Commercial vehicle active anti-rollover control method and system based on GA-mu optimization robust controller

Abstract

The invention discloses a commercial vehicle active anti-rollover control method and system based on a GA-mu optimization robust controller, and the method comprises the steps: building a rollover dynamic model, and building a rollover early warning system with a zero moment point as a rollover evaluation index, thereby determining the control switching-in time of a controller; the method comprises the following steps: performing uncertainty analysis modeling on a rollover kinetic model, processing parameter uncertainty and dynamic unmodeled uncertainty, performing performance weighting function optimization on a control system through a genetic optimization algorithm, and solving and designing a GA-mu robust controller by utilizing a D-K iterative algorithm. Compensation yawing moment needed by rollover prevention of the vehicle under the condition that the front wheel turning angle of a driver is input is calculated, differential brake wheels are selected, yawing moment distribution is achieved, and rollover of the vehicle is prevented. The problems that the control precision is insufficient, the performance robustness and the robustness stability are poor and the control effect is not ideal due to the fact that a traditional mu controller performance weighting function usually depends on experience and manual adjustment on system understanding are solved.

Description

Technical Field

[0001] The invention discloses a commercial vehicle active rollover prevention control method and system based on a GA-μ optimized robust controller, belonging to the field of vehicle intelligent control. Background Technique

[0002] In recent years, the number of fatal rollover accidents of commercial vehicles has been on the rise. Compared with ordinary passenger cars, commercial vehicles have a larger vehicle mass and a higher center of gravity, making them more prone to rollover accidents. Vehicle instability and rollover can cause a series of extremely dangerous traffic accidents, resulting in great social, personnel, and property hazards. According to the statistical data of the National Highway Traffic Safety Administration (NHTSA) in the United States, the number of deaths caused by rollover accidents is second only to that caused by vehicle collision accidents. The reason for rollover is that it is difficult for drivers to directly predict the risk of vehicle rollover. When they realize the vehicle is about to roll over, it is already very difficult to effectively control the vehicle, thus causing accidents. To protect people's lives and property safety, active rollover prevention control of commercial vehicles is one of the key tasks.

[0003] At present, most are various PID-based controls or linear quadratic controls, without considering the influence of system uncertainties. During actual operation, due to interference from external environmental factors and uncertainties in the vehicle model's own parameters, errors occur, resulting in poor robustness. And because the performance weight function of the traditional μ controller usually relies on experience and understanding of the system for repeated manual adjustment, the accuracy is insufficient and the control effect is not ideal. Designing a controller with better performance robustness, robust stability, and stronger adaptability to prevent vehicle rollover and ensure vehicle safety and stability is more meaningful. Summary of the Invention

[0004] The invention provides a robust control method for a commercial vehicle active rollover prevention system optimized by a genetic algorithm. The specific scheme is as follows:

[0005] A robust control method for a commercial vehicle active rollover prevention system optimized by a genetic algorithm, the method comprising the following steps:

[0006] Step 1: Establish a vehicle linear three-degree-of-freedom rollover dynamics model and a tire lateral mechanics model;

[0007] Step 2: Establish a vehicle rollover warning system based on the zero moment point;

[0008] Step 3: Design a GA-μ robust controller and calculate the compensating yaw moment required to prevent the vehicle from rolling over in an unstable state;

[0009] Step 4: Select the differential braking wheels according to the compensated yaw moment to achieve yaw moment distribution.

[0010] The specific content is as follows:

[0011] First step, establish a vehicle dynamics model and a tire side force model. Since the construction and analysis of a high-degree-of-freedom model are difficult and its real-time performance is poor, and considering the subsequent control strategy, the vehicle model adopted is a three-degree-of-freedom physical model of the vehicle that includes yaw motion, roll, and lateral motion, which is based on the classic two-degree-of-freedom vehicle model and adds the rotation of the vehicle around the X-axis. The equations are the dynamic equations obtained by analyzing the forces in each motion direction using Newton's second law. At the same time, the tire nonlinearity is regarded as a kind of parameter uncertainty to supplement the model. The specific vehicle dynamics equations are as follows:

[0012] Lateral motion:

[0013]

[0014] Yaw motion:

[0015]

[0016] Roll motion:

[0017]

[0018] Where:

[0019] F f = k f α f

[0020] F r = k r α r

[0021] Using the small-angle approximation, the slip angle can be written as:

[0022]

[0023] Where: m is the total mass of the vehicle; m s is the sprung mass; F f and F r are the tire side forces of the front and rear wheels respectively; α f and α r are the tire sideslip angles of the front and rear wheels respectively; δ f is the front wheel steering angle; v x is the vehicle longitudinal speed; v y is the lateral speed; g is the acceleration due to gravity; ω rr is the yaw rate of the vehicle; β is the sideslip angle of the center of mass; is the roll angle; represents the roll rate; is the roll acceleration; I x is the moment of inertia of the vehicle about the x-axis; I z is the moment of inertia of the vehicle about the z-axis; k f and k r are the cornering stiffness of the front wheels and the cornering stiffness of the rear wheels respectively; is the equivalent roll stiffness of the suspension; is the equivalent roll damping coefficient of the suspension; h r is the distance from the center of mass to the roll center; a and b are the distances from the center of mass to the front axle and the rear axle respectively; M z is the compensating yaw moment generated by the GA-μ controller and distributed by differential braking.

[0024] Based on the rollover model and adding the tire dynamics model, the differential equation of the commercial vehicle rollover model can be obtained as follows:

[0025]

[0026] Furthermore, the differential equation of the commercial vehicle rollover model is transformed into the form of a state-space equation. The state variables are The disturbance input and the control variable are respectively w = [δ f ; U = [M Z .

