Intelligent anti-interference control method and device for full-state dynamic constraint of nonlinear servo system

Abstract

The invention discloses an intelligent anti-interference control method and device for full-state dynamic constraint of a nonlinear servo system, and the method specifically comprises the steps: firstly constructing a nonlinear obstacle function, and converting a state constraint problem of the servo system into a stability control problem; then designing a multi-layer feedforward neural network and an uncertain observer, and estimating endogenous disturbance and external disturbance in the system; an intelligent anti-interference controller is designed, and feedforward compensation is carried out on internal source disturbance and external disturbance in the system; and finally, designing a neural network weight adaptive law, and selecting controller design parameters to realize a predetermined control target. According to the method, the problems of parameter uncertainty, structural uncertainty, unmodeled dynamics and external disturbance uncertainty existing in the nonlinear servo system can be solved at the same time, it is ensured that the full state of the system meets the preset dynamic constraint requirement, and the influence of differential explosion in the design process of a high-order nonlinear servo system controller is avoided; and large-scale application in industry and engineering is facilitated.

Description

Technical Field

[0001] This invention relates to the field of nonlinear system servo control technology, and in particular to an intelligent anti-disturbance control method and device for dynamic constraints of all states in nonlinear servo systems. Background Technology

[0002] In fields with high dynamic performance requirements, such as precision manufacturing, aerospace, and robotics, nonlinear servo systems play a core driving role. These systems prioritize high-precision position / velocity tracking, and their performance directly determines the overall level of high-end equipment. However, the core challenge does not stem from the design of control algorithms under ideal models, but rather from the ubiquitous and complex uncertainties of these models. A deep understanding of these uncertainties and their impact is the theoretical foundation for designing high-performance, highly robust control strategies.

[0003] Servo systems are essentially closed-loop motion control systems that receive command signals and drive the load to achieve precise tracking. Their nonlinear characteristics stem from various physical factors: frictional nonlinearity, actuator saturation and dead zones, flexible transmission and structural resonance, electromagnetic nonlinearity, and complex load disturbances. These inherent nonlinear factors make the system's dynamic equations highly complex, making it virtually impossible to establish a completely accurate mathematical model in engineering practice. The resulting model uncertainty becomes a major bottleneck restricting significant performance improvements. The model uncertainties faced by servo systems can be systematically categorized as follows: parameter uncertainty, structural uncertainty, unmodeled dynamics, and external disturbance uncertainty. Faced with such complex model uncertainties, traditional linear control (such as PID) and nonlinear control methods based on accurate model feedback linearization often prove inadequate. This has driven the development of advanced strategies such as robust control, adaptive control, and learning mechanisms.

[0004] Robust control: such as sliding mode variable structure control (SMC), H ∞ Control, in general, aims to design controllers that are insensitive to uncertainties within a specific range, guaranteeing stability and a certain level of performance. SMC (Slippery Manifold Control) forces the system state to arrive at and remain on the manifold within a finite time by designing a slippery manifold and switching control law, exhibiting strong robustness to matched uncertainties. However, its inherent high-frequency chattering problem requires special handling.

[0005] Adaptive control, such as Model Reference Adaptive Control (MRAC) and Self-Tuning Regulator (STR), automatically adjusts the controller to adapt to changes in uncertainty by estimating system or controller parameters online in real time, and is particularly effective for slowly time-varying parameter uncertainties. However, its convergence is highly dependent on parameter design, and sensor errors or environmental disturbances can significantly reduce control accuracy, limiting its applicability to certain scenarios.

[0006] Intelligent control includes technologies such as neural network control (NN), fuzzy logic control (FLC), and iterative learning control (ILC). NN / FLC do not rely on precise mathematical models; they approximate unknown nonlinear dynamics and compensate for uncertainties through learning or empirical rules. ILC, on the other hand, utilizes the characteristic of repeated operation to iteratively optimize the control input to gradually eliminate tracking errors caused by repetitive disturbances and model errors. However, it requires a large amount of data and computational resources, the training process is time-consuming and easily affected by data quality, resulting in high long-term operating costs.

[0007] Therefore, existing nonlinear servo system control methods mainly have the following shortcomings:

[0008] (1) It cannot simultaneously handle model uncertainties such as parameter uncertainty, structural uncertainty, unmodeled dynamics, and external disturbance uncertainty in the system;

[0009] (2) It cannot be guaranteed that the system meets specific constraint requirements in all states.

