CN106774273B - For the algorithm based on sliding mode prediction fault tolerant control method of time_varying delay control system actuator failures - Google Patents

Abstract

The invention discloses a kind of algorithm based on sliding mode prediction fault tolerant control methods for time_varying delay control system actuator failures.Design to have obtained the system algorithm based on sliding mode prediction model with time varying characteristic using pole-assignment according to system output errors, which can be while guaranteeing sliding mode asymptotically stability, and dynamic improves the motion qualities of system.Consider that time lag system is influenced by inner parameter perturbation and external disturbance simultaneously, propose a kind of novel discrete sliding mode prediction reference track, the reference locus can not only guarantee the state of system had good robustness during approaching sliding-mode surface with quick convergence, and can significantly inhibit sliding formwork chattering phenomenon.Using multi-agent particle swarm algorithm improvement rolling optimization process, control law can either be rapidly and accurately solved, and can effectively avoid the premature convergence problem of conventional particle group's algorithm.The present invention is used for the robust Fault-Tolerant Control of a kind of uncertain discrete-time system containing Time-varying time-delays.

Description

Sliding mode prediction fault-tolerant control method for actuator fault of variable time-lag control system

Technical Field

The invention relates to a sliding mode prediction fault-tolerant control method for faults of an actuator of a variable time-lag control system, and belongs to the technical field of robust fault-tolerant control of an uncertain discrete control system.

Background

With the rapid development of computer technology and the actual needs in the fields of industrial automation, etc., the analysis and design of discrete control systems have become an important component of control theory. In engineering practice, a certain error often exists in the modeling process of the discrete system, the physical structure of the system is inevitably influenced by working conditions, and meanwhile, inevitable external interference exists, and all uncertain factors can deeply influence the final control effect of the discrete control system. In addition, with the increasingly complex composition structure of an actual discrete control system, a large time delay is introduced in the processes of signal transmission, calculation solution, remote control and the like, and the existence of a time lag phenomenon can make the system analysis and control design more complex and difficult, especially for the control fields with fast response and high precision requirements, such as aerospace, fine machining and the like, the time lag often causes the control precision of the system to be greatly reduced, and the serious and even possible system instability and other consequences are caused. With the diversification of the tasks and the complexity of the structure of the control system, the sensors, the actuators and the internal elements of the system inevitably have faults when the system runs. Therefore, it is an urgent problem to solve the engineering application at present to discuss and analyze a fault-tolerant control algorithm suitable for a time-lag discrete uncertain system, and obtain good control accuracy and dynamic quality on the premise of ensuring the stability of the system.

The sliding mode control has stronger robustness to uncertain factors such as parameter perturbation and external disturbance in the system, so that the sliding mode control is widely researched and applied to uncertain discrete system control at present. However, when a time lag phenomenon exists in a discrete system, the sliding mode control shows obvious performance reduction on the control effect, and particularly when the time lag is large and the system has high requirement on rapidity, the sliding mode control is often difficult to meet the actual control requirement, and even the instability phenomenon can occur. Compared with sliding mode control, the prediction control method can estimate the system performance in a future period of time by utilizing the self prediction and optimization capability, further obtain an online optimization real-time control strategy, and is more suitable for eliminating the influence of time lag on the discrete system performance. Therefore, for an uncertain discrete system with time lag, sliding mode control and predictive control are combined, so that the good robust performance advantage of the sliding mode control in processing the uncertain discrete system containing parameter perturbation and external disturbance can be fully utilized, the influence of the time lag on the stability of the system can be effectively avoided through the predictive control, and the control effect is further optimized.

At present, although a sliding mode predictive control method becomes a feasible method for solving the problem of uncertain discrete system robust control, deep research and application are still lacked for a system with a time lag problem.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the prior art, the sliding mode prediction fault-tolerant control method for the actuator fault of the variable time lag control system is provided, the multi-agent particle swarm can be utilized to quickly and accurately optimize under the action of the designed discrete sliding mode prediction control law, the sliding mode buffeting phenomenon is effectively restrained through a novel reference track, and the time-varying uncertain time lag discrete system with the actuator fault keeps robust and stable.

