Corner Tracking Control Method for Electro-Hydraulic Composite Steer-by-Wire System Considering Hydraulic Delay

Abstract

The present invention discloses a corner tracking control method for an electro-hydraulic composite steer-by-wire system considering hydraulic time delay, belonging to the technical field of electro-hydraulic composite steering. The steps are as follows: establishing a T-S fuzzy model based on the time-varying characteristics of the electro-hydraulic composite steer-by-wire system; reconstructing the system Tube invariant set based on the characteristic that the value ranges of the electro-hydraulic composite steer-by-wire system are different under different state variables due to time-varying time delay; calculating the current optimal control quantity of the system by combining the cost function and the self-triggered Tube MPC algorithm; the present invention improves the corner control performance of the electro-hydraulic composite steer-by-wire system with time-varying hydraulic time delay.

Description

Technical Field

[0001] The present invention belongs to the technical field of electro-hydraulic composite steering, and particularly relates to a corner tracking control method for an electro-hydraulic composite by-wire steering system considering hydraulic delay. Background Art

[0002] Commercial vehicles have become one of the main transportation methods in China due to their advantages such as convenience, economy, and diverse cargo-carrying capabilities. Compared with passenger vehicles, commercial vehicles have a greater steering resistance due to their large mass, and a by-wire steering system driven solely by an electric motor cannot provide sufficient steering power. Therefore, an electro-hydraulic composite by-wire steering system is the development trend of future commercial vehicle by-wire steering systems. The electro-hydraulic composite by-wire steering system consists of an electric mechanism and a hydraulic mechanism. Compared with the electric mechanism, the hydraulic mechanism has a large input delay, which leads to asynchronous phenomena between the electric mechanism and the hydraulic mechanism and affects the front wheel corner tracking accuracy.

[0003] The input delay of the hydraulic mechanism is mainly caused by the spool dynamic effect and the characteristics of the elastic modulus of hydraulic oil. Within the frequency response range of the solenoid valve, the spool dynamic effect causes a bounded delay disturbance. The elastic modulus of hydraulic oil changes with the change of load pressure. When the load pressure is less than 3.5 MPa, the elastic modulus of hydraulic oil will decrease significantly, resulting in an input time-varying delay in the hydraulic mechanism. The input time-varying delay has a greater impact on the electro-hydraulic composite by-wire steering system than the input constant delay, leading to the change of the corner tracking performance of the steering system with the change of working conditions.

[0004] Currently, extensive research has been carried out on the delay problem of the hydraulic mechanism, and the main methods include delay observers, delay feedback compensation control, and delay robust control. However, the current delay control strategies do not consider the time-varying delay and the relationship between delay and pressure in the electro-hydraulic composite by-wire steering system, and these methods cannot effectively improve the performance of the electro-hydraulic composite by-wire steering system. Therefore, it is of great significance to propose a corner control strategy that conforms to the delay characteristics of the electro-hydraulic composite by-wire steering system to improve the steering performance of commercial vehicles. Summary of the Invention

[0005] Aiming at the deficiencies of the above-mentioned existing technologies, the purpose of the present invention is to provide a corner tracking control method for an electro-hydraulic composite by-wire steering system considering hydraulic delay, so as to improve the corner control performance of the electro-hydraulic composite by-wire steering system with hydraulic time-varying delay.

[0006] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0007] A corner tracking control method for an electro-hydraulic composite by-wire steering system considering hydraulic delay of the present invention is as follows:

[0008] 1) Establish a T-S fuzzy model based on the time-varying characteristics of the electro-hydraulic composite steer-by-wire system;

[0009] 11) Establish a mathematical model of the electro-hydraulic composite steer-by-wire system with time-varying time-delay characteristics, including an electric mechanism, a hydraulic mechanism, a steering system transmission mechanism, and tires;

[0010] 12) Design T-S fuzzy rules based on state variables to enable the T-S fuzzy model of the electro-hydraulic composite steer-by-wire system based on the T-S fuzzy set to represent the time-varying time-delay characteristics of the electro-hydraulic composite steer-by-wire system in all states;

[0011] 13) Real-time collect the state variables of the electro-hydraulic composite steer-by-wire system based on on-vehicle sensors;

[0012] 14) Calculate and reconstruct a T-S fuzzy model of the electro-hydraulic composite steer-by-wire system that satisfies the time-varying time-delay characteristics of the current system based on the current state variables of the system and the T-S fuzzy rules;

[0013] 2) Reconstruct the system Tube invariant set based on the characteristic that the time-varying time-delay of the electro-hydraulic composite steer-by-wire system has different value ranges under different state variables;