[0010] Faced with increasingly stringent application demands, intelligent composite control strategies integrating robustness, adaptability, and learning mechanisms represent a key development direction for overcoming model uncertainty challenges and unlocking the performance limits of nonlinear servo systems. Continued in-depth theoretical research and practical exploration are of paramount importance for promoting leaps in high-end equipment manufacturing and automation levels. Summary of the Invention

[0011] The purpose of this invention is to provide a control method for nonlinear servo systems that can simultaneously handle model uncertainties such as parameter uncertainty, structural uncertainty, unmodeled dynamics, and external disturbance uncertainty in the system, and ensure that the system meets specific constraint requirements in all states.

[0012] The technical solution to achieve the purpose of this invention is: an intelligent disturbance rejection control method for full-state dynamic constraints of nonlinear servo systems, comprising the following steps:

[0013] Step 1: Construct a nonlinear barrier function to transform the state constraint problem of the servo system into a stability control problem;

[0014] Step 2: Design a multi-layer feedforward neural network to estimate the intrinsic disturbances in the system;

[0015] Step 3: Design an uncertain observer to estimate external disturbances in the system;

[0016] Step 4: Design an intelligent disturbance rejection controller to perform feedforward compensation for internal disturbances and external interference in the system;

[0017] Step 5: Design the adaptive law of neural network weights and select the controller design parameters to achieve the predetermined control objective.

[0018] Furthermore, the construction of the nonlinear barrier function described in step 1 transforms the state constraint problem of the servo system into a stability control problem, as detailed below:

[0019] Define the state vector α = [α1, α2, ..., α n ] T Where n is the order of the system, and the variable is... s The subscript s in the α1, α2, ..., n values ​​can be 1, 2, ..., n; α1, α2, ..., αn. n For each state of the system, the state-space form of the mathematical model of the nonlinear servo system is:

[0020]

[0021] In the formula, the variable is... r The subscript r in ρ takes values ​​of 1, 2, ..., n-1. u Given a positive constant, u is the system control input, and y... o For the system's control output, To be consistent with system status The relevant endogenous disturbance, d s (t) represents time-varying external disturbances;

[0022] Control Objective: To design an intelligent disturbance rejection controller capable of simultaneously compensating for both internal disturbances and time-varying external disturbances in the system, thereby improving the system's output y. o Trace instruction α 1d Furthermore, all states of the system satisfy the following constraints:

[0023] β sp (t)<α s <β sb (t) (2)

[0024] In the formula, β sp (t) and β sb (t) is the time-varying constraint function;

[0025] Setting 1: The system expects to trace instruction α 1d Its first and second derivatives are both bounded;

[0026] Setting 2: Intrinsic disturbances of the system It is smooth and bounded;

[0027] Setting 3: Time-varying external disturbances of the system d s (t) and its first derivative are both bounded;

[0028] Setting 4: The estimated value of the representative, Indicates the estimation error of ·;

[0029] Constructing a nonlinear barrier function φ s for:

[0030]

[0031] In the formula, For β sp The upper bound of (t), β sb For β sb The lower bound of (t), that is:

[0032]

[0033] According to formula (3): as long as φ s If the system is bounded, then all states of the system satisfy the constraint condition (2);

[0034] Based on formula (3), we get:

[0035]

[0036] In the formula, φ sx and φ sz As an intermediate variable, the expression is:

[0037]

[0038] Based on formula (3), the nonlinear servo system (1) is transformed into:

[0039]

[0040] In the formula, To be consistent with system status The relevant internal disturbance, Δ s (t) represents the disturbance related to the time-varying external disturbance, μ sx As an intermediate variable, the expression is:

[0041]

[0042] Therefore, as long as the controller is designed to ensure that the closed-loop control system (7) is stable, all states of the system will satisfy the constraint condition (2), thus transforming the state constraint control problem of the system into the stability problem of the closed-loop control system.

[0043] Furthermore, the design of the multilayer feedforward neural network described in step 2 for estimating the intrinsic perturbations in the system is as follows:

[0044] For any smooth internal perturbation This can be expressed using a multilayer feedforward neural network as follows:

[0045]

[0046] In the formula, and Let M be the constant ideal weight matrix of a multilayer feedforward neural network, where M is the weight matrix of the network. s1 and M s2 For the number of neurons, The input vector and Ω s (·) represents the activation function, χ s (·) represents the function reconstruction error;

[0047] Design an uncertain approximator based on a multilayer feedforward neural network to approximate intrinsic perturbations in the system. Make an estimate:

[0048]

[0049] Furthermore, the design of the uncertain observer described in step 3 estimates the external disturbances in the system, as follows:

[0050] Based on equation (9) Expanding to a new state φ εs , that is to say Based on the expanded state equation, the uncertain observer based on a multilayer feedforward neural network is designed as follows:

[0051]

[0052] In the formula, κ os These are positive design parameters.