[0027]

[0028] Second, establish a vehicle rollover warning system based on the zero moment point. Based on the rollover warning index of the zero moment point, calculate the lateral position of the zero moment point. The lateral offset of the zero moment point can be used to predict the trend of vehicle roll, so it can be used as a criterion for vehicle roll stability. Specifically, it includes:

[0029] Establish the lateral position coordinates of the rollover warning index zero moment point:

[0030]

[0031] where, m s is the sprung mass; g is the acceleration due to gravity; is the roll angle; is the equivalent roll stiffness of the suspension; is the equivalent roll damping coefficient of the suspension; h r is the distance from the center of mass to the roll center; here B is the track width. Since y ZMP is more accurate in the linear region and difficult to control when the vehicle is at the rollover point, so the following constraints are imposed on y ZMP :

[0032]

[0033] In the formula is the threshold value of the lateral offset of the zero moment point, which is generally set to 0.8.

[0034] Step 3: Design a GA-μ robust controller. Calculate the yaw moment M required for compensation to avoid rollover when the vehicle has a rollover tendency or inclination through the upper-layer controller based on GA-μ z . The specific process of controller design is as follows:

[0035] 1. Uncertainty representation and processing:

[0036] Regard the nonlinearity of the tire as parameter uncertainty. Therefore, select the tire cornering stiffness k f , k r as the parameter uncertainties of the vehicle. At the same time, regard the moment of inertia I z as parameter uncertainty for processing, which can compensate for the error caused by model simplification. Define as:

[0037]

[0038] In the formula, and are the nominal values of the tire cornering stiffness of the front and rear wheels of the vehicle, respectively, that is, the tire cornering stiffness under linear conditions. The nominal value of the cornering stiffness is the result of the combined action of tire physical characteristics, experimental data, and vehicle engineering requirements, providing key parameters for the vehicle dynamics model, and the value is directly selected according to the actual vehicle; is the nominal value of the moment of inertia of the vehicle about the z-axis; d1, d2, and d3 are the percentage changes in the cornering stiffness of the front and rear wheels of the vehicle and the moment of inertia about the z-axis, respectively, that is, the degree of parameter perturbation; δ1, δ2, and δ3 are the unit value perturbations corresponding to the perturbations, and satisfy |δ i | ≤ 1.

[0039] Write the parameter uncertainty in the upper linear fractional transformation form:

[0040]

[0041] In the formula, F u (·) represents the upper linear fractional transformation; M i , i = 1, 2, 3 are the coefficient matrices of the corresponding linear fractional transformation.

[0042] Design the control weight function \(W_1\) to limit the output magnitude of the control quantity \(U\) and avoid saturation of the lower-level actuators. The upper bound of \(|1 / W_1|\) is the allowable maximum value. Generally, a constant value is taken as the control weight function. For example, the weight function for limiting the motor torque output is \(1 / 20\); the weight function for limiting the steering wheel angle output is \(4 / \pi\).

[0043] Design the disturbance weight function according to external disturbances such as sensor noise interference, crosswind disturbance, and road disturbance to represent the influence of external disturbances on the control system in different frequency ranges. Among them, \(W\) d1 , \(W\) d2 , \(W\) d3 correspond to the weights corresponding to the above external disturbances respectively.

[0044] Due to the non-structural modeling error in system modeling, multiplicative uncertainty is used to describe the modeling error of the system model. \(G(s)=G_0(s)(I + W\) u (s)\(\Delta\) u ), where \(I\) represents the identity matrix; \(G_0(s)\) is the nominal system transfer function model; \(\Delta\) u represents input uncertainty; design \(W\) u (s) as the weight function of multiplicative uncertainty, which reflects the magnitude of the modeling error at different frequencies, and its value can be obtained by the following formula:

[0045]

[0046] In control theory, \(s = j\omega\) means that the Laplace transform degenerates into the Fourier transform;

[0047] Design the control error \(e\), which is the difference between the expected zero-moment point lateral offset \(y\) ZMPd of the rollover warning index and the response value of the actual lateral position coordinate \(y\) ZMP of the vehicle. For \(e\), design the performance weight function \(W\) p (s) to enhance the system tracking performance.

[0048] 2. \(\mu\)-synthesis controller design:

[0049] As Figure 3 shown, construct the \(\mu\)-synthesis robust controller according to the vehicle dynamics model, parameter uncertainty, weight function design, and linear fractional transformation method established in the above steps.

[0050] Define the parameter uncertainty perturbation block \(\Delta\) G and the input uncertainty perturbation block \(\Delta\) u as the mixed uncertainty perturbation block \(\Delta\), and its diagonal matrix is as follows:

[0051]

[0052] Meanwhile, a virtual uncertain block Δ is introduced to reflect the requirements of rollover warning index threshold tracking and external disturbance suppression performance p , thus obtaining the augmented uncertain diagonal matrix of the system as follows:

[0053]

[0054] In the formula, C represents the set of complex numbers, that is, Δ p is a complex matrix of m×n. The input vector parameter of Δ p is the lateral offset control error z of the zero moment point p (z p represents the performance of tracking the target and suppressing interference), the output of the limiting control quantity output size control weight function z1, and the output vector parameter of Δ p is the compensation yaw moment M required to keep the vehicle in the critical state z , the driver's stress steering interference input δ f , the crosswind disturbance F w , the road disturbance d r and the sensor measurement noise interference n s ; the input and output of the mixed uncertainty are w and z, w includes the input vector p of the virtual uncertain block and the output of the modeling uncertainty perturbation block Δ u , and z includes the output vector q of the uncertain block and the output of the uncertain weighting function W u (s); y is the system measurement output, u is the control input, and the quantity it represents is the same as U. Use P to represent the nominal system dynamics model; K to represent the feedback controller; M to represent a transfer function obtained from a lower linear fractional transformation composed of P and K, and let M = F l (P, K), and Fl represents the lower linear fractional transformation.