[0014] 21) Initialize the initial Tube invariant set of the mathematical model of the electro-hydraulic composite steer-by-wire system that only contains the bounded time-delay disturbance generated by the spool dynamic effect and the hydraulic cylinder pressure is greater than 3.5 MPa;

[0015] 22) Reconstruct the Tube invariant set of the mathematical model of the current electro-hydraulic composite steer-by-wire system based on the T-S fuzzy rules and the initial Tube invariant set;

[0016] 3) Combine the cost function and the self-triggered Tube MPC algorithm to calculate the current optimal control quantity of the system;

[0017] 31) Construct a self-triggered MPC cost function of the electro-hydraulic composite steer-by-wire system with the error of the corner reference trajectory given by the tracking path planning controller and the control quantity as the objective, with the control quantity constraints composed of the upper limit of the motor current, the upper limit of the hydraulic cylinder pressure increase rate, and the upper limit of the hydraulic cylinder pressure, and with the Tube invariant set under the T-S fuzzy rules as the state constraint;

[0018] 32) Calculate the optimal control quantity and the self-triggered step size of the current electro-hydraulic composite steer-by-wire system based on the current state variables and the self-triggered MPC cost function.

[0019] Furthermore, the mathematical model of the electro-hydraulic composite steer-by-wire system with time-varying time-delay characteristics in step 11) is as follows:

[0020]

[0021]

[0022] u(t) = [i e , x v T

[0023]

[0024] C = [0 0 0 0 G2 0 0 0 0]

[0025] Among them, J lg is the moment of inertia of the steering column, B lg is the damping of the steering column, θ lg is the steering column angle, i e is the motor current, M lm is the mass of the steering nut, B lm is the damping of the steering nut, K cs is the torsional stiffness of the tooth sector, K lm is the stiffness of the steering nut, x lm is the displacement of the steering nut, J cs is the moment of inertia of the tooth sector, B cs is the moment of inertia of the tooth sector, θ cs is the angle of the tooth sector, r cs is the radius of the tooth sector, G1 is the reduction ratio of the steering motor, K e is the torque coefficient of the steering motor, x v is the solenoid valve opening, P L is the oil pressure in the hydraulic cylinder, A p is the cross-sectional area of the steering nut, C t is the leakage coefficient of the hydraulic cylinder, β e is the elastic modulus of the hydraulic oil, V t is the volume of the hydraulic cylinder, K q is the flow coefficient of the proportional valve, K c is the flow-pressure coefficient, a is the front wheelbase, b is the rear wheelbase, K f is the cornering stiffness of the front wheels, K r is the cornering stiffness of the rear wheels, M is the vehicle mass, u is the vehicle speed, G2 is the transmission ratio from the tooth sector to the wheels, I z is the moment of inertia of the vehicle body about the z-axis, β is the vehicle sideslip angle, ω r is the vehicle yaw rate, τ is the hydraulic delay coefficient, w is the equivalent delay of the spool dynamic effect, δ is the front wheel steering angle, A is the state matrix, B is the input matrix, C is the output matrix, x(t) is the state variable, u(t) is the input, y(t) is the output, x(t - τ) is the state variable with state delay;

[0026] The hydraulic delay coefficient τ is affected by the elastic modulus β of the hydraulic oil e ​Effect; when the oil pressure P in the hydraulic cylinder L is less than 3.5 MPa, the decrease of β e causes an increase in τ; when P L is greater than 3.5 MPa, the gas in the hydraulic oil is fully compressed, so that β e no longer changes and τ is small; considering the effect of τ equivalent to time-varying β e on the system state, the following formula is obtained based on Equation (1):

[0027]

[0028] where β e (t) is the equivalent elastic modulus of the hydraulic oil at time t.

[0029] Furthermore, the T-S fuzzy rules based on the state variables in step 12) are specifically as follows: The oil pressure P measured in real time by the hydraulic cylinder pressure sensor L is fuzzified as shown in Equation (2):

[0030]

[0031] where Low, Medium, High, and Stabilize represent fuzzy sets, Low represents low pressure, Medium represents medium pressure, High represents high pressure, and Stabilize represents the pressure range where the elastic modulus of the hydraulic oil does not change;

[0032] Based on the fuzzy set of Equation (2), an electro-hydraulic composite by-wire steering system T-S fuzzy model that can describe the time-varying time-delay characteristics of the hydraulic system is established, and the fuzzy inference rules are as follows:

[0033] Fuzzy rule 1: If State is Low, the mathematical model expression is as follows:

[0034]

[0035] Fuzzy rule 2: If State is Medium, the mathematical model expression is as follows:

[0036]

[0037] Fuzzy rule 3: If State is High, the mathematical model expression is as follows:

[0038]

[0039] Fuzzy rule 4: If State is Stabilize, the mathematical model expression is as follows:

[0040]

[0041] Among them, is the elastic modulus of the hydraulic oil when P L is 0.5 Mpa, is the elastic modulus of the hydraulic oil when P L is 1.75 Mpa, is the elastic modulus of the hydraulic oil when P L is 3 Mpa, is the elastic modulus of the hydraulic oil when P L is 3.5 Mpa.