[0053] Furthermore, the intelligent disturbance rejection controller designed in step 4 performs feedforward compensation for internal disturbances and external interferences in the system, as detailed below:

[0054] Define control error g s and h s for:

[0055]

[0056] In the formula, ρ rc For virtual control law ρ r The filtered value, q s As an auxiliary variable; φ 1d The instruction for refactoring is expressed as:

[0057]

[0058] Virtual control law ρ r The filtered value ρ rc Generated through the following filter:

[0059]

[0060] In the formula, θ r For positive design parameters, ρ rwc As an intermediate variable;

[0061] Auxiliary variable q s Generated by the following systems:

[0062]

[0063] In the formula, ω s For positive feedback gain;

[0064] The virtual control law ρ1 is designed as follows:

[0065]

[0066] Design virtual control law ρ k for:

[0067]

[0068] The actual control law u is designed as follows:

[0069]

[0070] Furthermore, the design of the neural network weight adaptive law and the selection of controller design parameters described in step 5 to achieve the predetermined control objective are as follows:

[0071] The adaptive law for neural networks is designed so that the weight parameters of a multilayer feedforward neural network are updated using the following formula:

[0072]

[0073] In the formula, Proj(·) is the continuous projection mapping function, and the variable is... Γ s and Υ s The adaptive law matrix for the weight parameters, ζ s All are adjustable normal values;

[0074] Set state constraints β sp (t), β sb and β sb The parameters of (t) are selected from the design parameters Γ of the adaptive law for the weight parameters of the multilayer feedforward neural network. s Υ s , and ζ s The value of κ is adjusted. os ω s and θ rThe value of α1 is used to ensure that the system output α1 can track the instruction α. 1d This ensures that all states of the system remain within the preset dynamic constraint range.

[0075] An intelligent disturbance rejection control device for full-state dynamic constraints of a nonlinear servo system is disclosed. This device is used to implement the aforementioned intelligent disturbance rejection control method for full-state dynamic constraints of a nonlinear servo system. The device comprises a first module to a fifth module, and the functions of each module are as follows:

[0076] The first module constructs a nonlinear barrier function, transforming the state constraint problem of the servo system into a stability control problem.

[0077] The second module designs a multi-layer feedforward neural network to estimate the intrinsic disturbances in the system.

[0078] The third module involves designing an uncertain observer to estimate external disturbances in the system.

[0079] The fourth module designs an intelligent disturbance rejection controller to perform feedforward compensation for internal disturbances and external interference in the system.

[0080] The fifth module involves designing an adaptive law for the neural network weights and selecting controller design parameters to achieve the predetermined control objective.

[0081] A mobile terminal includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the intelligent anti-disturbance control method for full-state dynamic constraints of a nonlinear servo system.

[0082] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the intelligent disturbance rejection control method for full-state dynamic constraints of a nonlinear servo system.

[0083] Compared with the prior art, the significant advantages of this invention are: (1) It can simultaneously handle model uncertainties such as parameter uncertainty, structural uncertainty, unmodeled dynamics, and external disturbance uncertainty in the system; (2) It can ensure that the system meets the predetermined dynamic constraint requirements in all states; (3) It avoids the "differential explosion" effect in the design process of high-order nonlinear servo system controllers, which facilitates large-scale application in industry and engineering. Attached Figure Description

[0084] Figure 1 This is a flowchart of the intelligent anti-disturbance control method for full-state dynamic constraints of nonlinear servo systems according to the present invention.

[0085] Figure 2This is a graph showing the change in the state α1 tracking performance of the system in this embodiment of the invention over time.

[0086] Figure 3 This is a graph showing the change in the state α2 tracking performance of the system in this embodiment of the invention over time.

[0087] Figure 4 This is a graph showing the change in the state α3 tracking performance of the system over time in an embodiment of the present invention.

[0088] Figure 5 This is a graph showing the state estimation performance of the system in this embodiment of the invention as a function of time.

[0089] Figure 6 This is a graph showing the change in the uncertainty estimation performance of the system in this embodiment of the invention over time. Detailed Implementation

[0090] Combination Figure 1 This invention provides an intelligent disturbance rejection control method for full-state dynamic constraints of nonlinear servo systems, comprising the following steps:

[0091] Step 1: Construct a nonlinear barrier function to transform the state constraint problem of the servo system into a stability control problem;

[0092] Step 2: Design a multi-layer feedforward neural network to estimate the intrinsic disturbances in the system;

[0093] Step 3: Design an uncertain observer to estimate external disturbances in the system;

[0094] Step 4: Design an intelligent disturbance rejection controller to perform feedforward compensation for internal disturbances and external interference in the system;

[0095] Step 5: Design the adaptive law of neural network weights and select the controller design parameters to achieve the predetermined control objective.