The technical scheme is as follows: a sliding mode prediction fault-tolerant control method aiming at faults of an actuator of a variable time lag control system is characterized in that a system sliding mode prediction model with time-varying characteristics is designed according to system output errors by adopting a pole allocation method, and the model can ensure gradual stability of a sliding mode and dynamically improve the motion quality of the system; considering the influence of the perturbation of internal parameters and the external disturbance on a time-lag system, a novel discrete sliding mode prediction reference track is provided, and the reference track not only can ensure that the state of the system has good robustness and rapid convergence in the process of approaching a sliding mode surface, but also can obviously inhibit the phenomenon of sliding mode buffeting; the method utilizes a multi-agent particle swarm algorithm to improve the rolling optimization process, can quickly and accurately solve the control law, can effectively avoid the premature problem of the traditional particle swarm algorithm, is used for the robust fault-tolerant control of a class of uncertain discrete systems with time-varying time lag, and comprises the following specific steps:

step 1) determining an uncertain discrete system model and parameters thereof:

step 1.1) determining an uncertain discrete system with actuator faults and time-varying time lags as formula (1), wherein x (k) epsilon RⁿFor the system state, u (k) e R^pFor system input, y (k) e R^qFor system output, Δ A, Δ B and Δ A_dPerturbation of system parameters, A, B, A, respectively_dC and E are real matrices of appropriate dimensions, v (k) E RⁿFor external interference, f (k) is a fault function, τ (k) e R⁺Time-varying time-lag;

step 1.2) rewriting system (1) into formula (2), wherein d (k) ═ Δ ax (k) + Δ bu (k) + Δ a_dx (k- τ (k)) + v (k)) + ef (k), and d (k) satisfies | d (k) < d (k) -d (k-1) | ≦ d₀And d_L≤|d(k)|≤d_U；

Step 2), design of a prediction model:

step 2.1) defining the system output error as formula (3), wherein y_r(k) Y (k) is the actual output for the desired output;

e(k)＝y(k)-y_r(k) (3)

step 2.2) adopts a linear sliding mode surface s (k) ═ σ e (k), σ ═ σ e (k)₁，σ₂，…，σ_q]The design can be carried out by a pole allocation method, and then a sliding mode prediction model (4) based on the system output error (3) can be obtained;

s(k+1)＝σe(k+1) (4)

step 2.3) nominal system x (k +1) ═ ax (k) + bu (k) + a according to system (2)_dx (k-tau (k)) can obtain the prediction output (5) of the prediction model at the time (k + P) and the vector form (6) of the prediction model;

S_PM(k)＝Gx(k)+HU(k)+FX_d(k)-σY_r(k) (6)

wherein P is a prediction time domain, M is a control time domain, and M is less than or equal to P, and u (k + M-1) is kept unchanged when j is more than or equal to M-1 and less than or equal to P; x_d(k)＝[x(k-τ(k))，x(k+1-τ(k+1))，...，x(k+P-1-τ(k+P-1))]^T；S_PM(k)＝[s(k+1)，s(k+2)，...，s(k+P)]^T；U(k)＝[u(k)，u(k+1)，..，u(M-1)]^T；G＝[(σCA)^T，(σCA²)^T，...，(σCA^P)^T]^T；Y_r(k)＝[y_r(k+1)，y_r(k+2)，...，y_r(k+P)]^T；

Step 3), designing a reference track:

step 3.1) designing a reference track as shown in formula (7):

wherein ζ (k) ═ σ d (k) ═ σ [ Δ ax (k) + Δ bu (k) + Δ a_dx(k-τ(k))+v(k)+Ef(k)]Representing the influence of the equivalent total disturbance of the system on the sliding mode output value,s₀by choosing appropriate s for designing the constants₀The relationship between the control signal amplitude being too large and the convergence to s (k) 0 being too slow can be coordinated; due to the uncertainty and fault interference of the system, interference suppression means is embedded in the reference track, and zeta is adopted₁Zeta (k) is compensated to maximally counteract the influence on the system performance, and when | s (k) | is smaller, i.e. s (k) gradually enters the quasi-sliding mode, compensation exists, so that the quasi-sliding mode can be enabledThereby effectively inhibiting the slip form from shaking;

step 3.2) approximate calculation by the one-step delay estimation method of formula (8)Pairing s can be done without d (k) being known_refSolution of (k +1), s_refThe vector form of (k +1) satisfies (9) where

