Non-linear servo system anti-interference control method based on state filtering

Abstract

The invention discloses a nonlinear servo system anti-interference control method based on state filtering. The method comprises the following steps: establishing a mathematical model of a nonlinear servo system; constructing a filter to respectively filter the system state and the virtual control law; designing a nonlinear servo system anti-interference control algorithm based on state filtering; controller design parameters are selected, convergence and stability of all signals in a closed-loop system are achieved, and meanwhile output of the system accurately tracks a control target of an expected instruction. According to the method, matched and non-matched internal source and external source disturbances can be processed at the same time, smooth and non-smooth internal source and external source disturbances can be processed at the same time, the influence of differential explosion in the design process of a high-order nonlinear servo system controller is avoided, the influence of state filtering errors and virtual control law filtering errors is eliminated, and the design accuracy of the high-order nonlinear servo system controller is improved. And the structure is simple, implementation is easy, and large-scale application in the industry and engineering is facilitated.

Description

Technical Field

[0001] The present invention relates to the technical field of servo control of nonlinear systems, and particularly to a disturbance rejection control method for a nonlinear servo system based on state filtering. Background Art

[0002] Nonlinear servo systems such as electro-hydraulic servo systems and motor servo systems are widely used in high-performance servo applications in the industrial control field with high control accuracy and fast response speed. However, in high-performance application scenarios, nonlinear servo systems are not only affected by endogenous disturbances related to the system state, but also affected by exogenous disturbances such as external interference. These disturbances will not only reduce the servo tracking performance of the system, but may even cause the entire closed-loop system to become unstable. How to overcome the disturbances existing in the system is of great significance for improving the servo tracking performance of the system.

[0003] Existing disturbance rejection control strategies for nonlinear servo systems mainly include methods such as adaptive robust control, control based on disturbance observers, and intelligent control based on artificial neural networks. Among them, the core idea of adaptive robust control is to estimate the constant unknown parameters in the system through direct adaptive control and suppress other uncertain non-linearities through deterministic robust control. However, this method requires the upper bound information of the uncertain non-linearity, and the uncertain non-linearity has the characteristics of strong randomness. It is difficult to obtain its upper bound in practical applications, and as the uncertain non-linearity increases, it may lead to excessive feedback gain, thus causing high-gain feedback phenomena. The core idea of the control method based on disturbance observers lies in estimating the disturbance by designing disturbance observers, including non-linear disturbance observers, high-gain disturbance observers, sliding mode disturbance observers, and extended state observers, and then using these estimated values for feedforward compensation of the disturbance when designing the controller. However, this method requires the disturbance to be continuously differentiable when estimating the disturbance, so it is difficult to effectively handle non-smooth disturbances. The core idea of intelligent control based on artificial neural networks is to online approximate the endogenous disturbances related to the system state existing in the system through artificial neural networks such as neural networks and fuzzy logic, and then use these approximated values for feedforward compensation of such disturbances when designing the controller. However, the approximation process of artificial neural networks often requires a large amount of computing power, which puts forward high requirements for the computing performance of the controller hardware. At the same time, a pure artificial neural network is difficult to handle the exogenous disturbances existing in the system, and combining other methods to handle such disturbances will further increase the complexity of the controller, making it difficult to be practical.

[0004] Therefore, the existing disturbance rejection control methods for nonlinear servo systems mainly have the following deficiencies:

[0005] (1) It is necessary to know the upper bound information of uncertain nonlinearity with randomness characteristics, which may lead to the phenomenon of high-gain feedback;

[0006] (2) It is necessary to have continuous and differentiable disturbances, making it difficult to effectively handle non-smooth disturbances;

[0007] (3) The controller structure is complex and requires a controller hardware with relatively high matching operation performance. Summary of the Invention

[0008] The purpose of the present invention is to provide a high-performance disturbance rejection control method that can simultaneously handle matching and non-matching types of internal and external disturbances, smooth and non-smooth internal and external disturbances, with a simple structure and easy to implement.

[0009] The technical solution to achieve the purpose of the present invention is: a disturbance rejection control method for a nonlinear servo system based on state filtering, including the following steps:

[0010] Step 1: Establish the mathematical model of the nonlinear servo system;

[0011] Step 2: Construct filters to filter the system state and virtual control law respectively;

[0012] Step 3: Design a disturbance rejection control algorithm for the nonlinear servo system based on state filtering;

[0013] Step 4: Select the controller design parameters to achieve the convergence and stability of all signals in the closed-loop system, and at the same time make the output of the system accurately track the control target of the desired instruction.