[0042] Furthermore, the vehicle-mounted sensors in step 13) include but are not limited to: hydraulic cylinder pressure sensor, steering motor current sensor, steering column angle sensor, steering nut displacement sensor, tooth sector angle sensor, vehicle yaw rate sensor and center of mass sideslip angle sensor.

[0043] Furthermore, the electro-hydraulic composite steer-by-wire system T-S fuzzy model that satisfies the time-varying time-delay characteristics of the current system in step 14) is obtained through the system state collected by the current vehicle-mounted sensors and T-S fuzzy rules, and the expression is as follows:

[0044]

[0045]

[0046] Among them, α i is the weighting coefficient and Trimf() is the triangular membership function.

[0047] Furthermore, the initial Tube invariant set Z0 in step 21) is generated by the spool dynamic effect; the equivalent time delay w caused by the spool dynamic effect has bounded and random characteristics, and the equivalent time delay w is obtained by testing the actual electro-hydraulic composite steer-by-wire system; a nominal model without considering the equivalent time delay w is established as shown in Equation (3), and the electro-hydraulic composite steer-by-wire system mathematical model when P L is greater than 3.5 Mpa is selected as the nominal model:

[0048]

[0049] Among them, is the nominal state, is the nominal control quantity;

[0050] Based on the upper bound of the equivalent time delay w and Equation (3), the initial Tube invariant set Z0 and the initial control gain K0 are derived using linear matrix inequalities, as shown in Equation (4):

[0051]

[0052] Among them, W is the value range of w, which is determined by the upper bound of w.

[0053] Further, the Tube invariant set for reconstructing the mathematical model of the current electro-hydraulic composite by-wire steering system based on the T-S fuzzy rule in step 22) is specifically: by comparing the β of the actual electro-hydraulic composite by-wire steering system under different rules e and the deviation value range Ф of i , on the basis of initializing the Tube invariant set Z0, the Tube invariant set Z i is constructed by superimposing the time-varying characteristics of the system parameters under each T-S fuzzy rule, so that it satisfies Equation (5); the time-varying characteristics of the system parameters are different under different pressures, so that within different pressure ranges and the β of the actual system e have different deviations, and the deviation range can be obtained through experiments. The Tube invariant set Z i is reconstructed based on the deviation range of different pressure ranges;

[0054]

[0055] Among them, K i is the control gain calculated based on the linear matrix inequality and Z under the i-th fuzzy rule i .

[0056] Further, the steering angle reference trajectory δ ref in step 31) is calculated by the path planning controller; the upper limit i Max of the motor current, the upper limit Q Max of the pressure increase rate of the hydraulic cylinder, and the upper limit P LMax of the hydraulic cylinder pressure are determined by the design standard of the actual electro-hydraulic composite by-wire steering system; the fuzzy Tube invariant set Z Fuzzy under the T-S fuzzy rule is the Tube invariant set Z i designed for the system characteristics of the current electro-hydraulic composite by-wire steering system under each T-S fuzzy rule, which is obtained by summing through the weight coefficient α i , as shown in Equation (6); the self-triggered MPC cost function of the electro-hydraulic composite by-wire steering system is shown in Equation (7). When the prediction step size is less than or equal to H, the nominal control quantity is a constant When the prediction step size is greater than H, the nominal control quantity is a variable; the prediction step size refers to how many future moments the self-triggered MPC predicts, and H is the number of steps for the actual execution of the control quantity;

[0057]

[0058]

[0059] Among them, K his the control gain calculated based on Z Fuzzy , U is the range of the control quantity, is the cost function, and γ is the weight coefficient and is greater than or equal to 1.

