, and friction feedforward compensation control obtained above together constitute the control torque control quantity, which is used to control the controlled object to achieve steer-by-wire road feel simulation.

[0128] To verify the effectiveness of the above method, this example uses a specific HWA as an application scenario. For example... Figure 10 The diagram shown is a hardware-in-the-loop (HWA) hardware-in-the-loop simulation diagram. Figure 11 The diagram of the test bench shows that the designed control torque algorithm, along with other algorithms, runs in the dSPACE Scalexio rapid control prototype. It collects in real time the acceleration and deceleration information of the driver through the pedal, the rotational speed and torsion bar torque at the lower end of the HWA column, calculates the HWA motor control command, and controls the motor to generate control torque.

[0129] Figure 12 and Figure 13 Based on the test results under slow-speed driving conditions of 60 kph, steering wheel operation frequency of 0.2 Hz, and amplitude of ±70 degrees, it can be concluded that the steering torque has high tracking accuracy; at the same time, the torque fluctuation of the steering torque is basically less than 0.1 Nm, which is below the general human perception threshold and has good smoothness.

[0130] Figure 14 Based on the test results of the small-angle rapid operation condition, it can be concluded that the tracking accuracy of the control torque is still high during rapid operation, and there is no "free-running" problem or torque fluctuation.

[0131] Figure 15 To simulate the working conditions of a bumpy road surface, a random excitation was superimposed on the desired control torque. The results of the Fast Fourier Transform (FFT) on the control torque measurement data show that the bandwidth of the torque control is greater than 20Hz.

[0132] Figure 16 and Figure 17The results of the real vehicle test slow operation and small angle fast operation are consistent with the semi-physical simulation results, the steering torque has good smoothness, tracking accuracy and stability, there is no "hand feeling empty" problem in small angle fast operation, and the effectiveness of the steering torque algorithm of the embodiment is verified.

[0133] The preferred embodiments of the application are described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and changes without creative work based on the concept of the present application. Therefore, any technical solutions obtained by logical analysis, reasoning or limited experiments based on the prior art within the concept of the present application should be within the protection scope determined by the claims.

Claims

1. A steering torque analysis and robust control method for steer-by-wire road feel simulation, characterized in that, The method comprises the following steps: Obtaining relevant parameters of the manipulated torque controlled object; Establishing a dynamic model of the manipulated torque controlled object based on the relevant parameters; Solving the manipulated torque control amount based on the dynamic model by considering the manipulated torque closed-loop control, the manipulated torque feedforward control and the friction feedforward compensation control of the expected manipulated torque to control the controlled object to perform the steer-by-wire road feeling simulation, wherein the specific steps of solving the manipulated torque control amount comprise: Considering the expected manipulated torque to obtain the robust performance optimal manipulated torque closed-loop control by using the robust control theory based on the dynamic model; Calculating the manipulated torque feedforward control by using the manipulated torque feedforward control method; Calculating the friction feedforward compensation control by using the friction feedforward compensation method; Obtaining the manipulated torque control amount based on the manipulated torque closed-loop control, the manipulated torque feedforward control and the friction feedforward compensation control; The obtaining step of the manipulated torque closed-loop control specifically comprises: Converting the dynamic model of the controlled object into the dynamic model of a generalized controlled object by introducing the weight function, the evaluation input and the evaluation output; Based on robust control theory, the generalized controlled object is established Norm constraint; Determining the weight function in the dynamic model of the generalized controlled object; Based on the determined weight function and the Norm constraint, the robust performance optimal control of the manipulation moment is obtained. The expression of the dynamic model of the generalized controlled object is: Wherein wherein is the evaluation output for the generalized controlled object, is the evaluation input for the generalized controlled object, , , , and and are weighting functions, and P is a transfer function matrix of the generalized controlled object, u fb is the output of the closed-loop controller, A, G are the response characteristic transfer function of the road feel motor and the dynamics transfer function of the controlled object, respectively, is the evaluation output of the torque tracking error , is the evaluation output of the control amount u , is the torque tracking error, is the evaluation input related to the reference input, is the evaluation input measuring the influence of the disturbance d , is the evaluation input measuring the influence of the noise , is the evaluation input measuring the influence of the high-frequency uncertainty of the system.

2. A steering torque analysis and robust control method for steer-by-wire road feel simulation according to claim 1, characterized in that, The expression of the dynamic model is: wherein, , Jup and Csup are the inertia and damping of the upper end of the column, and θup, ωup and αup are the angle, speed and angular acceleration of the upper end of the column, Mup is the input torque of the driver, K is the stiffness of the torsion bar, δ is the deformation of the torsion bar, , Jlow and Clow are the inertia and damping of the lower end of the column, equivalent to the worm gear reducer and the motor, and θlow, ωlow and αlow are the angle, speed and angular acceleration of the lower end of the column, Mlow is the torque of the motor output, equivalent to the lower end of the column, Ff is the nonlinear friction of the motor friction, equivalent to the lower end of the column, M is the torque of the torsion bar.

3. The steering torque analysis and robust control method for steer-by-wire road feel emulation according to claim 1, wherein The weight function W 3 is the product of two parts, expressed as: wherein is a weight function corresponding to the suppression of the nonlinear friction disturbance; is a weight function corresponding to the suppression of the driver load disturbance.

4. The steering torque analysis and robust control method for steer-by-wire road feel emulation according to claim 1, wherein, the generalized controlled object The norm constraint is wherein is the closed loop transfer function from the evaluation input to the evaluation output is the optimal value of the robustness performance, is the optimal value of the robustness performance, is the evaluation output of the generalized plant, is the evaluation input of the generalized plant.

5. The steering torque analysis and robust control method for steer-by-wire road feel emulation according to claim 1, wherein, The calculation expression of the manipulated torque feedforward control is: wherein is the manipulated torque feedforward control quantity, is the feedforward controller transfer function, T cmd is the desired manipulated torque.

6. A steering torque analysis and robust control method for steer-by-wire road feel simulation according to claim 5, characterized in that, The calculation expression of the expected manipulated torque is: wherein is the desired steering torque, is the response characteristic, , are the lower and upper steering angles, respectively, is the torsion bar torque, is the stiffness of the torsion bar.

7. The steering torque analysis and robust control method for steer-by-wire road feel emulation according to claim 1, wherein, The calculation expression of the friction feedforward compensation control is: In the formula, is a friction feed forward compensation amount, is a nonlinear friction model, is the rotational speed of the lower end of the pipe column.

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