All-wheel-drive system state feedback and interference suppression method based on integral transformation

Abstract

The invention discloses an all-wheel-drive system state feedback and interference suppression method based on integral transformation, and the method comprises the steps: firstly converting a complex nonlinear all-wheel-drive system model into a simpler state space model through employing an integral transformation method, and reducing the coupling degree of the system; then, an observer based on a filtering transfer function is designed, interference and uncertain items in the system are effectively estimated, the identification capability and the suppression effect on the interference are improved, and the influence of external interference on the performance of the system is reduced. And finally, interference information estimated by the observer is used for feeding back and adjusting system input in real time, a full-state feedback controller is designed, and it is ensured that the system can still keep stable under the condition that interference and uncertainty exist. By introducing a new state conversion technology, simplifying a system structure and combining a filtering transfer function, accurate estimation of interference and uncertain items in the system is realized, so that the control precision and stability of the system are improved, and solid technical support is provided for nonlinear system control.

Description

Technical Field

[0001] The present invention belongs to the field of nonlinear system control, and relates to a state feedback and interference suppression method of an all-wheel drive system, and specifically to a state feedback and interference suppression method of an all-wheel drive system based on integral transformation. Background Art

[0002] All-wheel drive systems are widely used in fields such as automation control, robotics, and aerospace, and their control accuracy and stability are critical to system performance. In these systems, the complexity of controller design is often affected by the dynamic characteristics of the system and external disturbances. In order to address these challenges, researchers and engineers are constantly exploring improved control strategies and methods. Traditional control methods often have difficulty providing sufficient control accuracy when faced with complex system models, especially in the presence of disturbances and uncertainties. For this reason, integral transform, as a mathematical tool, is widely used to simplify system models and improve the convenience of controller design. Through integral transform, complex nonlinear systems can be transformed into a more tractable form, thereby effectively designing control strategies.

[0003] However, there is still a lack of systematic methods in the prior art for all-wheel drive systems to combine integral transformation with state feedback and disturbance suppression techniques. Especially when dealing with disturbances and uncertainties in the system, how to effectively use state feedback control to enhance the robustness of the system is still a problem worthy of further study. Summary of the invention

[0004] In order to overcome the limitations of traditional methods, solve the control problems caused by interference, uncertainty and complex system models in the full-drive system, and provide reliable support for the control of nonlinear systems and the advancement of science and technology, the present invention provides a full-drive system state feedback and interference suppression method based on integral transformation. This method introduces new state conversion technology, simplifies the system structure, and combines the filter transfer function to achieve accurate estimation of interference and uncertainty in the system, thereby improving the control accuracy and stability of the system, and providing solid technical support for nonlinear system control.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A method for state feedback and interference suppression of an all-wheel drive system based on integral transformation comprises the following steps:

[0007] Step 1: Use the integral transformation method to transform the state variables of the nonlinear system and establish a nonlinear dynamic model of the all-wheel drive system. The specific steps are as follows:

[0008] Step 1: Consider the nonlinear system control problem with mismatched interference, and use the integral transformation method to transform the original all-wheel drive system variable xi ,d i Mapped into a new state ζ i and interference Δ i , which is transformed as follows:

[0009]

[0010] Among them, x i , i=1,…,n is the state of the original system; d i , i=1,…,n is the external interference of the original system; ζ i ,Δ i are the transformed state variables and disturbances; n is the order of the system;

[0011] Step 12: Based on the transformation in step 11, the following nonlinear dynamic model of the all-wheel drive system is obtained:

[0012]

[0013] Among them, u is the control input of the all-wheel drive system;

[0014] Step 2: After the state conversion, the new state variables are successively differentiated to derive the high-order dynamic equation of the all-wheel drive system. The specific steps are as follows:

[0015] Step 21: Considering the integral transformation in step 1, there exists an inverse function such that In order to simplify the structure of the all-wheel drive system, the following system model is further derived:

[0016]

[0017] in

[0018] Step 22: Through By taking derivatives in sequence, we get the high-order all-wheel drive system equation as follows:

[0019]

[0020] Step 3: Design a disturbance observer based on the filter transfer function for the disturbance and uncertainty in the all-wheel drive system. The specific steps are as follows:

[0021] Step 31: To estimate the lumped disturbance θ of the high-order full-drive system obtained in step 2 i ,i=2,…,n,,define θ i (s), is θ i (t), The Laplace transform of To estimate the uncertainty, consider the following filter transfer function:

[0022]

[0023] where τ i,j >0,j=1,…,n,π i,j >0,j=1,…,i-1 are the parameters of the filter. When θ i (t) is used as the input of the filter. As the output of this filter, we get:

[0024]

[0025] Step 32: Based on the filter structure in step 31, design an observer structure based on the filter transfer function:

[0026]

[0027] Among them, i is the state of the system, ξ i (t), y i (t),χ i (t) is an auxiliary variable, parameter α i,j ,β i,j Satisfy the following properties:

[0028]

[0029] Step 33: For the lumped disturbance θ1 of the high-order full-drive system obtained in step 2, a disturbance observer is constructed to estimate θ1 by combining the filter and observer structures of step 31 and step 32. The expression of the disturbance observer is:

[0030]

[0031] Where ζ1 is the state of the system, ξ1(t) is an auxiliary variable, is the estimated information of disturbance;

[0032] Step 4: Use the disturbance and uncertainty information estimated by the observer to design a full-state feedback controller. The specific form of the full-state feedback controller is:

[0033]

[0034] in is the estimated information of the disturbance, ζ1 is the state of the system, k i ,i=0,...,n-1 is the feedback gain coefficient;

[0035] Step 5: Combine the full-state feedback controller with the disturbance observer to form a closed-loop control structure of the system. In this closed-loop system, the disturbance observer estimates the disturbance in real time and feeds it back to the full-state controller. The full-state controller adjusts the input of the all-wheel drive system through feedback to achieve stable control of the all-wheel drive system.

[0036] Compared with the prior art, the present invention has the following advantages:

[0037] 1. Through the introduction of a new state space mapping method and a filter observer, the present invention not only simplifies the system model, but also effectively improves the estimation accuracy of interference and uncertainty, thereby optimizing the control performance and stability of the system. This method helps to overcome the shortcomings of traditional control methods, meet the needs of high-stability control, and provide a new solution for high-precision control of nonlinear systems.

[0038] 2. The present invention is not only innovative in theory, but also exhibits superior control performance in practical applications. It is particularly suitable for complex nonlinear systems that require precise control and strong anti-interference capabilities, such as unmanned vehicles, satellite attitude control, high-precision automation equipment, robotics, aerospace and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is the structural block diagram of the closed-loop control system;

[0040] Figure 2 is the response curve of state x1(t);

[0041] Figure 3 is the response curve of state x2(t);

[0042] Figure 4 is the estimated curve of the disturbance θ1(t);

[0043] Figure 5 For disturbance The estimated curve of

[0044] Figure 6 is the estimated curve of disturbance θ2(t);

[0045] Figure 7 is the response curve of the transformed all-wheel drive system state ζ1(t);

[0046] Figure 8 is the response curve of the transformed all-wheel drive system state ζ2(t);

[0047] Fig. 9 is the control input curve of the system. DETAILED DESCRIPTION

[0048] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0049] The present invention provides a state feedback and interference suppression method for an all-wheel drive system based on integral transformation. The method aims at the control problem of a nonlinear system with mismatched interference. First, the complex nonlinear all-wheel drive system model is converted into a simpler state space model by adopting the integral transformation method to reduce the coupling degree of the system. Then, an observer based on a filter transfer function is designed to effectively estimate the interference and uncertainty in the system, improve the recognition ability and suppression effect of the interference, and reduce the impact of external interference on the system performance. Finally, the interference information estimated by the observer is used to adjust the system input in real time, and a full-state feedback controller is designed to ensure that the system can remain stable in the presence of interference and uncertainty.

[0050] The specific steps are as follows:

[0051] Step 1: Use the integral transformation method to transform the state variables of the nonlinear system and establish a nonlinear dynamic model of the all-wheel drive system. Through integral transformation, the complex nonlinear system model is transformed into a more concise form, thereby simplifying the system description and controller design process. The specific steps are as follows:

[0052] Step 1: Consider the nonlinear system control problem with mismatched interference, and use the integral transformation method to transform the original all-wheel drive system variable x i ,d i Mapped into a new state ζ i and interference Δ i , which is transformed as follows:

[0053]

[0054] Among them, x i , i=1,…,n is the state of the original system; d i , i=1,…,n is the external interference of the original system; ζ i ,Δ i are the transformed state variables and disturbances; n is the order of the system.