[0060] Furthermore, in step 32), the control quantity and the execution step size are optimized with the goal of minimizing the self-triggered MPC cost function, as shown in Equations (8) and (9); the control quantity u(k) is executed within the next H steps according to the calculation result; when reaching H + 1, the vehicle steering system controller performs self-triggering, re-collects the system state and calculates a new optimal control quantity and self-triggered step size based on the self-triggered MPC cost function again;

[0061]

[0062]

[0063] where H max is the maximum trigger step size, represents the set composed of integers from 1 to H max , N is the prediction step size, represents solving for the control quantity u and the self-triggered step size that minimize the cost function when the prediction step size is N.

[0064] Advantages of the present invention:

[0065] Aiming at the problem that the time delay of the hydraulic mechanism in the electro-hydraulic composite by-wire steering system affects the control performance, the present invention adopts the T-S fuzzy model to solve the non-linearity of the steering system and proposes a self-triggered Tube MPC algorithm to suppress the influence of model error on the control performance and can effectively reduce the occupancy of communication resources;

[0066] 1. Formulate fuzzy rules according to the time delay characteristics of the hydraulic structure in the electro-hydraulic composite by-wire steering system, linearize the non-linear model based on fuzzy theory, and improve the calculation efficiency of the subsequent self-triggered Tube MPC;

[0067] 2. Reconstruct the Tube invariant set of the electro-hydraulic composite by-wire steering system model under different states based on the fuzzy rules, reduce the conservativeness of the controller, and improve the control accuracy;

[0068] 3. By designing the self-triggered Tube MPC to calculate the optimal control quantity and self-triggered step size with both the front wheel steering angle tracking error and the control quantity being small, not only the control accuracy is improved, but also the communication resources are effectively saved. Description of the Drawings

[0069] Figure 1 is the flow chart of the method of the present invention. Detailed Embodiment

[0070] For the convenience of understanding by those skilled in the art, the present invention will be further described below in conjunction with embodiments and the accompanying drawings. The content mentioned in the embodiments does not limit the present invention.

[0071] Refer to Figure 1 As shown, a corner tracking control method for an electro-hydraulic composite by-wire steering system considering hydraulic delay in the present invention is as follows:

[0072] 1) Establish a T-S fuzzy model based on the time-varying characteristics of the electro-hydraulic composite by-wire steering system;

[0073] 11) Establish a mathematical model of the electro-hydraulic composite by-wire steering system with time-varying delay characteristics, including an electric mechanism, a hydraulic mechanism, a steering system transmission mechanism, and a tire;

[0074] The mathematical model of the electro-hydraulic composite by-wire steering system with time-varying delay characteristics is as follows:

[0075]

[0076]

[0077] u(t) = [i e , x v T

[0078]

[0079] C = [0 0 0 0 G2 0 0 0 0]

[0080] Where, J lg is the moment of inertia of the steering column, B lg is the damping of the steering column, θ lg is the angle of the steering column, i e is the motor current, M lm is the mass of the steering nut, B lm is the damping of the steering nut, K cs is the torsional stiffness of the tooth sector, K lm is the stiffness of the steering nut, x lm is the displacement of the steering nut, J cs is the moment of inertia of the tooth sector, B cs is the moment of inertia of the tooth sector, θ cs is the angle of the tooth sector, r cs is the radius of the tooth sector, G1 is the reduction ratio of the steering motor, K e is the torque coefficient of the steering motor, x v is the solenoid valve opening, P L is the oil pressure in the hydraulic cylinder, A p is the cross-sectional area of the steering nut, C​t is the leakage coefficient of the hydraulic cylinder, β e is the elastic modulus of the hydraulic oil, V t is the volume of the hydraulic cylinder, K q is the flow coefficient of the proportional valve, K c is the flow-pressure coefficient, a is the front axle distance, b is the rear axle distance, K f is the cornering stiffness of the front wheel, K r is the cornering stiffness of the rear wheel, M is the vehicle mass, u is the vehicle speed, G2 is the transmission ratio from the gear sector to the wheel, I z is the moment of inertia of the vehicle body about the z-axis, β is the vehicle sideslip angle, ω r is the yaw rate of the vehicle, τ is the hydraulic delay coefficient, w is the equivalent delay of the spool dynamic effect, δ is the front wheel steering angle, A is the state matrix, B is the input matrix, C is the output matrix, x(t) is the state variable, u(t) is the input, y(t) is the output, and x(t - τ) is the state variable with state delay;

[0081] The hydraulic delay coefficient τ is affected by the elastic modulus β of the hydraulic oil e ; when the oil pressure P in the hydraulic cylinder L is less than 3.5 MPa, the decrease of β e causes an increase in τ; when P L is greater than 3.5 MPa, the gas in the hydraulic oil is fully compressed, so that β e no longer changes and τ is small; the influence of τ on the system state is equivalent to the time-varying β e Based on this, the following formula is obtained from Equation (1):

[0082]

[0083] where β e (t) is the equivalent elastic modulus of the hydraulic oil at time t.