[0014] Furthermore, the establishment of the mathematical model of the nonlinear servo system in Step 1 is specifically as follows:

[0015] Define the state vector x = [x1, x2,..., x n T , where n is the order of the system, and the subscript i in the variable · i takes values of 1, 2,..., n; x1, x2,..., x n are the elements in the vector, then the state space form of the nonlinear servo system model is:

[0016]

[0017]

[0018] y o = x1

[0019] In the formula, the subscript r in the variable · r takes values of 1, 2,..., n - 1, u is the control input of the system, y o ​is the control output of the system, is related to the system state and the integrated disturbance related to time t;

[0020] Assumption 1: The command trajectory y1 that the system is expected to track is twice continuously differentiable;

[0021] Assumption 2: The first derivative of the system state is bounded.

[0022] Furthermore, for the filter constructed in Step 2, filter the system state x i and the virtual control law α r specifically as follows:

[0023] For the system state x i and the virtual control law α r , construct a first-order filter:

[0024]

[0025]

[0026] In the formula, the subscript r of the variable · r takes values of 1, 2,..., n - 1; x if represents the filtered value of the system state x i , α rf represents the filtered value of the virtual control law α r , w xi is an adjustable positive parameter, w αr is an adjustable positive parameter.

[0027] 4 Furthermore, for the filter constructed in Step 2, specifically construct a second-order filter:

[0028]

[0029]

[0030] In the formula, ω xi is an adjustable positive parameter in the second-order filter, ω αr is an adjustable positive parameter in the second-order filter.

[0031] Furthermore, for the design of the nonlinear servo system disturbance rejection control algorithm based on state filtering in Step 3, specifically as follows:

[0032] Step 3.1. Define e i as the control error of the system, where e1 is the tracking error of the system. At the same time, define z i as the control error e i of the system and the auxiliary variable εi For the difference, then:

[0033] e1 = x1 - y1, e r+1 = x r+1 - α rf

[0034] z1 = e1 - ε1, z r+1 = e r+1 - ε r+1

[0035] In the formula, the auxiliary variable ε i is generated by the following auxiliary system:

[0036]

[0037]

[0038] In the formula, k1, k2,..., k n are adjustable positive feedback gains;

[0039] The role of the auxiliary system is to eliminate the state filtering error and the virtual control law filtering error; due to the existence of unmeasurable signals in the auxiliary system, ε is calculated by integrating both sides of the auxiliary system simultaneously i :

[0040]

[0041]

[0042] Step 3.2, design the virtual control law α1 as:

[0043]

[0044] In the formula, represents the computable part in, and its specific expression is:

[0045]

[0046] Step 3.3, design the virtual control law α l as:

[0047]

[0048] In the formula, the subscript l of the variable · l takes values 2, 3,..., n - 1; represents the computable part in, and the specific expression is:

[0049]

[0050] Step 3.4. Design the control input u of the system as follows:

[0051]

[0052] In the formula, represents the computable part in, and the specific expression is:

[0053]

[0054] Furthermore, the selection of the controller design parameters described in Step 4 is as follows:

[0055] Select the parameters w xi > 0, w αr > 0 and adjust the feedback gains k1 > 0, k l > 0, k n > 0, such that the gain k ε1 = k1 – 1 / (2w x1 ), the gain k εl = k l – 1 / (2w xl ), the gain k εn = k n – 1 / (2w xn ), the gain and the gain are all positive numbers, then the designed disturbance rejection controller based on state filtering can ensure that all signals in the entire closed-loop system converge and remain stable..

[0056] Compared with the prior art, the present invention has the following remarkable advantages: (1) By introducing the filtered value of the state, it can simultaneously handle the matching and non-matching types of internal and external disturbances without the need to know the upper bound of the disturbance. When using a first-order filter, it can simultaneously handle the smooth and non-smooth types of internal and external disturbances; (2) By introducing the filtered value of the virtual control law, it avoids the influence of "differential explosion" in the design process of the high-order nonlinear servo system controller; (3) By introducing an auxiliary system, it eliminates the influence of the state filtering error and the virtual control law filtering error in the controller; (4) It has a simple structure, is easy to implement, and is convenient for large-scale applications in industry and engineering. Brief Description of the Drawings

[0057] Figure 1 is a schematic flow chart of a disturbance rejection control method for a nonlinear servo system based on state filtering according to the present invention.