S_ref(k)＝[s_ref(k+1)，s_ref(k+2)，...，s_ref(k+P)]^T (9)

Step 4), feedback correction design:

step 4.1) calculating a prediction error at the time k as an expression (10), wherein s (k) is the actual output of a prediction model at the time k, s (k | k-P) is the prediction output of the time (k-P) to the time k, and the expression (11) is satisfied;

e_s(k)＝s(k)-s(k|k-P) (10)

step 4.2) after correction is added, the prediction output and the vector form of the P step are respectively (12) and (13);

wherein,

E_s(k)＝[s(k)-s(k|k-1)，s(k)-s(k|k-2)，...，s(k)-s(k|k-P)]^T，h_pto correct the coefficients, h is typically taken₁＝1，1＞h₂＞h₃＞…＞h_P0, namely, the feedback correction effect is gradually weakened along with the increase of the prediction step number;

step 5), rolling optimization design:

step 5.1) designing the optimized performance index at the k moment to be formula (14), wherein β_i、γ_lIs a non-negative weight value, β_iThe proportion of the error at the sampling moment in the performance index is shown; gamma ray_lIs a restriction on the input weight; its vector form is equation (15);

wherein,

step 5.2) determining the particle swarm size L, wherein the position of a particle i is u_i＝(u_i1，u_i2，...，u_iM) Velocity v_i＝(v_i1，v_i2，...，v_iM) Value range of weight coefficient w, maximum number of iterations t_maxLearning factor c₁、c₂Particle environment range δ;

step 5.3) taking the optimized performance index J (k) as an adaptive value function psi, and updating the particle position according to the information of the adjacent particles; assuming that n is a particle having the best adaptation value among neighboring particles of the particle i, if the adaptation value of the particle i is better than that of n, the particle is maintainedThe position of sub-i is not changed, otherwise, the position of particle i is updated according to equation (16), wherein ξ is [ -1, 1]The random number of (2); neighboring particles of particle i are taken to be positionally located { (n)_i1，n_i2，...，n_iM)| |n_ij-u_ijAll particles of i ≦ δ, j ≦ 1, 2., M } excluding particle i;

u_i′＝u_n+ξ(u_i-u_n) (16)

step 5.4) iteratively updating the position and the speed of the particles according to the updating equation of the formula (17) to obtain the optimal position of the population;

wherein the preferred location of history is p_i＝(p_i1，p_i2，...，p_iM)，r₁、r₂Is between [0, 1]Random number between, g ═ g (g)₁，g₂，...，g_M) Is the overall optimal position;

step 5.5), when the maximum iteration number is reached, optimizing is finished, the current control quantity is implemented, and k +1 → k returns to the step 2).

Has the advantages that: a sliding mode prediction fault-tolerant control method aiming at faults of an actuator of a variable time lag control system is characterized in that a system sliding mode prediction model with time-varying characteristics is designed according to system output errors by adopting a pole allocation method, and the model can ensure gradual stability of a sliding mode and dynamically improve the motion quality of the system; considering the influence of the perturbation of internal parameters and the external disturbance on a time-lag system, a novel discrete sliding mode prediction reference track is provided, and the reference track not only can ensure that the state of the system has good robustness and rapid convergence in the process of approaching a sliding mode surface, but also can obviously inhibit the phenomenon of sliding mode buffeting; the rolling optimization process is improved by using the multi-agent particle swarm algorithm, the control law can be solved quickly and accurately, the prematurity problem of the traditional particle swarm algorithm can be effectively avoided, and the method is used for robust fault-tolerant control of a class of uncertain discrete systems with time-varying time lag. Has the following specific advantages:

①, designing a sliding mode prediction model of the system by adopting a pole allocation method according to the system output error, wherein the model has time-varying characteristics, and can dynamically improve the motion quality of the system while ensuring the gradual stability of the sliding mode;

② A novel discrete sliding mode reference track considering both internal parameter perturbation and external disturbance influence can not only ensure that the state of the system has good robustness and rapid convergence in the sliding mode surface approaching process, but also can obviously inhibit the sliding mode buffeting phenomenon;

③ compared with the traditional derivation method, the improved rolling optimization process of the multi-agent particle swarm optimization not only can rapidly and accurately solve the control law meeting the conditions, but also can effectively avoid the problem that the traditional particle swarm optimization is easy to fall into local extreme points in the optimization process.

The robust fault-tolerant control method for the uncertain discrete system containing the actuator fault and the time-varying time lag has certain application significance, is easy to realize, good in real-time performance and high in accuracy, can effectively improve the safety of the control system, is strong in operability, saves time, is higher in efficiency, and can be widely applied to actuator fault-tolerant control of the uncertain discrete control system.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is an experimental setup Qball-X4 quad-rotor helicopter developed by Quanser to study control of a quad-rotor helicopter;

FIG. 3 is a graph of the X-axis position of a Qball-X4 quad-rotor helicopter;

FIG. 4 is a graph of the speed of the Qball-X4 quadrotor in the X-axis direction;

FIG. 5 is a Qball-X4 quad-rotor helicopter actuator dynamic graph;

FIG. 6 is a control law graph;

FIG. 7 is a partially enlarged control law graph.

Detailed Description

The invention is further explained below with reference to the drawings.

As shown in fig. 1, a sliding mode prediction fault-tolerant control method for a variable-time-lag control system actuator fault is designed by adopting a pole allocation method according to a system output error to obtain a system sliding mode prediction model with time-varying characteristics, and the model can dynamically improve the motion quality of a system while ensuring gradual stability of a sliding mode; considering the influence of the perturbation of internal parameters and the external disturbance on a time-lag system, a novel discrete sliding mode prediction reference track is provided, and the reference track not only can ensure that the state of the system has good robustness and rapid convergence in the process of approaching a sliding mode surface, but also can obviously inhibit the phenomenon of sliding mode buffeting; the method utilizes a multi-agent particle swarm algorithm to improve the rolling optimization process, can quickly and accurately solve the control law, can effectively avoid the premature problem of the traditional particle swarm algorithm, is used for the robust fault-tolerant control of a class of uncertain discrete systems with time-varying time lag, and comprises the following specific steps:

step 1) determining an uncertain discrete system model and parameters thereof:

step 1.1) determining an uncertain discrete system with actuator faults and time-varying time lags as formula (1), wherein x (k) epsilon RⁿFor the system state, u (k) e R^pFor system input, y (k) e R^qFor system output, Δ A, Δ B and Δ A_dAre respectively the perturbation of the system parameters,A、B、A_dc and E are real matrices of appropriate dimensions, v (k) E RⁿFor external interference, f (k) is a fault function, τ (k) e R⁺Time-varying time-lag;

step 1.2) rewriting system (1) into formula (2), wherein d (k) ═ Δ ax (k) + Δ bu (k) + Δ a_dx (k- τ (k)) + v (k)) + ef (k), and d (k) satisfies | d (k) < d (k) -d (k-1) | ≦ d₀And d_L≤|d(k)|≤d_U；

Step 2), design of a prediction model:

step 2.1) defining the system output error as formula (3), wherein y_r(k) Y (k) is the actual output for the desired output;

e(k)＝y(k)-y_r(k) (3)

step 2.2) adopts a linear sliding mode surface s (k) ═ σ e (k), σ ═ σ e (k)₁，σ₂，…，σ_q]The design can be carried out by a pole allocation method, and then a sliding mode prediction model (4) based on the system output error (3) can be obtained;

s(k+1)＝σe(k+1) (4)

step 2.3) nominal system x (k +1) ═ ax (k) + bu (k) + a according to system (2)_dx (k-tau (k)) can obtain the prediction output (5) of the prediction model at the time (k + P) and the vector form (6) of the prediction model;