[0084] 12) Design the T-S fuzzy rules based on the state variables so that the T-S fuzzy model of the electro-hydraulic composite by-wire steering system based on the T-S fuzzy set can describe the time-varying time-delay characteristics of the electro-hydraulic composite by-wire steering system under all states;

[0085] The T-S fuzzy rules based on the state variables are as follows: The oil pressure P measured in real time by the hydraulic cylinder pressure sensor L is fuzzified as shown in Equation (2):

[0086]

[0087] Among them, Low, Medium, High, and Stabilize represent fuzzy sets. Low represents low pressure, Medium represents medium pressure, High represents high pressure, and Stabilize represents the pressure range in which the elastic modulus of the hydraulic oil does not change;

[0088] Based on the fuzzy set in Equation (2), establish a T-S fuzzy model of the electro-hydraulic composite by-wire steering system that can describe the time-varying delay characteristics of the hydraulic system. The fuzzy inference rules are as follows:

[0089] Fuzzy rule 1: If State is Low, the mathematical model expression is as follows:

[0090]

[0091] Fuzzy rule 2: If State is Medium, the mathematical model expression is as follows:

[0092]

[0093] Fuzzy rule 3: If State is High, the mathematical model expression is as follows:

[0094]

[0095] Fuzzy rule 4: If State is Stabilize, the mathematical model expression is as follows:

[0096]

[0097] Among them, is the elastic modulus of the hydraulic oil when P L is 0.5 Mpa, is the elastic modulus of the hydraulic oil when P L is 1.75 Mpa, is the elastic modulus of the hydraulic oil when P L is 3 Mpa, is the elastic modulus of the hydraulic oil when P L is 3.5 Mpa.

[0098] 13) Based on on-vehicle sensors, collect the state variables of the electro-hydraulic composite by-wire steering system in real time;

[0099] The on-vehicle sensors include, but are not limited to: hydraulic cylinder pressure sensor, steering motor current sensor, steering column angle sensor, steering nut displacement sensor, tooth sector angle sensor, vehicle yaw rate sensor, and center of mass sideslip angle sensor.

[0100] 14) Based on the state variables of the current system and the T-S fuzzy rules, calculate and reconstruct a T-S fuzzy model of the electro-hydraulic composite by-wire steering system that meets the time-varying delay characteristics of the current system;

[0101] The T-S fuzzy model of the electro-hydraulic composite steer-by-wire system that meets the time-varying time-delay characteristics of the current system is obtained through the system state collected by the current vehicle-mounted sensors and the T-S fuzzy rules. The expression is as follows:

[0102]

[0103]

[0104] where, α i is the weighting coefficient and Trimf() is the triangular membership function.

[0105] 2) Reconstruct the system Tube invariant set based on the characteristics that the time-varying time-delay of the electro-hydraulic composite steer-by-wire system has different value ranges under different state variables;

[0106] 21) Initialize the initial Tube invariant set of the mathematical model of the electro-hydraulic composite steer-by-wire system that only contains the bounded time-delay disturbance generated by the spool dynamic effect and the hydraulic cylinder pressure is greater than 3.5 MPa;

[0107] Initialize the Tube invariant set Z0 generated by the spool dynamic effect; the equivalent time-delay w caused by the spool dynamic effect has the characteristics of being bounded and random, and the equivalent time-delay w is obtained by testing the actual electro-hydraulic composite steer-by-wire system; establish a nominal model without considering the equivalent time-delay w as shown in Equation (3), and select P L The mathematical model of the electro-hydraulic composite steer-by-wire system when it is greater than 3.5 Mpa is used as the nominal model:

[0108]

[0109] where, is the nominal state, is the nominal control variable;

[0110] Based on the linear matrix inequality, the upper bound of the equivalent time-delay w and Equation (3) are used to derive the initial Tube invariant set Z0 and the initial control gain K0, as shown in Equation (4):

[0111]

[0112] where, W is the value range of w, which is determined by the upper bound of w.