[0055] According to the μ-synthesis theory, the necessary and sufficient condition for designing a stable controller that can make the system satisfy robust stability and performance robustness is:

[0056]

[0057] In the formula represents the structured singular value, R represents the set of real numbers, s = jω, and its definition is as follows

[0058]

[0059] where is the maximum singular value of Δ. Generally speaking, The smaller the value, the greater the perturbation amplitude that the system can tolerate. Therefore, when using the μ-synthesis method for robust control of the system, the problem of maximizing the perturbation amplitude is equivalent to the problem of minimizing the SSV (Structured Singular Value). The robust controller is designed using the dksyn command in Matlab, and this instruction completes the design process through the D-K iteration method as follows:

[0060]

[0061] In the formula, D is the scaling transformation matrix, and D -1 is the inverse matrix of the D matrix. The specific process of the D-K iteration method is as follows:

[0062] [1] Fix the D matrix and use H ∞ theory to solve the minimization problem of the controller K, so as to find the optimal solution. In the first iteration, the D matrix is usually initialized as the identity matrix.

[0063] [2] Fix the controller K and determine the optimal scaling matrix at each frequency by calculating the upper bound of the structured singular value of the closed-loop system.

[0064] [3] Find a stable and minimum-phase matrix D that is as close as possible to the optimal scaling matrix at each frequency point.

[0065] [4] Repeatedly iterate the above steps until the predetermined accuracy requirement is reached, and finally obtain the required controller K.

[0066] 3. Optimize the controller performance weight function using genetic algorithm

[0067] The specific method for optimizing the μ-synthesis performance weight function based on genetic algorithm is as follows:

[0068] Use the structured singular value of the closed-loop system as the cost function of the genetic algorithm;

[0069] To ensure the tracking accuracy and steady-state performance of the reference signal in the low-frequency band throughout the process, avoid the system being too sensitive to low-frequency interference or model uncertainty, and at the same time ensure sufficient control force; be able to suppress the influence of high-frequency noise and unmodeled dynamics in the high-frequency band, prevent high-frequency noise from being over-amplified and the system from becoming unstable, and improve robustness. Therefore, the following constraint conditions are designed:

[0070]

[0071] Among them, K low and K high represent the low-frequency gain and high-frequency gain of the controller respectively. W p (jω) is the performance weight function, s = jω.

[0072] When the first-order transfer function form is selected, the expression of the performance weight function is as follows:

[0073]

[0074] Here, ABCD represents the formal parameters of the performance weight function;

[0075] Therefore, the constraint conditions can be converted into the following inequalities:

[0076]

[0077] Based on taking the violation of the constraint conditions as a penalty function, the reciprocal of the structured singular value is set as the fitness function of the genetic algorithm, and its expression is:

[0078]

[0079] Among them, F(x) is the fitness function, λ and μ are penalty coefficients, and λ·max(0, g(x)) and μ·max(0, h(x)) are penalty values.

[0080] First, initialize the population and encode the parameters to be optimized. The GA optimization starts with an initial population. Each chromosome in the population is generated by gene encoding and is regarded as a potential solution. The parameters of the population include the population size (the number of chromosomes) and the chromosome length. The chromosome adopts binary encoding. The decoding process of this method is relatively simple. By setting different binary string lengths, numbers with different precisions can be represented. Their upper and lower limits are respectively restricted to ensure the convergence of the optimization process. The relationship between the parameter value range and the string length is expressed as:

[0081]

[0082] Among them, k is the parameter to be optimized, k max and k min are respectively the upper and lower limits of the parameter setting, and x is the size of the number represented by the binary string.

[0083] Calculate the fitness value F(x) of the individual and the penalty values λ·max(0, g(x)), μ·max(0, h(x));

[0084] Select, crossover, and mutate the population to generate a new population.

[0085] The roulette method is used in the selection process. Specifically: select excellent individuals from the current population so that they have the opportunity to be parents to reproduce offspring for the next generation. The selection principle is that individuals with strong adaptability have a greater probability of contributing one or more offspring to the next generation. The relative fitness of each individual is the probability that each individual is inherited into the next generation population:

[0086] The relative fitness, i.e., the genetic probability is:

[0087]

[0088] where n is the population size.

[0089] Traverse each individual and perform crossover and mutation operations. Usually, at the initial stage of the genetic algorithm evolution, a relatively large crossover probability P c (0.7 - 0.9) and a relatively small mutation probability P m (0.001 - 0.05) should be selected. According to the value ranges of P c and P m at the initial stage of evolution, the adjustment formula varying with the number of evolution generations is designed as follows:

[0090]

[0091] P c0 = 0.5 + 0.2 × rand(0, 1)

[0092] P m0 = 0.008 + 0.049 × rand(0, 1)

[0093] where: gen1 is the number of evolution generations, rand(0, 1) is a random number generated between 0 and 1, c1 and c2 are adjustable constants in [0, ∞), and P c0 and P m0 are the crossover probability and mutation probability of the initial population respectively.

[0094] Judge the condition for terminating the iteration. The number of iterations is set in advance. Regardless of the current optimization result, the optimization process will not terminate until the number of iterations is reached. After reaching the number of iterations, it is necessary to judge whether the final optimization result meets the condition of the minimum structured singular value. If it meets, output the parameters of the performance weight function. Otherwise, it is necessary to update the algorithm parameters (including the form of the performance weight function and the crossover probability, mutation probability, etc.) until the parameters of the performance weight function that meet the requirements can be output.