[0096] As a specific example, the construction of the nonlinear barrier function in step 1 transforms the state constraint problem of the servo system into a stability control problem, as detailed below:

[0097] Define the state vector α = [α1, α2, ..., α n ] T Where n is the order of the system, and the variable is... s The subscript s in the α1, α2, ..., n values ​​can be 1, 2, ..., n; α1, α2, ..., αn. n For each state of the system, the state-space form of the mathematical model of the nonlinear servo system is:

[0098]

[0099] In the formula, the variable is... r The subscript r in ρ takes values ​​of 1, 2, ..., n-1. u Given a positive constant, u is the system control input, and y... o For the system's control output, To be consistent with system status The relevant endogenous disturbance, d s (t) represents time-varying external disturbances;

[0100] Control Objective: To design an intelligent disturbance rejection controller capable of simultaneously compensating for both internal disturbances and time-varying external disturbances in the system, thereby improving the system's output y. o Precisely track instruction α 1d Furthermore, all states of the system satisfy the following constraints:

[0101] β sp (t)<α s <β sb (t) (2)

[0102] In the formula, β sp (t) and β sb (t) is the time-varying constraint function;

[0103] Setting 1: The system expects to trace instruction α 1d Its first and second derivatives are both bounded;

[0104] Setting 2: Intrinsic disturbances of the system It is smooth and bounded;

[0105] Setting 3: Time-varying external disturbances of the system d s (t) and its first derivative are both bounded;

[0106] Setting 4: The estimated value of the representative, The estimation error is represented by ·.

[0107] Constructing a nonlinear barrier function φ s for:

[0108]

[0109] In the formula, For β sp The upper bound of (t), β sb For β sb The lower bound of (t), that is:

[0110]

[0111] From formula (3), we can see that as long as φ is ensured sIf the system is bounded, then all states of the system can satisfy the constraint condition (2);

[0112] Based on formula (3), we can obtain:

[0113]

[0114] In the formula, φ sx and φ sz As an intermediate variable, its expression is:

[0115]

[0116] Based on formula (3), the nonlinear servo system (1) can be converted into:

[0117]

[0118] In the formula, To be consistent with system status The relevant internal disturbance, Δ s (t) represents the disturbance related to the time-varying external disturbance, μ sx As an intermediate variable, its expression is:

[0119]

[0120] Therefore, as long as the controller is designed to ensure that the closed-loop control system (7) is stable, all states of the system can satisfy the constraint condition (2), thus transforming the state constraint control problem of the system into the stability problem of the closed-loop control system.

[0121] As a specific example, step 2 describes the design of a multi-layer feedforward neural network to estimate the intrinsic perturbations in the system, as follows:

[0122] For any smooth internal perturbation This can be expressed using a multilayer feedforward neural network as follows:

[0123]

[0124] In the formula, and Let M be the constant ideal weight matrix of a multilayer feedforward neural network, where M is the weight matrix of the network. s1 and M s2 For the number of neurons, The input vector and Ω s (·) represents the activation function, χ s (·) represents the function reconstruction error;

[0125] Design an uncertain approximator based on a multilayer feedforward neural network to approximate intrinsic perturbations in the system. Make an estimate:

[0126]

[0127] As a specific example, step 3 describes designing an uncertain observer to estimate external disturbances in the system, as follows:

[0128] Based on equation (9) Expanding to a new state φ εs , that is to say Based on the expanded state equation, the uncertain observer based on a multilayer feedforward neural network is designed as follows:

[0129]

[0130] In the formula, κ os Positive design parameters;

[0131] Based on the expanded state equation (11), the uncertain observer based on a multilayer feedforward neural network is designed as follows:

[0132]

[0133] In equation (12), κ os Positive design parameters;

[0134] To simplify the subsequent stability analysis of the closed-loop control system, a vector is defined. The system observation error can be dynamically summarized as follows:

[0135]

[0136] In equation (13),

[0137]

[0138] Therefore, there must exist a positive definite matrix C. o Make This holds true, where I is the identity matrix.