[0113] 22) Reconstruct the Tube invariant set of the mathematical model of the current hydraulic composite steer-by-wire system based on the T-S fuzzy rules and the initial Tube invariant set;

[0114] The Tube invariant set for reconstructing the mathematical model of the current electro-hydraulic composite by-wire steering system based on T-S fuzzy rules is as follows: By comparing the deviation value range Ф of β of the actual electro-hydraulic composite by-wire steering system under different rules e and , on the basis of initializing the Tube invariant set Z0, the Tube invariant set Z i is constructed by superimposing the time-varying characteristics of the system parameters under each T-S fuzzy rule, so that it satisfies Equation (5); the time-varying characteristics of the system parameters are different under different pressures, so that within different pressure ranges i and the β of the actual system have different deviations, and the deviation range can be obtained through experiments. The Tube invariant set Z e is reconstructed based on the deviation ranges of different pressure intervals i ;

[0115]

[0116] where K i is the control gain calculated based on the linear matrix inequality and Z i under the i-th fuzzy rule;

[0117] 3) Combine the cost function and the self-triggered Tube MPC algorithm to calculate the current optimal control quantity of the system;

[0118] 31) Construct a self-triggered MPC cost function for the electro-hydraulic composite by-wire steering system with the error of the corner reference trajectory given by the tracking path planning controller and the control quantity as the objective, the control quantity constraints composed of the upper limit of the motor current, the upper limit of the hydraulic cylinder pressure increase rate, and the upper limit of the hydraulic cylinder pressure, and the Tube invariant set under the T-S fuzzy rule as the state constraint;

[0119] The corner reference trajectory δ ref is calculated by the path planning controller; the upper limit of the motor current i Max , the upper limit of the hydraulic cylinder pressure increase rate Q Max and the upper limit of the hydraulic cylinder pressure P LMax are determined by the design standards of the actual electro-hydraulic composite by-wire steering system; the fuzzy Tube invariant set Z Fuzzy under the T-S fuzzy rule is the Tube invariant set Z i designed for the system characteristics of the current electro-hydraulic composite by-wire steering system under each T-S fuzzy rule i obtained by summing with the weight coefficient α, as shown in Equation (6); the self-triggered MPC cost function of the electro-hydraulic composite by-wire steering system is as shown in Equation (7), and when the prediction step size is less than or equal to H, the nominal control quantity is a constant When the prediction step size is greater than H, the nominal control quantity is a variable; the prediction step size refers to how many future moments the self-triggered MPC predicts, and H is the number of steps for the actual execution of the control quantity;

[0120]

[0121]

[0122] where K h is the control gain calculated based on Z Fuzzy , U is the value range of the control quantity, is the cost function, and γ is the weight coefficient and is greater than or equal to 1.

[0123] 32) Calculate the optimal control quantity and the self-triggered step size of the current electro-hydraulic composite by-wire steering system based on the current state quantity and the self-triggered MPC cost function;

[0124] Optimize the control quantity and the execution step size with the goal of minimizing the self-triggered MPC cost function, as shown in Equations (8) and (9); execute the control quantity u(k) within the next H steps according to the calculation results; when reaching H + 1, the vehicle-mounted steering system controller performs self-triggering, re-collects the system state and calculates the new optimal control quantity and the self-triggered step size again based on the self-triggered MPC cost function;

[0125]

[0126]

[0127] where H max is the maximum trigger step size, represents the set composed of integers from 1 to H max , N is the prediction step size, represents solving for the control quantity u that minimizes the cost function and the self-triggered step size when the prediction step size is N.