S_PM(k)＝Gx(k)+HU(k)+FX_d(k)-σY_r(k) (6)

wherein P is a prediction time domain, M is a control time domain, and M is less than or equal to P, and u (k + M-1) is kept unchanged when j is more than or equal to M-1 and less than or equal to P; x_d(k)＝[x(k-τ(k))，x(k+1-τ(k+1))，...，x(k+P-1-τ(k+P-1))]^T；

S_PM(k)＝[s(k+1)，s(k+2)，...，s(k+P)]^T；U(k)＝[u(k)，u(k+1)，...，u(M-1)]^T；

G＝[(σCA)^T，(σCA²)^T，...，(σCA^P)^T]^T；Y_r(k)＝[y_r(k+1)，y_r(k+2)，...，y_r(k+P)]^T；

Step 3), designing a reference track:

step 3.1) designing a reference track as shown in formula (7):

wherein ζ (k) ═ σ d (k) ═ σ [ Δ ax (k) + Δ bu (k) + Δ a_dx(k-τ(k))+v(k)+Ef(k)]Representing the influence of the equivalent total disturbance of the system on the sliding mode output value,s₀by choosing appropriate s for designing the constants₀The control signal amplitude can be coordinated to be too large and the control signal can be converged to be too slow when s (k) is 0A relationship; due to the uncertainty and fault interference of the system, interference suppression means is embedded in the reference track, and zeta is adopted₁Zeta (k) is compensated to maximally counteract the influence on the system performance, and when | s (k) | is smaller, i.e. s (k) gradually enters the quasi-sliding mode, compensation exists, so that the quasi-sliding mode can be enabledThereby effectively inhibiting the slip form from shaking;

step 3.2) approximate calculation by the one-step delay estimation method of formula (8)Pairing s can be done without d (k) being known_refSolution of (k +1), s_refThe vector form of (k +1) satisfies (9) where

S_ref(k)＝[s_ref(k+1)，s_ref(k+2)，...，s_ref(k+P)]^T (9)

Step 4), feedback correction design:

step 4.1) calculating a prediction error at the time k as an expression (10), wherein s (k) is the actual output of a prediction model at the time k, s (k | k-P) is the prediction output of the time (k-P) to the time k, and the expression (11) is satisfied;

e_s(k)＝s(k)-s(k|k-P) (10)

step 4.2) after correction is added, the prediction output and the vector form of the P step are respectively (12) and (13);

wherein,

E_s(k)＝[s(k)-s(k|k-1)，s(k)-s(k|k-2)，...，s(k)-s(k|k-P)]^T，h_pto correct the coefficients, h is typically taken₁＝1，1＞h₂＞h₃＞…＞h_P0, namely, the feedback correction effect is gradually weakened along with the increase of the prediction step number;

step 5), rolling optimization design:

step 5.1) designing the optimized performance index at the k moment to be formula (14), wherein β_i、γ_lIs a non-negative weight value, β_iThe proportion of the error at the sampling moment in the performance index is shown; gamma ray_lIs a restriction on the input weight; its vector form is equation (15);

wherein,

step 5.2) determining the particle swarm size L, wherein the position of a particle i is u_i＝(u_i1，u_i2，...，u_iM) Velocity v_i＝(v_i1，v_i2，...，v_iM) Value range of weight coefficient w, maximum number of iterations t_maxLearning factor c₁、c₂Particle environment range δ;

and 5.3) taking the optimized performance index J (k) as an adaptive value function psi, updating the positions of the particles according to the information of the adjacent particles, assuming that n is the particle with the best adaptive value in the adjacent particles of the particle i, if the adaptive value of the particle i is better than the adaptive value of n, keeping the position of the particle i unchanged, and otherwise, updating the position of the particle i according to a formula (16), wherein ξ is [ -1, 1]The random number of (2); neighboring particles of particle i are taken to be positionally located { (n)_i1，n_i2，...，n_iM)| |n_ij-u_ijAll particles of i ≦ δ, j ≦ 1, 2., M } excluding particle i;