[0058] Figure 2 is a schematic structural diagram of a single-rod electro-hydraulic servo system in an embodiment of the present invention.

[0059] Figure 3 It is a curve graph showing the variation of the tracking error of the system adopting the method of the present invention and the comparative method with time in the embodiment of the present invention.

[0060] Figure 4 It is a curve graph showing the variation of the estimation performance of the system state x2 with time in the embodiment of the present invention.

[0061] Figure 5 It is a curve graph showing the variation of the estimation performance of the system state x3 with time in the embodiment of the present invention.

[0062] Figure 6 It is a curve graph showing the variation of the control input voltage with time in the embodiment of the present invention. Detailed implementation manners

[0063] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0064] In conjunction with Figure 1 , the present invention discloses a disturbance rejection control method for a nonlinear servo system based on state filtering, which includes the following steps:

[0065] Step 1: Establish a mathematical model of the nonlinear servo system;

[0066] Step 2: Construct filters to filter the system state and the virtual control law respectively;

[0067] Step 3: Design a disturbance rejection control algorithm for the nonlinear servo system based on state filtering;

[0068] Step 4: Select the controller design parameters to achieve the convergence and stability of all signals in the closed-loop system, and at the same time make the output of the system accurately track the control target of the desired instruction.

[0069] As a specific example, the establishment of the mathematical model of the nonlinear servo system in Step 1 is as follows:

[0070] Set n as the order of the system, and the subscript i in the variable · i takes values of 1, 2,..., n, and the subscript r in the variable · r takes values of 1, 2,..., n - 1, and the subscript l in the variable · l takes values of 2, 3,..., n - 1.

[0071] Step 1: Establish a mathematical model of the nonlinear servo system, which is as follows:

[0072] Define the state vector x = [x1, x2,..., x n T , where n is the order of the system, and x1, x2,..., x n ​If it is an element in the vector, the state - space form of the non - linear servo system model is as follows:

[0073]

[0074] where u is the control input of the system, and y o is the control output of the system, is the integrated disturbance related to the system state and time t;

[0075] Assumption 1: The desired command trajectory y1 that the system expects to track is twice - continuously differentiable;

[0076] Assumption 2: The first - order derivative of the system state is bounded.

[0077] As a specific example, for the filter constructed in step 2, the system state and the virtual control law are filtered respectively, as follows:

[0078] For the system state x i and the virtual control law α r , a first - order filter is designed:

[0079]

[0080]

[0081] where x if represents the filtered value of the system state x i , α rf represents the filtered value of the virtual control law α r , w xi is an adjustable positive parameter, and w αr is an adjustable positive parameter;

[0082] From equations (2) and (3), the dynamic of the filtering error of the first - order filter can be obtained as:

[0083]

[0084]

[0085] where represents the filtering error of the virtual control law α r , represents the filtering error of the system state x i ;

[0086] In addition to using the first - order filter, the following second - order filter can also be used:

[0087]

[0088]

[0089] where ω xi is an adjustable positive parameter in the second-order filter, and ω αr is an adjustable positive parameter in the second-order filter.

[0090] Furthermore, other filters other than the first-order filter and the second-order filter can also be constructed. Filtering the system state x i and the virtual control law α r using any form of filter falls within the scope of protection of this claim; when using other filters other than the first-order filter, it may be different from the settings 1 and 2 made during the controller design.

[0091] As a specific example, the anti-disturbance control algorithm for a nonlinear servo system based on state filtering described in step 3 is as follows:

[0092] Step 3.1. Define e i as the control error of the system, where e1 is the tracking error of the system. At the same time, define z i as the difference between the control error e i of the system and the auxiliary variable ε i , then:

[0093]

[0094] where the auxiliary variable ε i is generated by the following auxiliary system:

[0095]

[0096] where k1, k2,..., k n are adjustable positive feedback gains;

[0097] The main function of the auxiliary system is to eliminate the state filtering error and the virtual control law filtering error; since there are unmeasurable signals in the auxiliary system, ε i can be calculated by integrating both sides of the auxiliary system:

[0098]

[0099] Step 3.2. Design the virtual control law α1:

[0100] From formula (1) and formula (8), it can be obtained:

[0101]