[0128] The specific application ways of the present invention are numerous. The above description is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements can still be made, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. An electro-hydraulic composite steer-by-wire system corner tracking control method considering hydraulic delay, characterized in that, The steps are as follows: 1) Establish a T-S fuzzy model based on the time-varying characteristics of the electro-hydraulic composite by-wire steering system; 2) Reconstruct the system Tube invariant set based on the characteristics that the time-varying time delay of the electro-hydraulic composite by-wire steering system has different value ranges under different state variables; 3) Calculate the current optimal control quantity of the system by combining the cost function and the self-triggered Tube MPC algorithm; The specific content of step 1) includes: 11) Establish a mathematical model of the electro-hydraulic composite by-wire steering system with time-varying time delay characteristics, including an electric mechanism, a hydraulic mechanism, a steering system transmission mechanism, and tires; 12) Design T-S fuzzy rules based on state variables, so that the T-S fuzzy model of the electro-hydraulic composite by-wire steering system based on the T-S fuzzy set can describe the time-varying time delay characteristics of the electro-hydraulic composite by-wire steering system in all states; 13) Real-time collect the state variables of the electro-hydraulic composite by-wire steering system based on on-vehicle sensors; 14) Calculate and reconstruct the T-S fuzzy model of the electro-hydraulic composite by-wire steering system that satisfies the time-varying time delay characteristics of the current system based on the state variables of the current system and the T-S fuzzy rules; The mathematical model of the electro-hydraulic composite by-wire steering system with time-varying time delay characteristics in step 11) is as follows: u(t) = [i e , x v T ​ Among them, J lg is the moment of inertia of the steering column, B lg is the damping of the steering column, θ lg is the steering column angle, i e is the motor current, M lm is the mass of the steering nut, B lm is the damping of the steering nut, K cs is the torsional stiffness of the tooth sector, K lm is the stiffness of the steering nut, x lm is the displacement of the steering nut, J cs is the moment of inertia of the tooth sector, B cs is the moment of inertia of the tooth sector, θ cs is the angle of the tooth sector, r cs is the radius of the tooth sector, G1 is the reduction ratio of the steering motor, K e is the torque coefficient of the steering motor, x v is the solenoid valve opening, P L is the oil pressure in the hydraulic cylinder, A p is the cross-sectional area of the steering nut, C t is the leakage coefficient of the hydraulic cylinder, β e is the elastic modulus of the hydraulic oil, V t is the volume of the hydraulic cylinder, K q is the flow coefficient of the proportional valve, K c is the flow-pressure coefficient, a is the front wheelbase, b is the rear wheelbase, K f is the cornering stiffness of the front wheels, K r is the cornering stiffness of the rear wheels, M is the vehicle mass, u is the vehicle speed, G2 is the transmission ratio from the tooth sector to the wheels, I z is the moment of inertia of the vehicle body about the z-axis, β is the vehicle sideslip angle, ω r is the vehicle yaw rate, τ is the hydraulic delay coefficient, w is the equivalent delay of the spool dynamic effect, δ is the front wheel angle, A is the state matrix, B is the input matrix, C is the output matrix, x(t) is the state variable, u(t) is the input, y(t) is the output, x(t - τ) is the state variable with state delay; The hydraulic delay coefficient τ is affected by the elastic modulus β of the hydraulic oil e ; when the oil pressure P in the hydraulic cylinder L is less than 3.5 MPa, the decrease of β e causes an increase in τ; when P L is greater than 3.5 MPa, the gas in the hydraulic oil is fully compressed, so that β e no longer changes and τ is small; by equating τ to the effect of the time-varying β e on the system state, the following equation is obtained based on Equation (1): Among them, β e (t) is the equivalent elastic modulus of hydraulic oil at time t; The T-S fuzzy rules based on state variables in step 12) are as follows: The oil pressure P measured in real time by the hydraulic cylinder pressure sensor L is subjected to the fuzzy processing as shown in Equation (2): Among them, Low, Medium, High, and Stabilize represent fuzzy sets, Low represents low pressure, Medium represents medium pressure, High represents high pressure, and Stabilize represents the pressure range where the elastic modulus of the hydraulic oil does not change; Based on the fuzzy set of formula (2), establish a T-S fuzzy model of the electro-hydraulic composite by-wire steering system that can describe the time-varying time delay characteristics of the hydraulic system. The fuzzy inference rules are as follows: Fuzzy rule 1: If State is Low, the mathematical model expression is as follows: Fuzzy rule 2: If State is Medium, the mathematical model expression is as follows: Fuzzy rule 3: If State is High, the mathematical model expression is as follows: Fuzzy rule 4: If State is Stabilize, the mathematical model expression is as follows: Among them, is the elastic modulus of the hydraulic oil when P L is 0.5 Mpa, is the elastic modulus of the hydraulic oil when P L is 1.75 Mpa, is the elastic modulus of the hydraulic oil when P L is 3 Mpa, is the elastic modulus of the hydraulic oil when P L is 3.5 Mpa.

2. The electro-hydraulic composite steer-by-wire system corner tracking control method considering hydraulic delay according to claim 1, characterized in that, The T-S fuzzy model of the electro-hydraulic composite by-wire steering system that satisfies the time-varying time delay characteristics of the current system in step 14) is obtained through the system state collected by the current on-vehicle sensor and the T-S fuzzy rules. The expression is as follows: Among them, α i is a weighting coefficient and Trimf() is a triangular membership function.

3. The corner tracking control method for the electro-hydraulic composite by-wire steering system considering hydraulic delay according to claim 2, wherein, The specific content of step 2) includes: 21) Initialize the initial Tube invariant set of the mathematical model of the electro-hydraulic composite by-wire steering system that only contains the bounded time delay disturbance generated by the spool dynamic effect and the hydraulic cylinder pressure is greater than 3.5 MPa; 22) Reconstruct the Tube invariant set of the current electro-hydraulic composite by-wire steering system mathematical model based on the T-S fuzzy rules and the initial Tube invariant set.