u_i′＝u_n+ξ(u_i-u_n) (16)

step 5.4) iteratively updating the position and the speed of the particles according to the updating equation of the formula (17) to obtain the optimal position of the population;

wherein the preferred location of history is p_i＝(p_i1，p_i2，...，p_iM)，r₁、r₂Is between [0, 1]Random number between, g ═ g (g)₁，g₂，...，g_M) Is the overall optimal position;

step 5.5), when the maximum iteration number is reached, optimizing is finished, the current control quantity is implemented, and k +1 → k returns to the step 2).

The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

The effectiveness of the implementation is illustrated in the following by a practical case simulation.

The Qball-X4 quad-rotor helicopter flight control system actuators, developed by Quanser, Canada, were used as the subject of the application. The Qball-X4 experimental subject is shown in FIG. 2. The Qball-X4 four-rotor helicopter has six-dimensional variables (X, Y, Z, psi, theta, phi), wherein X, Y and Z are position variables, psi is yaw angle, theta is pitch angle and phi is roll angle. The simulation of the case selects the channel signal in the forward direction of the X axis as a research object.

The motion of the body about the X axis is affected by the total thrust and roll angle phi/pitch angle theta. Assuming a yaw angle ψ of 0, the dynamic equation for the X-axis is described as follows:

wherein M is_gThe mass of the machine body is shown, and X is the position in the X-axis direction. F is the thrust generated by the rotor:

wherein, K_gPositive gain, ω actuator bandwidth. Define v as actuator dynamics:

the state space expression is as follows:

in the X-axis position control model, a pitch angle theta is coupled with the X-axis position control model, the integral control can be divided into two stages, one stage is a pitch angle control stage, and the second stage, namely the position control stage, is started after the pitch angle is controlled to a preset value. And when the position reaches the set position, the pitch angle theta is reset to zero through the pitch angle control channel. Under the condition that theta is smaller, a model of an X-axis direction under an ideal condition without external disturbance, parameter perturbation and time-varying time lag is obtained through linearization, and the model is as follows:

suppose that the pitch angle has been set at the X-axis position control stageConsidering external disturbance, parameter perturbation, network delay and actuator faults, introducing dynamic disturbance, perturbation, time delay and faults of the actuator, and taking values of all matrixes in the system (1) as follows:

C＝[1 0 0]，ΔA＝0.1A，ΔB＝0.1B，ΔA_d＝0.1A_d，x(0)＝[1 1 1]^T，f(k)＝1.5+[0.3sin(6k) 0 0.2sin(2k)]elements of x (k), v (k)Taking white Gaussian noise with the mean value of zero, and taking the coefficient matrix sigma of the sliding mode surface as sigma ═ 1]. Particle swarm learning factor c₁＝2，c₂2, weight coefficient w_min＝0.2，w_max0.9, 20 particle group size, and maximum iteration number t_maxThe environmental range δ is 50, 6. The optimization time domain P represents that the output of the future P step is interested in an expected value at the moment k, and the optimization time domain P should cover the main part of the dynamic influence of the controlled object. Practice shows that increasing P reduces system rapidity and enhances system stability; decreasing P, the opposite is true. Therefore, the prediction time domain P which has both rapidity and stability is selected to be 4 in the simulation of the case. The control time domain M represents the change number of future control quantity to be determined, the influence of increasing and reducing M on the system is just opposite to P, and the control time domain M is generally selected to be 1-2 for the system with less complex dynamic characteristics, so that the control time domain M is selected to be 2 in the simulation of the case. The simulation time domain takes K as 1000, wherein the value of the body parameter is K as 120N, ω as 15rad/s, and M as 1.4 kg. The control input PWM may introduce a time lag and thus affect the vertical acceleration dynamics. Because the time lag is uncertain, the simulation time-varying time lag of the embodiment is taken as [1, 3 ]]Random integer between.