[0139] As a specific example, the design of the intelligent disturbance rejection controller described in step 4, which performs feedforward compensation for internal disturbances and external interferences in the system, is as follows:

[0140] Define control error g s and h s for:

[0141]

[0142] In the formula, ρ rc For virtual control law ρ r The filtered value, q sAs an auxiliary variable, φ 1d The instruction for refactoring is expressed as:

[0143]

[0144] Virtual control law ρ r The filtered value ρ rc This can be generated using the following filters:

[0145]

[0146] In the formula, θ r For positive design parameters, ρ rwc As an intermediate variable;

[0147] Auxiliary variable q s Generated by the following systems:

[0148]

[0149] In the formula, ω s For positive feedback gain;

[0150] Based on formulas (7), (12), and (15), differentiating h1 yields:

[0151]

[0152] Based on formula (11), we can obtain:

[0153]

[0154] Based on formula (15-2), the virtual control law ρ1 can be designed as follows:

[0155]

[0156] Substituting formula (16) into (15-2), we get:

[0157]

[0158] Based on formulas (7), (12), and (15), for h k Differentiation yields:

[0159]

[0160] Based on formula (11), we can obtain:

[0161]

[0162] Based on formula (16-3), a virtual control law ρ can be designed. k for:

[0163]

[0164] Substituting formula (17) into (16-3), we get:

[0165]

[0166] Based on formulas (7), (12), and (15), for h n Differentiation yields:

[0167]

[0168] Based on formula (11), we can obtain:

[0169]

[0170] Based on formula (17-3), the actual control law u can be designed as follows:

[0171]

[0172] Substituting formula (18) into (17-3), we get:

[0173]

[0174] As a specific example, the design of the neural network weight adaptive law and the selection of controller design parameters in step 5 to achieve the predetermined control objective are as follows:

[0175] The adaptive law for neural networks is designed so that the weight parameters of a multilayer feedforward neural network are updated using the following formula:

[0176]

[0177] In the formula, Proj(·) is the continuous projection mapping function, and the variable is... Γ s and Υ s The adaptive law matrix for the weight parameters, ζ s All are adjustable positive values;

[0178] Set state constraints βsp(t), β sb The parameters of βsb(t) are selected, and the design parameters Γ of the adaptive law for the weight parameters of the multilayer feedforward neural network are chosen. s Υ s , and ζ s The value of κ is adjusted. os ω s and θ r The value of α1 is determined to ensure that the system output α1 can track the instruction α as accurately as possible.1d This ensures that all states of the system remain within the preset dynamic constraint range.

[0179] Based on the stability analysis of the system in control theory, a nonnegative function F is selected. L Taking its derivative, we get:

[0180]

[0181] In the formula, tr(·) represents the trace of a certain matrix ·;

[0182] Assume the following inequalities hold:

[0183]

[0184] In the formula, υ hs υ qs υ Yr υ Xs and D F All are unknown positive numbers;

[0185] Based on equation (21), equation (20) can be rearranged as follows:

[0186]

[0187] In the formula,

[0188]

[0189] Furthermore, equation (23) can be rearranged as follows:

[0190]

[0191] In the formula, α V For unknown positive constants;

[0192] Therefore, it can be demonstrated that the expected control objectives can be achieved.

[0193] This invention also provides an intelligent disturbance rejection control device for full-state dynamic constraints of a nonlinear servo system. This device is used to implement the aforementioned intelligent disturbance rejection control method for full-state dynamic constraints of a nonlinear servo system. The device includes a first module to a fifth module, and the functions of each module are as follows:

[0194] The first module constructs a nonlinear barrier function, transforming the state constraint problem of the servo system into a stability control problem.

[0195] The second module designs a multi-layer feedforward neural network to estimate the intrinsic disturbances in the system.

[0196] The third module involves designing an uncertain observer to estimate external disturbances in the system.

[0197] The fourth module designs an intelligent disturbance rejection controller to perform feedforward compensation for internal disturbances and external interference in the system.

[0198] The fifth module involves designing an adaptive law for the neural network weights and selecting controller design parameters to achieve the predetermined control objective.

[0199] The present invention also provides a mobile terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the intelligent anti-disturbance control method for full-state dynamic constraints of nonlinear servo systems.

[0200] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the steps in the intelligent anti-disturbance control method for full-state dynamic constraints of a nonlinear servo system.