[0095] Step 4: Based on the GA-μ controller, calculate the compensating yaw moment required to avoid rollover when the vehicle has a rollover tendency or inclination, select the differential braking wheels, and realize the yaw moment distribution. The specific method is as follows:

[0096] Design the differential braking rule. The yaw moment effect on the vehicle when applying braking forces to different wheels is as Figure 5 shown. It can be seen that the yaw moment effect is the most obvious when braking the rear inner wheel of the vehicle, followed by the front outer wheel. Select the braking wheels based on the compensating yaw moment calculated by the GA-μ controller combined with the driver input signal as shown in Table 1 below:

[0097] Table 1 Determination of the Braking Wheels

[0098]

[0099] Braking Torque Distribution:

[0100]

[0101] Where: T LF 、T LR 、T RF 、T RR are the braking torques distributed to the left front, left rear, right front, and right rear respectively; R is the wheel radius; F z is the force in the vertical direction received by each wheel; M z is the compensating yaw moment obtained based on the GA-μ controller; d f and d r are the wheelbases of the front and rear wheels of the vehicle respectively.

[0102] Based on the above control method, the present invention also proposes a system for the active rollover prevention control method of commercial vehicles based on the GA-μ optimized robust controller, including the rollover dynamics model part established in step 1, the vehicle rollover warning part based on the zero moment point established in step 2, the GA-μ robust controller part established in step 3, and the yaw moment distribution part in step 4.

[0103] Advantages of the Present Invention:

[0104] (1) The GA-μ control method proposed by the present invention improves the traditional μ-synthesis control, proposes to optimize the performance weight function using the genetic algorithm. Compared with the traditional empirical method, it reduces complex parameter adjustment and more accurately describes the uncertainty range and performance objectives of the system, reasonably distributes the priorities of performance and robustness in different frequency ranges, so as to find the best balance between the two, and further designs a more robust controller to ensure that the system can still operate stably under the influence of multi-source perturbations and has stronger anti-interference ability.

[0105] (2) Based on the GA-μ controller for rollover prevention control, it can more effectively suppress the rollover tendency of commercial vehicles during high-speed turning motion, ensure the safety and stability of vehicle active rollover prevention control, and improve the rollover prevention effect of the vehicle. Description of the Drawings

[0106] Figure 1 is the flowchart for implementing the rollover prevention control method of the present invention.

[0107] Figure 2 is the vehicle dynamics model of the rollover prevention vehicle of the present invention.

[0108] Figure 3 This is the design diagram of the GA-μ controller of the present invention.

[0109] Figure 4 This is the flow chart of the genetic algorithm for optimizing the performance weight function.

[0110] Figure 5 This is the effect diagram of the yaw moment generated on the vehicle when braking forces are applied to different wheels. Specific embodiments

[0111] The present invention will be further described below in conjunction with the accompanying drawings.

[0112] As Figure 1 shown, the implementation process of the present invention includes the following four steps:

[0113] In the first step, a vehicle dynamics model and a tire side force model are established. Since the construction and analysis of a high-degree-of-freedom model are difficult and its real-time performance is poor, and considering the subsequent control strategy, the vehicle model adopted is a three-degree-of-freedom physical model of a vehicle that includes yaw motion, roll, and lateral motion, which is based on the classic two-degree-of-freedom vehicle model and adds the rotation of the vehicle around the X-axis. The dynamic equations are obtained by applying Newton's second law to analyze the forces in each motion direction. At the same time, the tire nonlinearity is regarded as a kind of parameter uncertainty to supplement the model. The specific vehicle dynamics equations are as follows:

[0114] Lateral motion:

[0115]

[0116] Yaw motion:

[0117]

[0118] Roll motion:

[0119]

[0120] Where:

[0121] F f = k f α f

[0122] F r = k r α r

[0123] Using small angle approximation, the slip angle can be written as:

[0124]

[0125] Where: m is the total mass of the vehicle; ms is the sprung mass; F f and F r are the lateral forces of the front and rear tires respectively; α f and α r are the tire sideslip angles of the front and rear tires respectively; δ f is the front wheel steering angle; v x is the vehicle longitudinal speed; v y is the lateral speed; g is the acceleration due to gravity; ω r is the vehicle yaw angular velocity; β is the center of mass sideslip angle; is the roll angle; represents the roll angular velocity; is the roll angular acceleration; I x is the moment of inertia of the vehicle about the x-axis; I z is the moment of inertia of the vehicle about the z-axis; k f and k r are the front tire cornering stiffness and the rear tire cornering stiffness respectively; is the equivalent roll stiffness of the suspension; is the equivalent roll damping coefficient of the suspension; h r is the distance from the center of mass to the roll center; a and b are the distances from the center of mass to the front axle and the rear axle respectively; M z is the compensated yaw moment generated by the GA-μ controller and distributed by differential braking.

[0126] Based on the rollover model and adding the tire dynamics model, the differential equation of the commercial vehicle rollover model can be obtained as follows:

[0127]

[0128] Furthermore, the differential equation of the commercial vehicle rollover model is transformed into the form of the state space equation. The state variables are The disturbance input and the control variables are w = [δ f ; U = [M Z .

[0129]

[0130] Second, establish a vehicle rollover warning system based on the zero moment point. Based on the rollover warning index of the zero moment point, calculate the lateral position of the zero moment point. The lateral offset of the zero moment point can be used to predict the trend of vehicle roll, so it can be used as a criterion for vehicle roll stability. Specifically, it includes:

[0131] Establish the lateral position coordinates of the zero moment point of the rollover warning index:

[0132]

[0133] where, m sis the sprung mass; g is the acceleration due to gravity; is the roll angle; is the equivalent roll stiffness of the suspension; is the equivalent roll damping coefficient of the suspension; h r is the distance from the center of mass to the roll center; here B is the track width. Since y ZMP is more accurate in the linear region and difficult to control when the vehicle is at the rollover point, so for y ZMP the following constraints are imposed:

[0134]

[0135] In the formula is the threshold value of the lateral offset of the zero moment point, generally set to 0.8.