[0055] Step 12: Based on the transformation in step 11, the following nonlinear dynamic model of the all-wheel drive system is obtained:

[0056]

[0057] Among them, u is the control input of the all-wheel drive system.

[0058] Step 2: After the state conversion, the new state variables are successively differentiated to derive the high-order dynamic equation of the all-wheel drive system. This high-order equation can more accurately describe the dynamic behavior of the all-wheel drive system, especially when dealing with high-order dynamic characteristics, which can improve the accuracy and applicability of system modeling, thereby better coping with complex control tasks. The specific steps are as follows:

[0059] Step 21: Considering the integral transformation in step 1, we know that there is an inverse function such that In order to simplify the structure of the all-wheel drive system, the following system model is further derived:

[0060]

[0061] in

[0062] Step 22: Through By taking derivatives in sequence, we get the high-order all-wheel drive system equation as follows:

[0063]

[0064] Step 3: Design a disturbance observer based on the filter transfer function to address the disturbance and uncertainty in the all-wheel drive system. The observer monitors the system output signal in real time and combines the filter transfer function to estimate the disturbance and uncertainty in the system, thereby improving the ability to identify system disturbances and the effect of interference suppression. The specific steps are as follows:

[0065] Step 31: To estimate the lumped disturbance θ of the high-order full-drive system obtained in step 2 i ,i=2,…,n,,define θ i (s), is θ i (t), The Laplace transform of is an estimate of the uncertainty. Consider the following filter transfer function:

[0066]

[0067] where τ i,j >0,j=1,…,n,π i,j >0,j=1,…,i-1 are the parameters of the filter. i (t) is used as the input of the filter. As the output of this filter, we have:

[0068]

[0069] Step 32: According to the filter structure in step 31, design an observer structure based on the filter transfer function. The observer can dynamically adjust the estimated value of the disturbance by utilizing the feedback of auxiliary variables and system state, thereby maintaining stability and accuracy in complex systems. The specific observer design is:

[0070]

[0071] Among them, i is the state of the system, ξ i (t), y i (t),χ i (t) is an auxiliary variable, parameter α i,j ,β i,j Satisfies the following properties

[0072]

[0073] Step 33: For the lumped disturbance θ1 of the high-order full-drive system obtained in step 2, a specific disturbance observer is constructed to estimate θ1 by combining the filter and observer structures of steps 31 and 32. Its expression is:

[0074]

[0075] Where ζ1 is the state of the system, ξ1(t) is an auxiliary variable, is the estimated information of the disturbance.

[0076] Step 4: Design a full state feedback controller using the disturbance and uncertainty information estimated by the disturbance observer. The specific form of the state feedback controller is:

[0077]

[0078] in is the estimated information of the disturbance, ζ1 is the state of the system, and the selected feedback gain coefficient k i , i = 0, ..., n-1, so that the polynomial s n +k n-1 s (n-1) +…+k1s+k0 is the Hurwitz polynomial.

[0079] Step 5: Combine the full-state feedback controller with the disturbance observer to form a closed-loop control structure of the system. In this closed-loop system, the disturbance observer estimates the disturbance in real time and feeds it back to the full-state controller, which adjusts the input of the all-wheel drive system through feedback to achieve stable control of the all-wheel drive system. This closed-loop control system can ensure the stability and high-precision dynamic performance of the all-wheel drive system in the presence of disturbances and uncertainties.

[0080] Example:

[0081] For a high-order nonlinear system with mismatched disturbances, consider the following model:

[0082]

[0083] Among them, x i ∈R, i=1,…,n is the state of the system; d i ∈R, i=1,…,n is the external disturbance of the system; u is the control input of the system; f i (x i ), i=1,…,n is a smooth nonlinear function and satisfies the following assumptions: Assumption 1: For any x i ∈R,i=1,…,n, nonlinear function satisfies f i (x i )≠0,i=1,…,n.