The simulation result shows that the fault-tolerant control method designed by the simulation of the embodiment has stronger robustness on the time-lag uncertain system with the actuator fault and can quickly approach to stability. Compared with the traditional sliding mode control method, the four-rotor helicopter body has the advantages that under the action of the control method designed by the simulation of the embodiment, the X-axis position speed and the actuator dynamic change curve are more gentle and can not obviously shake in the whole flying process as shown in the figures 3-5. Meanwhile, the control law is fast converged and does not generate large fluctuation, and no obvious buffeting exists after convergence, as shown in fig. 6. Although there is still some buffeting with the simulation method of this example, the buffeting amplitude is cut by nearly half, as shown in fig. 7. In general, the simulated control method of the embodiment is effective for an actuator fault system containing parameter perturbation, external disturbance and time-varying time lag.

Claims (1)

1. A sliding mode prediction fault-tolerant control method for actuator faults of a variable time-lag control system is characterized by comprising the following steps: a system sliding mode prediction model with time-varying characteristics is designed and obtained by adopting a pole allocation method according to system output errors, and the model can dynamically improve the motion quality of a system while ensuring gradual stability of a sliding mode; considering the influence of the perturbation of internal parameters and the external disturbance on a time-lag system, a novel discrete sliding mode prediction reference track is provided, and the reference track not only can ensure that the state of the system has good robustness and rapid convergence in the process of approaching a sliding mode surface, but also can obviously inhibit the phenomenon of sliding mode buffeting; the method utilizes a multi-agent particle swarm algorithm to improve the rolling optimization process, can quickly and accurately solve the control law, can effectively avoid the premature problem of the traditional particle swarm algorithm, is used for the robust fault-tolerant control of a class of uncertain discrete systems with time-varying time lag, and comprises the following specific steps:

step 1) determining an uncertain discrete system model and parameters thereof:

step 1.1) determining an uncertain discrete system with actuator faults and time-varying time lags as formula (1), wherein x (k) epsilon RⁿFor the system state, u (k) e R^pFor system input, y (k) e R^qFor system output, Δ A, Δ B and Δ A_dPerturbation of system parameters, A, B, A, respectively_dC and E are real matrices of appropriate dimensions, v (k) E RⁿFor external interference, f (k) is a fault function, τ (k) e R⁺Time-varying time-lag;

step 1.2) rewriting system (I) into formula (2), wherein d (k) ═ Δ ax (k) + Δ bu (k) + Δ a_dx (k- τ (k)) + v (k)) + ef (k), and d (k) satisfies | d (k) < d (k) -d (k-1) | ≦ d₀And d_L≤|d(k)|≤d_U；

Step 2), design of a prediction model:

step 2.1) defining the system output error as formula (3), wherein y_r(k) Y (k) is the actual output for the desired output;

e(k)＝y(k)-y_r(k) (3)

step 2.2) adopts a linear sliding mode surface s (k) ═ σ e (k), σ ═ σ e (k)₁，σ₂，…，σ_q]The design can be carried out by a pole allocation method, and then a sliding mode prediction model (4) based on the system output error (3) can be obtained;

s(k+1)＝σe(k+1) (4)

step 2.3) nominal system x (k +1) ═ ax (k) + bu (k) + a according to system (2)_dx (k-tau (k)) can obtain the prediction output (5) of the prediction model at the time (k + P) and the vector form (6) of the prediction model;

S_PM(k)＝Gx(k)+HU(k)+FX_d(k)-σY_r(k) (6)

wherein P is a prediction time domain, M is a control time domain, and M is less than or equal to P, and u (k + M-1) is kept unchanged when j is more than or equal to M-1 and less than or equal to P; x_d(k)＝[x(k-τ(k))，x(k+1-τ(k+1))，...，x(k+P-1-τ(k+P-1))]^T；S_PM(k)＝[s(k+1)，s(k+2)，...，s(k+P)]^T；U(k)＝[u(k)，u(k+1)，...，u(M-1)]^T；G＝[(σCA)^T，(σCA²)^T，...，(σCA^P)^T]^T；Y_r(k)＝[y_r(k+1)，y_r(k+2)，...，y_r(k+P)]^T；