[0136] In the third step, design a GA-μ robust controller. When the vehicle has a tendency to roll over or is inclined to roll over, calculate the yaw moment M z required for compensation to avoid rollover through the upper-layer controller based on GA-μ. The specific process of controller design is as follows:

[0137] 4. Uncertainty representation and processing:

[0138] Regard the nonlinearity of the tire as parameter uncertainty. Therefore, select the tire cornering stiffness k f , k r as the parameter uncertainties of the vehicle. At the same time, regard the moment of inertia I z as parameter uncertainty for processing, which can compensate for the error caused by model simplification. Define as:

[0139]

[0140] In the formula, and are the nominal values of the tire cornering stiffness of the front and rear wheels of the vehicle respectively, that is, the tire cornering stiffness under linear conditions. The nominal value of the cornering stiffness is the result of the combined action of tire physical characteristics, experimental data, and vehicle engineering requirements, providing key parameters for the vehicle dynamics model, and the numerical value is directly selected according to the actual vehicle; is the nominal value of the moment of inertia of the vehicle about the z-axis; d1, d2, and d3 are the percentage changes in the cornering stiffness of the front and rear wheels of the vehicle and the moment of inertia about the z-axis respectively, that is, the degree of parameter perturbation; δ1, δ2, and δ3 are the unit value perturbations corresponding to the perturbations, and satisfy |δ i | ≤ 1.

[0141] Write the parameter uncertainty in the upper linear fractional transformation form:

[0142]

[0143] Where F u (·) represents the upper linear fractional transformation; M i , i = 1, 2, 3 are the coefficient matrices corresponding to the linear fractional transformations.

[0144] Design the control weight function W1 to limit the output magnitude of the control quantity U and avoid saturation of the lower-level actuators. The upper bound of |1 / W1| is the allowable maximum value. Generally, a constant value is taken as the control weight function. For example, the weight function for limiting the motor torque output is 1 / 20; the weight function for limiting the steering wheel angle output is 4 / π.

[0145] Design the disturbance weight function according to external disturbances such as sensor noise interference, crosswind disturbance, and road disturbance to represent the influence of external disturbances on the control system in different frequency ranges. Among them, W d1 , W d2 , W d3 correspond to the weights corresponding to the above external disturbances respectively.

[0146] Due to the non-structural modeling error during system modeling, multiplicative uncertainty is used to describe the modeling error of the system model. G(s) = G0(s)(I + W u (s)Δ u ), where I represents the identity matrix; G0(s) is the nominal system transfer function model; Δ u represents the input uncertainty; design W u (s) as the weight function of multiplicative uncertainty, which reflects the magnitude of the modeling error at different frequencies. Its value can be obtained by the following formula:

[0147]

[0148] In control theory, s = jω means that the Laplace transform degenerates into the Fourier transform;

[0149] Design the control error e, which is the difference between the expected zero-moment point lateral offset y ZMPd of the rollover warning index and the response value of the actual lateral position coordinate y ZMP of the vehicle. For e, design the performance weight function W p (s) to enhance the system tracking performance.

[0150] 5. μ-synthesis controller design:

[0151] As Figure 3 shown, construct the μ-synthesis robust controller according to the vehicle dynamics model, parameter uncertainty, weight function design, and linear fractional transformation method established in the above steps.

[0152] The parameter uncertainty perturbation block Δ Gand the input uncertainty perturbation block Δ u is defined as the mixed uncertainty perturbation block Δ, and its diagonal matrix is as follows:

[0153]

[0154] Meanwhile, a virtual uncertainty block Δ reflecting the requirements of rollover warning index threshold tracking and external disturbance suppression performance is introduced p , so the augmented uncertain diagonal matrix of the system is obtained as:

[0155]

[0156] where C represents the set of complex numbers, that is, Δ p is an m×n complex matrix. The input vector parameter of Δ p is the lateral offset control error z of the zero moment point p (z p represents the performance of tracking the target and suppressing interference), the output of the limiting control quantity output size control weight function z1, and the output vector parameter of Δ p is the compensating yaw moment M required to keep the vehicle in the critical state z , the driver's emergency steering interference input δ f , the crosswind disturbance F w , the road disturbance d r and the sensor measurement noise interference n s ; the input and output of the mixed uncertainty are w and z, w includes the input vector p of the virtual uncertainty block and the output of the modeling uncertainty perturbation block Δ u , z includes the output vector q of the uncertainty block and the output of the uncertainty weighting function W u (s); y is the system measurement output, u is the control input, and the quantity it represents is the same as U. Use P to represent the nominal system dynamic model; K to represent the feedback controller; M to represent a transfer function obtained from the lower linear fractional transformation composed of P and K, and let M = F l (P, K), and Fl represents the lower linear fractional transformation.

[0157] According to the μ-synthesis theory, the necessary and sufficient condition for designing a stable controller that can make the system satisfy robust stability and performance robustness is:

[0158]

[0159] where represents the structured singular value, R represents the set of real numbers, s = jω, and its definition is as follows

[0160]

[0161] where is the largest singular value of Δ. Generally speaking, The smaller the value of, the larger the perturbation amplitude that the system can tolerate. Therefore, when using the μ-synthesis method to perform robust control on the system, the problem of maximizing the perturbation amplitude is equivalent to the problem of minimizing the SSV (Structured Singular Value). The robust controller is designed using the dksyn command in Matlab, and this instruction completes the design process through the D-K iteration method as follows:

[0162]

[0163] where D is the scaling transformation matrix, and D -1 is the inverse matrix of the D matrix. The specific process of the D-K iteration method is as follows:

[0164] [5] Fix the D matrix and use the H ∞ theory to solve the minimization problem of the controller K, so as to find the optimal solution. In the first iteration, the D matrix is usually initialized as the identity matrix.

[0165] [6] Fix the controller K and determine the optimal scaling matrix at each frequency by calculating the upper bound of the structured singular value of the closed-loop system.

[0166] [7] Find a stable and minimum-phase matrix D that is as close as possible to the optimal scaling matrix at each frequency point.

[0167] [8] By repeatedly iterating the above steps until the predetermined accuracy requirement is reached, the required controller K is finally obtained.