[0084] In order to design the state feedback control law u, the state x of the system i ,i=1,…,n is stable. First, according to Assumption 1, we can know that the following formula holds:

[0085]

[0086] make

[0087]

[0088] The original system equation (1) can be written as:

[0089]

[0090] By observation, it can be found that when the state of the original system x i ,i=1,…,n converges to 0, the auxiliary variables are also equal to 0. Therefore, we can use the auxiliary variable ζ i ,i=1,…,n design control law. System (2) has a simpler structure than the original system (1), which has significant advantages in designing controller.

[0091] Since the intermediate variable ζ i ,i=1,…,n are x i ,i=1,…,n, that is, ζ i =z i (x i ). i (·) represents the transition from state x i Mapping to ζ i At the same time, we know that there is an inverse function such that Furthermore, it can be concluded that:

[0092]

[0093] in right Taking the derivatives in sequence, we get:

[0094]

[0095] For disturbances and uncertainties in the all-wheel drive system (3) i , an observer based on filter transfer function is designed to compensate for the impact on the system. The observer monitors the system output signal in real time and combines the filtering algorithm to estimate the interference and uncertainty in the system, thereby improving the ability to identify system interference and the interference suppression effect. First, in order to estimate the lumped disturbance θ in the high-order all-wheel drive system i ,i=2,…,n, the transfer function of the designed filter is:

[0096]

[0097] where τ i,j >0,j=1,…,n,π i,j >0,j=1,…,i-1. Define θ i (s), is θ i (t), The Laplace transform of is the estimate of the uncertain term. i (t) is used as the input of the filter. As the output of this filter, we have:

[0098]

[0099] This transfer function-based filter design method makes the disturbance estimation more flexible, and different filter parameters can be selected according to different system requirements to balance response speed and robustness. Then, through the inverse Laplace transform, it can be deduced:

[0100]

[0101] The parameter α i,j ,β i,j Satisfy the following properties:

[0102]

[0103] To obtain the observer, auxiliary variables are defined as:

[0104]

[0105] where ξ i ,L i is the variable to be determined. Substituting the above auxiliary variables into the equation, we can get:

[0106]

[0107] Considering zero initial conditions, integrating both sides of the equation gives:

[0108]

[0109] Comparing both sides of the equation we can get:

[0110]

[0111] Therefore, the uncertainty term θ can be deduced i ,i=2,…,n,the observer is:

[0112]

[0113] In order to verify that the proposed observer (6) can effectively estimate the uncertainty, the Lyapunov stability theorem is used to prove that the observation error can converge to a bounded region. According to observer (6), we can get:

[0114]

[0115] According to the definition of variables (5), the observation error is In order to facilitate analysis, Then the equation can be written in the following compact form:

[0116]

[0117] in

[0118]

[0119] For uncertain terms in the system, there is an upper bound satisfy:

[0120]

[0121] Furthermore, consider the following Lyapunov function:

[0122]

[0123] Where P i is a positive definite matrix. Taking its derivative, we get:

[0124]

[0125] Because A i is a Hurwitz matrix, and its eigenvalues ​​are You can know Established, that is:

[0126]

[0127] when hour, is a negative number, the observation error will converge to Therefore, it can be concluded that the designed observer based on the filter transfer function can ensure the observation error Converges to a bounded region. For the uncertain term θ1(t) in system (3), similarly, the following observer is constructed:

[0128]

[0129] The full-state feedback controller is designed by using the disturbance and uncertainty information estimated by the observer. The full-state feedback controller ensures the stability and performance optimization of the system through feedback adjustment of the system state, and enhances the system's anti-interference ability and control accuracy. The state feedback controller is:

[0130]

[0131] Among them, the selected feedback gain coefficient k i , i = 0, ..., n-1, so that the polynomial s n +k n-1 s (n-1) +…+k1s+k0 is the Hurwitz polynomial.

[0132] The structural block diagram of the entire closed-loop control system is as follows: Figure 1 shown.

[0133] To simulate a nonlinear system, consider the following form:

[0134]

[0135] External interference: d1 = 0.01sin (0.12t), d2 = 0.0.1cos (0.12t) + 0.1e -t .