[0201] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0202] Example

[0203] This embodiment provides an intelligent disturbance rejection control method for full-state dynamic constraints of a third-order nonlinear servo system, including the following steps:

[0204] Step 1: Establish a mathematical model for a class of third-order nonlinear servo systems, transforming the state constraint problem of the servo system into a stability control problem, as detailed below:

[0205] Define the state vector α = [α1, α2, α3] T Then the state-space form of the mathematical model of the third-order nonlinear servo system is:

[0206]

[0207] In the formula, u is the control input of the system, and y o For the system's control output, and To be consistent with system status and The relevant internal disturbances, d1(t), d2(t), and d3(t) are time-varying external disturbances;

[0208] Control Objective: To design an intelligent disturbance rejection controller capable of simultaneously compensating for both internal disturbances and time-varying external disturbances in the system, thereby improving the system's output y. o Precisely track instruction α 1d Furthermore, all states of the system satisfy the following constraints:

[0209] β1p (t)<α1<β 1b (t),β 2p (t)<α2<β 2b (t),β 3p (t)<α3<β 3b (t) (1-2)

[0210] In the formula, β 1p (t), β 1b (t), β 2p (t), β 2b (t), β 3p (t) and β 3b (t) is the time-varying constraint function;

[0211] Setting 1: The system expects to trace instruction α 1d Its first and second derivatives are both bounded;

[0212] Setting 2: Intrinsic disturbances of the system and It is smooth and bounded;

[0213] Setting 3: The time-varying external disturbances d1(t), d2(t), and d3(t) of the system and their first derivatives are all bounded;

[0214] Setting 4: The estimated value of the representative, The estimation error is represented by ·.

[0215] The nonlinear barrier functions φ1, φ2, and φ3 are constructed as follows:

[0216]

[0217] In the formula, and β 1p (t), β 2p (t) and β 3p The upper bound of (t), β 1b β 2b and β 3b For β 1b (t), β 2b (t) and β 3b The lower bound of (t), that is:

[0218]

[0219] From formula (1-3), we can see that as long as φ1, φ2 and φ3 are bounded, all states of the system can satisfy the constraint condition (1-2).

[0220] Based on formula (1-3), we can obtain:

[0221]

[0222] In the formula, φ 1x φ 1z φ 2x φ 2z φ 3x and φ 3z As an intermediate variable, its expression is:

[0223]

[0224] Based on formula (1-3), the nonlinear servo system (1-1) can be converted into:

[0225]

[0226] In equation (1-7), and To be consistent with system status and The relevant internal disturbances, Δ1(t), Δ2(t), and Δ3(t), are disturbances related to time-varying external disturbances, μ 1x μ 2x and μ 3x Its expression is as follows:

[0227]

[0228] Step 2: Design a multi-layer feedforward neural network to estimate the intrinsic perturbations in the system, as follows:

[0229] For any smooth internal perturbation and It can be approximated by a multilayer feedforward neural network as follows:

[0230]

[0231] In the formula, and Let M be the constant ideal weight matrix of a multilayer feedforward neural network, where M is the weight matrix of the network. 11 M 12 M 21 M 22 M 31 and M 32 For the number of neurons, and The input vector and and Ω1(·), Ω2(·), and Ω3(·) represent activation functions.

[0232] Step 3: Design an uncertain observer to estimate external disturbances in the system, as follows:

[0233] Will and And χ3(·) represents the function reconstruction error, which is then expanded into the new state φ. ε1 φ ε2 and φ ε3 Based on the expanded state equation, an uncertain observer based on a multilayer feedforward neural network is designed as follows:

[0234]

[0235] In the formula, κ o1 κ o2 and κ o3 These are positive design parameters.

[0236] Step 4: Design an intelligent disturbance rejection controller to perform feedforward compensation for internal disturbances and external interferences in the system, as detailed below:

[0237] Define the control errors g1, h1, g2, h2, g3, and h3 as follows:

[0238]

[0239] In the formula, ρ 1c and ρ 2c ρ1 and ρ2 are the filter values ​​of the virtual control laws, respectively, q1, q2, and q3 are auxiliary variables, and φ is the filter value of the virtual control law. 1d The instruction for refactoring is expressed as:

[0240]

[0241] The filtered value of the virtual control law can be generated using the following filters:

[0242]

[0243] In the formula, θ1 and θ2 are positive design parameters, and ρ 1wc and ρ 2wc As an intermediate variable;

[0244] The auxiliary variables are generated by the following system:

[0245]

[0246] In the formula, ω1, ω2 and ω3 are the positive feedback gains;

[0247] Design the virtual control laws ρ1, ρ2 and the actual control law u as follows:

[0248]

[0249] Step 5: Design the adaptive law for neural network weights and select the controller design parameters to achieve the predetermined control objective, as detailed below:

[0250] The adaptive law for neural networks is designed so that the weight parameters of a multilayer feedforward neural network are updated using the following formula:

[0251]

[0252] In equation (16), Proj(·) is the continuous projection mapping function, and the variable is... Γ1, Υ1, Γ2, Υ2, Γ3, and Υ3 are the adaptive law matrices for the weight parameters. ζ1、 ζ2、 Both ζ3 and ζ4 are adjustable positive constants;

[0253] The parameters of the state constraints are set, the design parameters of the adaptive law for the weight parameters of the multilayer feedforward neural network are selected, and other controller design parameters are adjusted to ensure that the system output α1 can track the command α as accurately as possible. 1d This ensures that all states of the system remain within the preset dynamic constraint range.