[0168] 6. Optimizing the controller performance weight function using genetic algorithms

[0169] The specific method for optimizing the μ-synthesis performance weight function based on genetic algorithms is as follows:

[0170] Use the structured singular value of the closed-loop system as the cost function of the genetic algorithm;

[0171] To ensure the tracking accuracy and steady-state performance of the reference signal in the low-frequency band throughout the process, avoid the system being too sensitive to low-frequency interference or model uncertainty, and at the same time ensure sufficient control force; be able to suppress the influence of high-frequency noise and unmodeled dynamics in the high-frequency band, prevent the high-frequency noise from being over-amplified and the system from becoming unstable, and improve the robustness. Therefore, the following constraint conditions are designed:

[0172]

[0173] where K low and K high represent the low-frequency gain and high-frequency gain of the controller respectively. W p(jω) is the performance weight function, and s = jω.

[0174] When selecting the first-order transfer function form, the expression of the performance weight function is:

[0175]

[0176] Here, ABCD represents the form parameters of the performance weight function;

[0177] Therefore, the constraint conditions can be converted into the following inequalities:

[0178]

[0179] Based on taking the violation of the constraint conditions as the penalty function, the reciprocal of the structured singular value is set as the fitness function of the genetic algorithm, and its expression is:

[0180]

[0181] Among them, F(x) is the fitness function, λ and μ are penalty coefficients, and λ·max(0, g(x)) and μ·max(0, h(x)) are penalty values.

[0182] First, initialize the population and encode the parameters to be optimized. The GA optimization starts with an initial population. Each chromosome in the population is generated by gene encoding and is regarded as a potential solution. The parameters of the population include the population size (the number of chromosomes) and the chromosome length. The chromosome adopts binary encoding, and the decoding process of this method is relatively simple. By setting different binary string lengths, numbers with different precisions can be represented. Their upper and lower limits are respectively restricted to ensure the convergence of the optimization process. The relationship between the parameter value range and the string length is expressed as:

[0183]

[0184] Among them, k is the parameter to be optimized, k max and k min are respectively the upper and lower limits of the parameter setting, and x is the size of the number represented by the binary string.

[0185] Calculate the fitness value F(x) of the individual and the penalty values λ·max(0, g(x)) and μ·max(0, h(x));

[0186] Select, cross, and mutate the population to generate a new population.

[0187] The selection process uses the roulette wheel method. Specifically: Select excellent individuals from the current population so that they have the opportunity to serve as parents to reproduce offspring for the next generation. The selection principle is that individuals with strong adaptability have a greater probability of contributing one or more offspring to the next generation. The relative fitness of each individual is the probability that each individual is inherited into the next generation population:

[0188] The relative fitness, that is, the genetic probability is:

[0189]

[0190] where n is the population size.

[0191] Traverse each individual and perform crossover and mutation operations. Usually, a larger crossover probability P c (0.7 - 0.9) and a smaller mutation probability P m (0.001 - 0.05) should be selected in the initial stage of genetic algorithm evolution. According to the value ranges of P c and P m in the initial stage of evolution, the adjustment formula that changes with the number of evolution generations is designed as follows:

[0192]

[0193] P c0 = 0.5 + 0.2×rand(0, 1)

[0194] P m0 = 0.008 + 0.049×rand(0, 1)

[0195] where: gen1 is the number of evolution generations, rand(0, 1) is a random number generated between 0 and 1, c1, c2 are adjustable constants in [0, ∞), P c0 and P m0 are the crossover probability and mutation probability of the initial population respectively.

[0196] Judge the condition for terminating the iteration. The number of iterations is set in advance. Regardless of the current optimization result, the optimization process will not terminate until the number of iterations is reached. After reaching the number of iterations, it is necessary to judge whether the final optimization result meets the condition of the minimum structured singular value. If it meets, output the parameters of the performance weight function. Otherwise, it is necessary to update the algorithm parameters (including the form of the performance weight function and the crossover probability, mutation probability, etc.) until the parameters of the performance weight function that meet the requirements can be output.

[0197] In the fourth step, based on the GA-μ controller, calculate the compensation yaw moment required to avoid rollover when the vehicle has a rollover tendency or inclination, select the differential braking wheels, and realize the yaw moment distribution. The specific method is as follows:

[0198] Design differential braking rules. The yaw moment effect on the vehicle when applying braking forces to different wheels is as Figure 5 shown. It can be seen that the yaw moment effect is the most obvious when braking the rear inner wheel of the vehicle, followed by the front outer wheel. Based on the compensated yaw moment calculated by the GA-μ controller and the driver input signal, the braking wheels are selected as shown in Table 1 below:

[0199] Table 1 Determination of Braking Wheels

[0200]

[0201] Braking Torque Distribution:

[0202]

[0203] Where: T LF , T LR , T RF , T RR are the distributed braking torques for the left front, left rear, right front, and right rear respectively; R is the wheel radius; F z is the vertical force received by each wheel; M z is the compensated yaw moment obtained based on the GA-μ controller; d f and d r are the wheelbases of the front and rear wheels of the vehicle respectively.

[0204] The embodiment of the present invention further includes: Based on the above control method, the present invention also proposes a control system for the active rollover prevention control method of commercial vehicles based on the GA-μ optimized robust controller, including the rollover dynamics model part established in step 1, the vehicle rollover warning part based on the zero moment point established in step 2, the GA-μ robust controller part established in step 3, and the yaw moment distribution part in step 4, a total of 4 parts. This control system can be configured in the control equipment of commercial vehicles.

[0205] The GA-μ control method proposed by the present invention improves the traditional μ-synthesis control, proposes to use the genetic algorithm to optimize the performance weight function. Compared with the traditional empirical method, it reduces complex parameter adjustment and more accurately describes the uncertainty range and performance objectives of the system, reasonably distributes the priorities of performance and robustness in different frequency ranges, so as to find the best balance point between the two, and further designs a more robust controller to ensure that the system can still operate stably in the environment affected by multi-source perturbations and has stronger anti-interference ability.