[0136] Simulation experiments were carried out based on the proposed modal observers (6), (7) and control law (8). The simulation results are shown in Figures 2 to 9 As shown. Figure 2 and Figure 3It can be clearly seen that in the presence of interference, the system states x1(t) and x2(t) can quickly converge to 0, showing good convergence characteristics. Figure 4 and Figure 5 are the disturbance θ1 and its derivative respectively The observer can effectively estimate the disturbance and provide accurate feedback. Figure 6 is the estimated curve of the disturbance θ2, which further verifies the observer's ability to accurately estimate the disturbance in the system. Figure 7 and Figure 8 The response curves of the transformed all-wheel drive system states ζ1 and ζ2 are shown, indicating that the control system designed by the present invention can still maintain stable dynamic performance in the face of interference and uncertainty. Fig. 9 is the control input curve of the system, which reflects the smooth control of the controller on the system input signal under the feedback of the observer. Figures 2 to 9 The simulation results show that the observer based on filter transfer function and full-state feedback controller proposed in the present invention can effectively realize stable control of the system under complex interference environment, improve the control accuracy and dynamic response speed of the system, and verify the effectiveness of the method proposed in the present invention in improving system stability and control accuracy.

Claims

1. A method for state feedback and interference suppression of an all-wheel drive system based on integral transformation, characterized in that The method comprises the following steps: Step 1: Use the integral transformation method to transform the state variables of the nonlinear system and establish a nonlinear dynamic model of the all-wheel drive system. The specific steps are as follows: Step 1: Consider the nonlinear system control problem with mismatched interference, and use the integral transformation method to transform the original all-wheel drive system variable x i ,d i Mapped into a new state ζ i and interference Δ i , which is transformed as follows: Among them, x i , i=1,…,n is the state of the original system; d i , i=1,…,n is the external interference of the original system; ζ i ,Δ i are the transformed state variables and disturbances; n is the order of the system; Step 12: Based on the transformation in step 11, the following nonlinear dynamic model of the all-wheel drive system is obtained: Among them, u is the control input of the all-wheel drive system; Step 2: After the state conversion, the new state variables are successively differentiated to derive the high-order dynamic equation of the all-wheel drive system. The specific steps are as follows: Step 21: Considering the integral transformation in step 1, there exists an inverse function such that In order to simplify the structure of the all-wheel drive system, the following system model is further derived: among them i=1,…,n-1,θ n =D n ; Step 22: Through By taking derivatives in sequence, we get the high-order all-wheel drive system equation as follows: Step 3: Design a disturbance observer based on the filter transfer function for the disturbance and uncertainty in the all-wheel drive system. The specific steps are as follows: Step 31: To estimate the lumped disturbance θ of the high-order full-drive system obtained in step 2 i ,i=2,…,n,,Definition for The Laplace transform of To estimate the uncertainty, consider the following filter transfer function: where τ i,j >0,j=1,…,n,π i,j >0,j=1,…,i-1 are the parameters of the filter. When θ i (t) is used as the input of the filter. As the output of this filter, we get: Step 32: Based on the filter structure in step 31, design an observer structure based on the filter transfer function: Among them, i is the state of the system, ξ i (t), y i (t),χ i (t) is an auxiliary variable, α i,j ,β i,j is the parameter; Step 33: For the lumped disturbance θ1 of the high-order full-drive system obtained in step 2, a disturbance observer is constructed to estimate θ1 by combining the filter and observer structures of step 31 and step 32. The expression of the disturbance observer is: Where ζ1 is the state of the system, ξ1(t) is an auxiliary variable, is the estimated information of disturbance; Step 4: Design a full state feedback controller using the disturbance and uncertainty information estimated by the observer: in is the estimated information of the disturbance, ζ1 is the state of the system, k i ,i=0,...,n-1 is the feedback gain coefficient; Step 5: Combine the full-state feedback controller with the disturbance observer to form a closed-loop control structure of the system. In this closed-loop system, the disturbance observer estimates the disturbance in real time and feeds it back to the full-state controller. The full-state controller adjusts the input of the all-wheel drive system through feedback to achieve stable control of the all-wheel drive system.

2. The method for state feedback and interference suppression of an all-wheel drive system based on integral transformation according to claim 1, characterized in that In step 32, parameter α i,j ,β i,j Satisfy the following properties:

3. The method for state feedback and interference suppression of an all-wheel drive system based on integral transformation according to claim 1, characterized in that In step 4, the feedback gain coefficient k i So that the polynomial s n +k n-1 s (n-1) +…+k1s+k0 is the Hurwitz polynomial.

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