4. The corner tracking control method for the electro-hydraulic composite by-wire steering system considering hydraulic delay according to claim 3, wherein, In the above step 21), the initial Tube invariant set Z0 is generated by the spool dynamic effect; the equivalent time delay w caused by the spool dynamic effect has the characteristics of being bounded and random, and the equivalent time delay w is obtained by testing the actual electro-hydraulic composite steer-by-wire system; a nominal model without considering the equivalent time delay w is established as shown in Equation (3), and P L The mathematical model of the electro-hydraulic composite steer-by-wire system when it is greater than 3.5 Mpa is used as the nominal model: Among them, is the nominal state, is the nominal control quantity; Use linear matrix inequalities to derive the initial Tube invariant set Z0 and the initial control gain K0 based on the upper bound of the equivalent time delay w and formula (3), as shown in formula (4): Among them, W is the value range of w, which is determined by the upper bound of w.

5. The corner tracking control method for the electro-hydraulic composite by-wire steering system considering hydraulic delay according to claim 4, wherein, The Tube invariant set for reconstructing the mathematical model of the current electro-hydraulic composite steer-by-wire system based on the T-S fuzzy rule in step 22) is specifically as follows: By comparing the deviation value range Ф of β of the actual electro-hydraulic composite steer-by-wire system under different rules e and in the initialized Tube invariant set Z0, the system parameter time-varying characteristics under each T-S fuzzy rule are superimposed to construct the Tube invariant set Z i such that it satisfies equation (5); the system parameter time-varying characteristics are different under different pressures, so that in different pressure ranges i there are different deviations between and the β of the actual system , and the deviation range can be obtained through experiments. The Tube invariant set Z e is reconstructed based on the deviation ranges of different pressure ranges i ; Among them, K i is the control gain calculated based on the linear matrix inequality and Z under the i-th fuzzy rule i ​ 6. The corner tracking control method for the electro-hydraulic composite by-wire steering system considering hydraulic delay according to claim 5, wherein, The specific content of step 3) includes: 31) Construct a self-triggered MPC cost function for the electro-hydraulic composite by-wire steering system with the error of the corner reference trajectory and the control quantity given by the tracking path planning controller as the objective, the control quantity constraints composed of the upper limit of the motor current, the upper limit of the hydraulic cylinder pressure increase rate, and the upper limit of the hydraulic cylinder pressure, and the Tube invariant set under the T-S fuzzy rule as the state constraint; 32) Calculate the optimal control quantity and the self-triggered step size of the current electro-hydraulic composite by-wire steering system based on the current state quantity and the self-triggered MPC cost function.

7. The corner tracking control method for the electro-hydraulic composite by-wire steering system considering hydraulic delay according to claim 6, wherein, The corner reference trajectory δ in step 31) ref is calculated by the path planning controller; the upper limit of the motor current i Max , the upper limit of the pressure increase rate of the hydraulic cylinder Q Max and the upper limit of the hydraulic cylinder pressure P LMax are determined by the design standards of the actual electro-hydraulic composite by-wire steering system; the fuzzy Tube invariant set Z under the T-S fuzzy rules Fuzzy is the Tube invariant set Z designed for the system characteristics of the current electro-hydraulic composite by-wire steering system under each T-S fuzzy rule i and is obtained by summing with the weight coefficient α i as shown in Equation (6); the self-triggered MPC cost function of the electro-hydraulic composite by-wire steering system is as shown in Equation (7). When the prediction step size is less than or equal to H, the nominal control quantity is a constant When the prediction step size is greater than H, the nominal control quantity is a variable; the prediction step size refers to how many future moments the self-triggered MPC predicts, and H is the number of steps for the actual execution of the control quantity; Among them, K h is the control gain calculated based on Z Fuzzy , U is the value range of the control quantity, is the cost function, and γ is the weight coefficient and is greater than or equal to 1; In step 32), the control quantity and the execution step size are optimized with the minimum of the self-triggered MPC cost function as the objective, as shown in equations (8) and (9); the control quantity u(k) is executed within the next H steps according to the calculation results; when reaching H + 1, the vehicle-mounted steering system controller performs self-triggering, re-collects the system state, and calculates the new optimal control quantity and the self-triggered step size again based on the self-triggered MPC cost function; Among them, H max is the maximum triggering step size, represents the set composed of integers from 1 to H max , N is the prediction step size, represents solving for the control variable u that minimizes the cost function and the self-triggering step size when the prediction step size is N.

Images