[0206] Based on the GA-μ controller for rollover prevention control, it can more effectively suppress the rollover tendency of commercial vehicles during high-speed turning motion, ensure the safety and stability of vehicle active rollover prevention control, and improve the rollover prevention effect of the vehicle.

[0207] The series of detailed descriptions listed above are only specific descriptions of the feasible implementation manners of the present invention, and they are not intended to limit the protection scope of the present invention. Any equivalent manners or modifications that do not depart from the technology created by the present invention should be included within the protection scope of the present invention.

Claims

1. A commercial vehicle active rollover prevention control method based on a GA-μ optimized robust controller, characterized in that, It includes the following steps: Step 1: Establish a vehicle linear three-degree-of-freedom roll dynamics model and a tire lateral mechanics model; Step 2: Establish a vehicle rollover warning strategy based on the zero moment point; Step 3: Design a GA-μ robust controller and calculate the yaw moment required to compensate for preventing the vehicle from rolling over in an unstable state; Step 4: Select differential braking wheels to achieve yaw moment distribution.

2. The active rollover prevention control method for commercial vehicles based on a GA-μ optimized robust controller according to claim 1, characterized in that, The three-degree-of-freedom roll dynamics model in Step 1 is based on the classical two-degree-of-freedom vehicle model, with the addition of the vehicle's rotation around the X-axis, including a three-degree-of-freedom physical model of the vehicle's yaw motion, roll, and lateral motion. The equations are the dynamic equations obtained by analyzing the forces in each motion direction using Newton's second law. At the same time, the tire nonlinearity is regarded as a kind of parameter uncertainty to supplement the model. The specific vehicle dynamics equations are as follows: Lateral motion: Yaw motion: Roll motion: Wherein: F f = k f α f F r = k r α r Using the small-angle approximation, the slip angle can be written as: where: m is the total vehicle mass; m s is the sprung mass; F f and F r are the lateral forces of the front and rear tires respectively; α f and α r are the tire sideslip angles of the front and rear tires respectively; δ f is the front wheel steering angle; v x is the vehicle longitudinal speed; v y is the lateral speed; g is the acceleration due to gravity; ω r is the vehicle yaw rate; β is the center of mass sideslip angle; is the roll angle; represents the roll angular velocity; is the roll angular acceleration; I x is the moment of inertia of the vehicle about the x-axis; I z is the moment of inertia of the vehicle about the z-axis; k f and k r are the front and rear tire cornering stiffnesses respectively; is the equivalent roll stiffness of the suspension; is the equivalent roll damping coefficient of the suspension; h r is the distance from the center of mass to the roll center; a and b are the distances from the center of mass to the front and rear axles respectively; M z is the compensating yaw moment generated by the GA-μ controller and distributed by differential braking.

3. The active rollover prevention control method for commercial vehicles based on a GA-μ optimized robust controller according to claim 2, characterized in that ,, Regarding the tire nonlinearity as a kind of parameter uncertainty to supplement the model, and adding the tire dynamics model on the basis of the roll dynamics model, the differential equation of the commercial vehicle rollover model is obtained:

4. A commercial vehicle active rollover prevention control method based on a GA-μ optimized robust controller according to claim 3, characterized in that, Convert the differential equation of the commercial vehicle rollover model into the form of a state-space equation, where the state variables are The disturbance input and the control variable are respectively w = [δ f , U = [M Z ; 5. A commercial vehicle active rollover prevention control method based on a GA-μ optimized robust controller according to claim 1, characterized in that, The specific implementation of Step 2 includes: Establish the lateral position coordinate of the zero moment point of the rollover warning index: where m s is the sprung mass; g is the acceleration due to gravity; is the roll angle; is the equivalent roll stiffness of the suspension; is the equivalent roll damping coefficient of the suspension; h r is the distance from the center of mass to the roll center; here B is the track width, since y ZMP is more accurate in the linear region and difficult to control when the vehicle is at the rollover point, so the following constraint is imposed on y ZMP : In the formula is the threshold of the lateral offset of the zero moment point, generally set to 0.

8.

6. A commercial vehicle active rollover prevention control method based on a GA-μ optimized robust controller according to claim 1, characterized in that The specific implementation of Step 3 includes the representation and processing of uncertainties, specifically as follows: Step 3.1, considering the nonlinearity of the tire as parameter uncertainty, select the cornering stiffness of the tire as the parameter uncertainty of the vehicle. At the same time, regard the moment of inertia I z as parameter uncertainty, and obtain: In the formula, and are respectively the nominal values of the cornering stiffness of the front and rear tires of the vehicle, that is, the cornering stiffness of the tire under linear conditions. The nominal value of the cornering stiffness is the result of the combined action of the physical characteristics of the tire, experimental data, and vehicle engineering requirements, providing key parameters for the vehicle dynamics model, and the numerical value is directly selected according to the actual vehicle; is the nominal value of the moment of inertia of the vehicle about the z-axis; d1, d2, and d3 are respectively the percentage changes in the cornering stiffness of the front and rear wheels of the vehicle and the moment of inertia about the z-axis, that is, the degree of parameter perturbation; δ1, δ2, and δ3 are respectively the unit value perturbations corresponding to the perturbations, and satisfy |δ i | ≤ 1; Step 3.2, Write the parameter uncertainty in the upper linear fractional transformation form: where, F u (·) represents a upper linear fractional transformation; M i , i = 1, 2, 3 are coefficient matrices corresponding to the linear fractional transformations; Step 3.3, Design the control weight function W1 to limit the output size of the control quantity U and avoid saturation of the lower-level actuator. The upper bound of |1 / W1| is the allowable maximum value; Step 3.4, design an interference weight function according to sensor noise interference, crosswind disturbance, and road disturbance to represent the influence of external interference on the control system in different frequency ranges; where W d1 , W d2 , W d3 correspond to the weights corresponding to the above external interferences respectively; Step 3.5, for the non-structural modeling error existing during modeling, multiplicative uncertainty is used to describe the modeling error, G(s) = G0(s)(I + W u (s)Δ u ), where I represents the identity matrix; G0(s) is the nominal system transfer function model; Δ u represents the input uncertainty; W u (s) is designed as the weight function of multiplicative uncertainty, which reflects the magnitude of the modeling error at different frequencies, and its value can be obtained by the following formula: where s = jω. ; Step 3.6, design the control error e, which is the lateral offset y of the expected zero-moment point of the rollover warning index ZMPd and the actual lateral y ZMP of the vehicle response value. For e, design the performance weight function W p (s) to enhance the system tracking performance.