[0254] In this embodiment, the system expects to track the instruction α. 1d =2sin(t)(1-e -0.5t ).

[0255] Controller design parameters:

[0256] The controller parameters proposed in this invention patent are selected as follows: ω1 = 100, ω2 = 100, ω3 = 1 × 10⁻⁶. -4 , β 1p (t)=2sin(t)-2.5,β1b(t)2sin(t)+2.5,β 1b = -0.3 β 2p (t)=4sin(t)-36.8、β2b(t)=4sin(t)+36.8、β 2b =31.5 β 3p (t)=2sin(t)-50、β3b(t)=2sin(t)+140、β 3b =135, κ o1 =500, κ o2 =500, κ o3 =500, θ1=3000, θ2=3000, Γ1=5×10 4 I 14Υ1=1×10 6 I 14 Γ2=1×10 4 I 14 Υ2=1×10 6 I 14 Γ3=1×10 -3 I 14 Υ3=1×10 7 I 14 , ζ1=1×10 -5 , ζ2=1×10 -5 , and ζ3=1×10 -5 .

[0257] Figure 2 This is a graph showing the change in the state α1 tracking performance of the system under the control of the controller designed in this invention over time. It can be seen that state α1 is always within the preset constraints and its tracking error reaches 10. -4 The order of magnitude.

[0258] Figure 3 This is a graph showing the change in the state α2 tracking performance of the system under the action of the controller designed in this invention over time. It can be seen that state α2 is always within the preset constraints.

[0259] Figure 4 This is a curve showing the change of the state α3 tracking performance of the system under the action of the controller designed in this invention over time. It can be seen that state α3 is always within the preset constraints.

[0260] Figure 5 This is a graph showing the state estimation performance of the system under the action of the controller designed in this invention over time. It can be seen that the designed observer can accurately observe the corresponding state, laying an important foundation for estimating the uncertainty in the system.

[0261] Figure 6 This is a graph showing the performance of the system's uncertainty estimation over time under the control of the controller designed in this invention. It can be seen that the uncertainty in the system can be accurately estimated, which lays an important foundation for compensating for uncertainties in the system.

[0262] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An intelligent disturbance rejection control method for full-state dynamic constraints of nonlinear servo systems, characterized in that, Includes the following steps: Step 1: Construct a nonlinear barrier function to transform the state constraint problem of the servo system into a stability control problem; Step 2: Design a multi-layer feedforward neural network to estimate the intrinsic disturbances in the system; Step 3: Design an uncertain observer to estimate external disturbances in the system; Step 4: Design an intelligent disturbance rejection controller to perform feedforward compensation for internal disturbances and external interference in the system; Step 5: Design the adaptive law of neural network weights and select the controller design parameters to achieve the predetermined control objective.

2. The intelligent disturbance rejection control method for full-state dynamic constraints of nonlinear servo systems according to claim 1, characterized in that, Step 1 involves constructing a nonlinear barrier function, which transforms the state constraint problem of the servo system into a stability control problem, as detailed below: Define the state vector α = [α1, α2, ..., α n ] T Where n is the order of the system, and the variable is... s The subscript s in the α1, α2, ..., n values ​​can be 1, 2, ..., n; α1, α2, ..., αn. n For each state of the system, the state-space form of the mathematical model of the nonlinear servo system is: In the formula, the variable is... r The subscript r in ρ takes values ​​of 1, 2, ..., n-1. u Given a positive constant, u is the system control input, and y... o For the system's control output, To be consistent with system status The relevant endogenous disturbance, d s (t) represents time-varying external disturbances; Control Objective: To design an intelligent disturbance rejection controller capable of simultaneously compensating for both internal disturbances and time-varying external disturbances in the system, thereby improving the system's output y. o Trace instruction α 1d Furthermore, all states of the system satisfy the following constraints: b sp (t)<α s <b sb (t) (2) In the formula, β sp (t) and β sb (t) is the time-varying constraint function; Setting 1: The system expects to trace instruction α 1d Its first and second derivatives are both bounded; Setting 2: Intrinsic disturbances of the system It is smooth and bounded; Setting 3: Time-varying external disturbances of the system d s (t) and its first derivative are both bounded; Setting 4: The estimated value of the representative, Indicates the estimation error of ·; Constructing a nonlinear barrier function φ s for: In the formula, For β sp The upper bound of (t), β sb For β sb The lower bound of (t), that is: According to formula (3): as long as φ s If the system is bounded, then all states of the system satisfy the constraint condition (2); Based on formula (3), we get: In the formula, φ sx and φ sz As an intermediate variable, the expression is: Based on formula (3), the nonlinear servo system (1) is transformed into: In the formula, To be consistent with system status The relevant internal disturbance, Δ s (t) represents the disturbance related to the time-varying external disturbance, μ sx As an intermediate variable, the expression is: Therefore, as long as the controller is designed to ensure that the closed-loop control system (7) is stable, all states of the system will satisfy the constraint condition (2), thus transforming the state constraint control problem of the system into the stability problem of the closed-loop control system.