[0102] Based on the filtered value of state x1, it can be further expressed as:

[0103]

[0104] In the formula, represents the computable part in, and its specific expression is:

[0105]

[0106] Based on formula (11) and formula (12), the virtual control law α1 can be designed as:

[0107]

[0108] Substituting formula (14) into formula (11), we can get:

[0109]

[0110] Step 3.3. Design the virtual control law α l :

[0111] From formula (1) and formula (8), we can get:

[0112]

[0113] Based on the filtered value of state x l , it can be further expressed as:

[0114]

[0115] In the formula, represents the computable part in, and its specific expression is:

[0116]

[0117] Based on formula (16) and formula (17), the virtual control law α l is:

[0118]

[0119] Substituting formula (19) into formula (16), we can get:

[0120]

[0121] Step 3.4. Design the control input u of the system:

[0122] From formula (1) and formula (8), we can get:

[0123]

[0124] Based on the state x n of the filtered value, can be further expressed as:

[0125]

[0126] In the formula, represents the computable part in, and its specific expression is:

[0127]

[0128] Based on formula (21) and formula (22), the control input u of the system can be designed as:

[0129]

[0130] Substituting formula (24) into formula (23), we can get:

[0131]

[0132] According to the Lyapunov stability theory, select the positive function L V as:

[0133]

[0134] It can be proved that the designed disturbance rejection controller based on state filtering can ensure that all signals in the entire closed-loop system converge and remain stable.

[0135] As a specific example, the control objective of selecting the controller design parameters in step 4 to achieve the convergence and stability of all signals in the closed-loop system and at the same time make the output of the system accurately track the desired command is as follows:

[0136] Select the parameters w xi > 0, w αr > 0 and adjust the feedback gains k1> 0, k l > 0, k n > 0, so that the gain k ε1 = k1 – 1 / (2w x1 ), the gain k εl = k l – 1 / (2w xl ), the gain k εn = k n – 1 / (2w xn ), the gain and the gain If they are all positive numbers, the designed disturbance rejection controller based on state filtering can ensure that all signals in the entire closed-loop system converge and remain stable, while enabling the output of the system to accurately track the desired command.

[0137] The following further elaborates on the present invention in conjunction with the accompanying drawings and specific embodiments.

[0138] Embodiment

[0139] This embodiment provides a disturbance rejection control method for a single-rod electro-hydraulic position servo system based on state filtering, including the following steps:

[0140] Step 1: Establish the non-linear mathematical model of the single-rod electro-hydraulic position servo system, combined with Figure 2 , specifically as follows:

[0141] Define the state x1 as the displacement of the load, the state x2 as the velocity of the load, and the state x3 as the vector (A1P1 - A2P2) / m, where m is the mass of the load, P1 and P2 are the oil pressures in the rodless chamber and the rod chamber of the hydraulic cylinder respectively, and A1 and A2 are the effective acting areas of the piston rods in the rodless chamber and the rod chamber of the hydraulic cylinder. Then the state-space form of the system non-linear model is:

[0142]

[0143] In the formula, u is the control input voltage of the system;

[0144] The expressions of other parts are as follows:

[0145]

[0146] In the formula, β e is the elastic modulus of the hydraulic oil; V1 and V2 are the volumes of the rodless chamber and the rod chamber of the hydraulic cylinder respectively; f1(x2), g1(x2, P1, P2), and g2(x2, P1, P2) are unknown functions related to the system state; d1(t), p1(t), and p2(t) are time-varying external disturbances; is the total flow gain of the servo valve, where C q1 , C q2 are the flow coefficients of the throttle holes of the servo valves in the rodless chamber and the rod chamber respectively, w q1 , w q2 are the area gradients of the throttle holes in the rodless chamber and the rod chamber respectively, k q1 , k q2 are the spool displacement flow gains of the servo valves in the rodless chamber and the rod chamber respectively; s(u) = (1 + tanh(k s u)) / 2, tanh(·) is the hyperbolic tangent function, and k s is a positive constant; P s is the system oil source pressure, Pr is the system return oil pressure;

[0147] Setting 1: The command trajectory y1 that the system expects to track is second-order continuously differentiable;

[0148] Setting 2: The first-order derivatives and of the system state are bounded.