7. A commercial vehicle active rollover prevention control method based on a GA-μ optimized robust controller according to claim 6, characterized in that The specific implementation of Step 3 also includes designing a μ-synthesis controller, specifically as follows: Define the parametric uncertainty perturbation block Δ G and the input uncertainty perturbation block Δ u as the mixed uncertainty perturbation block Δ, whose diagonal matrix is as follows: Meanwhile, a virtual uncertain block Δ that tracks the reaction rollover warning index threshold and has the performance requirement of external disturbance suppression is introduced. p , and the augmented uncertain diagonal matrix is as follows: where \(C\) represents the set of complex numbers, i.e., \(\Delta\) p is an \(m\times n\) complex matrix, \(\Delta\) p The input vector parameter of is the lateral offset control error \(z\) of the zero moment point p (\(z\) p represents the performance of tracking the target and suppressing interference), the control weight function output \(z_1\) that limits the output magnitude of the control quantity, \(\Delta\) p The output vector parameter of is the compensating yaw moment \(M\) required to keep the vehicle in the critical state z , the driver's stress steering interference input \(\delta\) f , the crosswind disturbance \(F\) w , the road disturbance \(d\) r and the sensor measurement noise disturbance \(n\) s ; The input-output of the mixed uncertainty is \(w\) and \(z\), \(w\) includes the virtual uncertainty block input vector \(p\) and the modeling uncertainty perturbation block \(\Delta\) u The output of, \(z\) includes the uncertainty block output vector \(q\) and the uncertainty weighting function \(W\) u (\(s\)) The output; \(y\) is the system measurement output, \(u\) is the control input, the quantity it represents is the same as \(U\), the nominal system dynamics model is represented by \(P\); \(K\) represents the feedback controller; \(M\) represents a transfer function obtained from a lower linear fractional transformation composed of \(P\) and \(K\), let \(M = F\) l (\(P,K\)), \(F\) l represents the lower linear fractional transformation; According to the μ-synthesis theory, the necessary and sufficient condition for designing a stable controller that can make the system satisfy robust stability and performance robustness is: where μ Δ [M(jω)] represents the structured singular value, R represents the set of real numbers, s = jω, and its definition is as follows Among them, is the largest singular value of Δ. Generally speaking, μ Δ (M(s)) has a smaller value, and the system can tolerate a larger perturbation amplitude. Therefore, when using the μ-synthesis method to perform robust control on the system, the problem of maximizing the perturbation amplitude is equivalent to the problem of minimizing the SSV (Structured Singular Value). The design is completed through the D-K iteration method as follows: where D is the scaling transformation matrix, D -1 is the inverse matrix of the D matrix.

8. A commercial vehicle active rollover prevention control method based on a GA-μ optimized robust controller according to claim 7, characterized in that, The specific implementation of Step 3 also includes optimizing the controller performance weight function based on the genetic algorithm, specifically as follows: Taking the structured singular value of the closed-loop system as the cost function of the genetic algorithm; to ensure the tracking accuracy and steady-state performance of the reference signal in the low-frequency band during the whole process, avoid the system being too sensitive to low-frequency interference or model uncertainty, and at the same time ensure sufficient control force; in the high-frequency band, it can suppress the influence of high-frequency noise and unmodeled dynamics, prevent the high-frequency noise from being over-amplified and the system from becoming unstable, and improve the robustness. Therefore, the following constraint conditions are designed: Among them, K low and K high represent the low-frequency gain and high-frequency gain of the controller respectively, and W p (jω) is the performance weight function, s = jω; When selecting the first-order transfer function form, the expression of the performance weight function is: Here, ABCD represents the form parameters of the performance weight function; Therefore, the constraint conditions can be converted into the following inequalities: Taking the violation of the constraint conditions as the penalty function, set the reciprocal of the structured singular value as the fitness function of the genetic algorithm, and its expression is: where F(x) is the fitness function, λ and μ are penalty coefficients, and λ·max(0, g(x)) and μ·max(0, h(x)) are penalty values.

9. A commercial vehicle active rollover prevention control method based on a GA-μ optimized robust controller according to claim 1, characterized in that, The specific implementation of Step 4 includes: Design differential braking rules, and select the braking wheels based on the compensated yaw moment calculated by the GA-μ controller combined with the driver input signal as shown in Table 1 below: Table 1 Determination of braking wheels Braking torque distribution: Where: T LF , T LR , T RF , T RR are the braking torques allocated to the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; R is the wheel radius; F z is the force in the vertical direction received by each wheel; M z is the compensating yaw moment obtained based on the GA-μ controller; d f and d r are the wheelbases of the front wheels and rear wheels of the vehicle respectively.

10. The system of the commercial vehicle active rollover prevention control method based on the GA-μ optimized robust controller according to claim 1, characterized in that, Including the part of the roll dynamics model established in Step 1, the part of vehicle rollover warning based on the zero moment point established in Step 2, the part of the GA-μ robust controller established in Step 3, and the part of yaw moment distribution in Step 4.

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