Step 3), designing a reference track:

step 3.1) designing a reference track as shown in formula (7):

wherein ζ (k) ═ σ d (k) ═ σ [ Δ ax (k) + Δ bu (k) + Δ a_dx(k-τ(k))+v(k)+Ef(k)]Representing the influence of the equivalent total disturbance of the system on the sliding mode output value,s₀by choosing appropriate s for designing the constants₀The relationship between the control signal amplitude being too large and the convergence to s (k) 0 being too slow can be coordinated; due to the uncertainty and fault interference of the system, interference suppression means is embedded in the reference track, and zeta is adopted₁Zeta (k) is compensated to maximally counteract the influence on the system performance, and when | s (k) | is smaller, i.e. s (k) gradually enters the quasi-sliding mode, compensation exists, so that the quasi-sliding mode can be enabledThereby effectively inhibiting the slip form from shaking;

step 3.2) approximate calculation by the one-step delay estimation method of formula (8)Pairing s can be done without d (k) being known_refSolution of (k +1), s_refThe vector form of (k +1) satisfies (9) where

S_ref(k)＝[s_ref(k+1)，s_ref(k+2)，...，s_ref(k+P)]^T (9)

Step 4), feedback correction design:

step 4.1) calculating a prediction error at the time k as an expression (10), wherein s (k) is the actual output of a prediction model at the time k, s (k | k-P) is the prediction output of the time (k-P) to the time k, and the expression (11) is satisfied;

e_s(k)＝s(k)-s(k|k-P) (10)

step 4.2) after correction is added, the prediction output and the vector form of the P step are respectively (12) and (13);

wherein,E_S(k)＝[s(k)-s(k|k-1)，s(k)-s(k|k-2)，...，s(k)-s(k|k-P)]^T，h_pto correct the coefficients, h is typically taken₁＝1，1＞h₂＞h₃＞…＞h_P0, namely, the feedback correction effect is gradually weakened along with the increase of the prediction step number;

step 5), rolling optimization design:

step 5.1) designing the optimized performance index at the k moment to be formula (14), wherein β_i、γ_lIs a non-negative weight value, β_iThe proportion of the error at the sampling moment in the performance index is shown; gamma ray_lIs a restriction on the input weight; its vector form is equation (15);

wherein,

step 5.2) determining the particle swarm size L, wherein the position of a particle i is u_i＝(u_i1，u_i2，...，u_iM) Velocity v_i＝(v_i1，v_i2，...，v_iM) Value range of weight coefficient w, maximum number of iterations t_maxLearning factor c₁、c₂Particle environment range δ;

and 5.3) taking the optimized performance index J (k) as an adaptive value function psi, updating the positions of the particles according to the information of the adjacent particles, assuming that n is the particle with the best adaptive value in the adjacent particles of the particle i, if the adaptive value of the particle i is better than the adaptive value of n, keeping the position of the particle i unchanged, and otherwise, updating the position of the particle i according to a formula (16), wherein ξ is [ -1, 1]The random number of (2); neighboring particles of particle i are taken to be positionally located { (n)_i1，n_i2，...，n_iM)| |n_ij-u_ijAll particles of i ≦ δ, j ≦ 1, 2., M } excluding particle i;

u_i′＝u_n+ξ(u_i-u_n) (16)

step 5.4) iteratively updating the position and the speed of the particles according to the updating equation of the formula (17) to obtain the optimal position of the population;

wherein the preferred location of history is p_i＝(p_i1，p_i2，...，p_iM)，r₁、r₂Is between [0, 1]Random number between, g ═ g (g)₁，g₂，...，g_M) Is the overall optimal position;

step 5.5), when the maximum iteration number is reached, optimizing is finished, the current control quantity is implemented, and k +1 → k returns to the step 2).