[0149] Step 2: Construct filters to filter the system state x2, state x3, virtual control law α1, and virtual control law α2 respectively, as follows:

[0150] For the system state x2, state x3, virtual control law α1, and virtual control law α2, design a first-order filter:

[0151]

[0152]

[0153] where x 2f represents the filtered value of the system state x2, x 3f represents the filtered value of the system state x3, α 1f represents the filtered value of the virtual control law α1, α 2f represents the filtered value of the virtual control law α2, w x2 is an adjustable positive parameter, w x3 is an adjustable positive parameter, w α1 is an adjustable positive parameter, w α2 is an adjustable positive parameter;

[0154] Step 3: Construct a nonlinear servo system disturbance rejection control algorithm based on state filtering, as follows:

[0155] Step 3.1: Define e1 as the tracking error of the system, e2 and e3 as the control errors of the system, and at the same time define the errors z1, z2, and z3 as:

[0156]

[0157] where the auxiliary variables ε1, ε2, and ε3 are generated by the following auxiliary system:

[0158]

[0159] where k1, k2, and k3 are adjustable positive feedback gains;

[0160] Solve for ε2 and ε3 by integrating both sides of formula (32):

[0161]

[0162] Step 3.2. Design the virtual control law α1 as follows:

[0163]

[0164] Step 3.3. Design the virtual control law α2 as follows:

[0165]

[0166] wherein, represents the computable part in, and its specific expression is:

[0167]

[0168] Step 3.4. Design the control input u of the system as follows:

[0169]

[0170] wherein, represents the computable part in, and its specific expression is:

[0171]

[0172] According to the Lyapunov stability theory, select the positive function L V as:

[0173]

[0174] In Step 4, select the filter parameters w x1 > 0, w x2 > 0, w x3 > 0, w α1 > 0, w α2 > 0 and adjust the feedback gains k1 > 0, k l > 0, k n > 0 such that the gain k ε1 = k1 – 1 / (2w x1 ), the gain k ε2 = k2 – 1 / (2w x2 ), the gain k ε3 = k3 – 1 / (2w x3 ), the gain the gain the gain the gain and the gain are all positive numbers, then the designed disturbance rejection controller based on state filtering can ensure that all signals in the entire closed-loop system converge and remain stable, and at the same time make the output of the system accurately track the desired command.

[0175] The parameters of the single-rod electro-hydraulic servo system provided in this embodiment are: m = 46 kg, A1 = 2×10 -3 m 2 , A2 = 1×10 -3 m 2 , P s = 1×10 7 Pa, P r = 0, β e = 2.1×10 8 Pa, V1 = 2×10 -4 + 2×10 -3 x1m 3 , V2 = 1×10 -4 - 1×10 - 3 x1m 3 , k s = 10; The added system uncertainty function f1(x2) = -1000x2 - (2 / π)×60×atan(50x2), g1(x2, P1, P2) = -2×10 -3 x2 - 1.23×10 -11 (P1 - P2) - 5.13×10 -13 (P1 - P r ), d1(t) = 1000sin(t), g2(x2, P1, P2) = 1×10 -3 x2 + 1.26×10 -11 (P1 - P2) - 5.16×10 -13 (P2 - P r ), p1(t) = sin(t), p2(t) = 1.2sin(t). The position command that the system expects to track is a curve

[0176] Controller design parameters:

[0177] Identify SFDRC as the controller proposed in this invention patent, and identify FLC as the controller that is the same as SFDRC but without disturbance compensation. After continuous adjustment, the SFDRC control parameters are selected as k1 = 450, k2 = 450, k3 = 450; w x2 = 1.2×10 -3 , w x3 = 1.2×10 -3 ; w α1 = 3×10 -3 , w α2 = 3×10 -3 ; The parameters selected in the FLC controller are the same as the corresponding parameters in SFDRC.

[0178] Figure 3 are the curves of the tracking error of the system varying with time under the action of the controller SFDRC designed by the present invention and the comparative controller FLC. It can be seen from Figure 3 that under the action of the controller designed by the present invention, its steady-state tracking error reaches a relatively high tracking accuracy, and is several orders of magnitude smaller than the steady-state tracking error under the action of the controller FLC, thus verifying the effectiveness of the method of the present invention.

[0179] Figure 4 is the curve of the filtering performance of the system state x2 varying with time under the action of the controller designed by the present invention. It can be seen from Figure 4 that the filtered value x of x2 2f is basically consistent with x2.

[0180] Figure 5 is the curve of the filtering performance of the system state x3 varying with time under the action of the controller designed by the present invention. It can be seen from Figure 5 that the filtered value x of x3 3f is basically consistent with x3.