3. The intelligent disturbance rejection control method for full-state dynamic constraints of nonlinear servo systems according to claim 2, characterized in that, Step 2 describes the design of a multi-layer feedforward neural network to estimate the intrinsic perturbations in the system, as detailed below: For any smooth internal perturbation This can be expressed using a multilayer feedforward neural network as follows: In the formula, and Let M be the constant ideal weight matrix of a multilayer feedforward neural network, where M is the weight matrix of the network. s1 and M s2 For the number of neurons, The input vector and Ω s (·) represents the activation function, χ s (·) represents the function reconstruction error; Design an uncertain approximator based on a multilayer feedforward neural network to approximate intrinsic perturbations in the system. Make an estimate:

4. The intelligent disturbance rejection control method for full-state dynamic constraints of nonlinear servo systems according to claim 3, characterized in that, Step 3 describes the design of an uncertain observer to estimate external disturbances in the system, as detailed below: Based on equation (9) Expanding to a new state φ εs , that is to say Based on the expanded state equation, the uncertain observer based on a multilayer feedforward neural network is designed as follows: In the formula, κ os These are positive design parameters.

5. The intelligent disturbance rejection control method for full-state dynamic constraints of nonlinear servo systems according to claim 4, characterized in that, Step 4 describes the design of an intelligent disturbance rejection controller to perform feedforward compensation for internal disturbances and external interference in the system, as detailed below: Define control error g s and h s for: In the formula, ρ rc For virtual control law ρ r The filtered value, q s As an auxiliary variable; φ 1d The instruction for refactoring is expressed as: Virtual control law ρ r The filtered value ρ rc Generated through the following filter: In the formula, θ r For positive design parameters, ρ rwc As an intermediate variable; Auxiliary variable q s Generated by the following systems: In the formula, ω s For positive feedback gain; The virtual control law ρ1 is designed as follows: Design virtual control law ρ k for: The actual control law u is designed as follows:

6. The intelligent disturbance rejection control method for full-state dynamic constraints of nonlinear servo systems according to claim 5, characterized in that, Step 5, which involves designing the adaptive law for the neural network weights and selecting the controller design parameters to achieve the predetermined control objective, is detailed below: The adaptive law for neural networks is designed so that the weight parameters of a multilayer feedforward neural network are updated using the following formula: In the formula, Proj(·) is the continuous projection mapping function, and the variable is... Γ s and Υ s The adaptive law matrix for the weight parameters, ζ s All are adjustable normal values; Set state constraints β sp (t), β sb and β sb The parameters of (t) are selected from the design parameters Γ of the adaptive law for the weight parameters of the multilayer feedforward neural network. s Υ s , and ζ s The value of κ is adjusted. os ω s and θ r The value of α1 is used to ensure that the system output α1 can track the instruction α. 1d This ensures that all states of the system remain within the preset dynamic constraint range.

7. An intelligent disturbance rejection control device for full-state dynamic constraints of a nonlinear servo system, characterized in that, This device is used to implement the intelligent disturbance rejection control method for full-state dynamic constraints of nonlinear servo systems as described in any one of claims 1 to 6. The device includes a first module to a fifth module, and the functions of each module are as follows: The first module constructs a nonlinear barrier function, transforming the state constraint problem of the servo system into a stability control problem. The second module designs a multi-layer feedforward neural network to estimate the intrinsic disturbances in the system. The third module involves designing an uncertain observer to estimate external disturbances in the system. The fourth module designs an intelligent disturbance rejection controller to perform feedforward compensation for internal disturbances and external interference in the system. The fifth module involves designing an adaptive law for the neural network weights and selecting controller design parameters to achieve the predetermined control objective.

8. A mobile terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the intelligent anti-disturbance control method for full-state dynamic constraints of nonlinear servo systems as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the intelligent anti-disturbance control method for full-state dynamic constraints of nonlinear servo systems as described in any one of claims 1 to 6.

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