[0181] Figure 6 is the curve of the control input voltage of the controller designed by the present invention varying with time. It can be seen from the figure that the obtained control input signal of the present invention is continuously differentiable and bounded, which is beneficial to the application in engineering practice.

[0182] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A disturbance rejection control method for a non-linear servo system based on state filtering, characterized in that, It includes the following steps: Step 1: Establish the mathematical model of the nonlinear servo system; Step 2: Construct filters to filter the system state and virtual control law respectively; Step 3: Design the disturbance rejection control algorithm for the nonlinear servo system based on state filtering; Step 4: Select the controller design parameters to achieve the convergence and stability of all signals in the closed-loop system, and at the same time make the output of the system accurately track the control objective of the desired instruction.

2. The anti-disturbance control method for a non-linear servo system based on state filtering according to claim 1, characterized in that, The establishment of the mathematical model of the nonlinear servo system described in Step 1 is as follows: Define the state vector \(x = [x_1, x_2, \ldots, x n T , where \(n\) is the order of the system, and the subscript \(i\) in the variable · i takes values 1, 2, \(\ldots\), \(n\); \(x_1, x_2, \ldots, x n are the elements in the vector. Then the state - space form of the nonlinear servo - system model is:​ y o = x1 wherein, the variable · r the subscript r in takes values of 1, 2, …, n−1, u is the control input of the system, and y o is the control output of the system, is related to the system state and the integrated disturbance related to time t; Assumption 1: The command trajectory y1 that the system expects to track is twice continuously differentiable; Set 2: The first derivative of the system state is bounded.

3. The anti-disturbance control method for a non-linear servo system based on state filtering according to claim 2, wherein, The filter constructed in Step 2 filters the system state x i and the virtual control law α r respectively, as follows: For the system state x i and the virtual control law α r , a first-order filter is constructed as follows: In the formula, the subscript r of the variable · r takes values 1, 2, …, n−1; x if represents the filtered value of the system state x i , α rf represents the filtered value of the virtual control law α r , w xi is an adjustable positive parameter, w αr is an adjustable positive parameter.

4. The anti-disturbance control method for a non-linear servo system based on state filtering according to claim 2, characterized in that The construction of the filter described in Step 2 is specifically to construct a second-order filter: where ω xi is an adjustable positive parameter in the second-order filter, and ω αr is an adjustable positive parameter in the second-order filter.

5. The anti-disturbance control method for a non-linear servo system based on state filtering according to claim 3 or 4, characterized in that The design of the disturbance rejection control algorithm for the nonlinear servo system based on state filtering described in Step 3 is as follows: Step 3.

1. Define e i as the control error of the system, where e1 is the tracking error of the system. Meanwhile, define z i as the difference between the control error e i of the system and the auxiliary variable ε i . Then: e1 = x1 - y1, e r+1 = x r+1 - α rf z1 = e1 - ε1, z r+1 = e r+1 - ε r+1 In the formula, the auxiliary variable ε i is generated by the following auxiliary system: where k1, k2, …, k n are adjustable positive feedback gains; The role of the auxiliary system is to eliminate the state filtering error and the virtual control law filtering error; since there are unmeasurable signals in the auxiliary system, ε is calculated by integrating both sides of the auxiliary system simultaneously. i : Step 3.2: Design the virtual control law α1 as: In the formula, represents the computable part in, and its specific expression is: Step 3.3: Design the virtual control law α l It is: In the formula, the variable · l The subscript l in takes values of 2, 3, …, n−1; represents the computable part in, and the specific expression is: Step 3.4: Design the control input u of the system as: In the formula, represents the computable part in, and the specific expression is:

6. The anti-disturbance control method for a non-linear servo system based on state filtering according to claim 5, characterized in that, The selection of the controller design parameters described in Step 4 is as follows: Select the parameters w of the filter xi > 0, w αr > 0 and adjust the feedback gains k1 > 0, k l > 0, k n > 0 such that the gain k ε1 = k1 – 1 / (2w x1 ) – 3 / 2, the gain k εl = k l – 1 / (2w xl ) – 2, the gain k εn = k n – 1 / (2w xn ) – 1, the gain and the gain are all positive, then the designed disturbance rejection controller based on state filtering can ensure that all signals in the entire closed-loop system converge and remain stable.

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