CN106774273A - 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 method for time_varying delay control system actuator failures.The system algorithm based on sliding mode prediction model with time varying characteristic is obtained using pole-assignment design according to system output errors, the model can be while sliding mode asymptotically stability be ensured, dynamic improves the motion qualities of system.Consider that time lag system is influenceed by inner parameter perturbation and external disturbance simultaneously, propose a kind of new discrete sliding mode prediction reference track, the reference locus can not only ensure that the state of system has good robustness and quick convergence during convergence sliding-mode surface, and can significantly suppress sliding formwork chattering phenomenon.Using multi-agent particle swarm algorithm improvement rolling optimization process, control law can either be rapidly and accurately solved, the premature convergence problem of conventional particle group's algorithm can be prevented effectively from again.The present invention contains the robust Fault-Tolerant Control of the uncertain discrete-time system of Time-varying time-delays for a class.

Description

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

Technical field

The present invention relates to a kind of algorithm based on sliding mode prediction fault tolerant control method for time_varying delay control system actuator failures, belong to The robust Fault-Tolerant Control technical field of uncertain discrete control system.

Background technology

With developing rapidly for computer technology and being actually needed for the field such as industrial automation, discrete control system point Analysis has become an important component of control theory with design.In engineering practice, the modeling process of discrete system is past Toward there is certain error, the physical arrangement of system will necessarily also be influenceed by condition of work, while also exist to keep away The external disturbance exempted from, all these uncertain factors all will produce deep shadow to the final control effect of discrete control system Ring.Additionally, constituting the increasingly complication of structure with actual discrete control system, in signal transmission, solution, remote control are calculated Larger time delay can be introduced Deng during, the presence of time delay can cause that network analysis and control design case become more Complicated and difficult, the control field with fast-response and high-precision requirement particularly with Aero-Space, retrofit etc., time lag is past Toward the control accuracy of system can be caused to be greatly reduced, serious possibly even causes the consequences such as system unstability.With control system The variation and the complication of structure of task, make system operationally, and sensor, actuator and internal system element all can not Can break down with avoiding.Therefore, the fault-tolerant control algorithm suitable for Discrete Time-delay uncertain system with analysis is inquired into, is being ensured On the premise of system stabilization, good control accuracy and dynamic quality is obtained, this has turned into current engineer applied urgently to be resolved hurrily Problem.

Sliding formwork control has stronger robust for uncertain factors such as Parameter Perturbation present in system, external disturbances Property, thus extensive research and application have been obtained in uncertain discrete-time system control at present.But in the presence of discrete system During stagnant phenomenon, sliding formwork control shows obvious performance reduction in control effect, especially larger when time lag, and system pair When rapidity requirement is higher, sliding formwork control is often difficult to meet actual control requirement, or even unstable phenomenon occurs.Compared to cunning Mould is controlled, and forecast Control Algorithm can utilize prediction and the optimization ability of its own, estimates the systematic function of following a period of time, And then a Real-Time Control Strategy for on-line optimization is obtained, it is more applicable for eliminating the shadow that time lag causes discrete system performance Ring.Therefore, for the uncertain discrete-time system with time lag, sliding formwork control is combined with PREDICTIVE CONTROL, can not only be abundant The good robustness having on uncertain discrete-time system of the treatment containing Parameter Perturbation and external disturbance using sliding formwork control Energy advantage, can also be prevented effectively from influence of the time lag to the stability of a system, further optimal control effect by PREDICTIVE CONTROL.

At present, although sliding mode predictive control method turned into one solution uncertain discrete-time system kinds of robust control problems can Row method, but be directed to while the system that there is Time Delay still lacks in-depth study with application.

The content of the invention

Goal of the invention：For above-mentioned prior art, a kind of sliding formwork for time_varying delay control system actuator failures is proposed Prediction fault tolerant control method, can be in the presence of designed discrete sliding mode Predictive control law, by using multiple agent grain Subgroup quick and precisely optimizing, and restrained effectively sliding formwork chattering phenomenon by a kind of new reference locus so that with execution Time-varying time-delays uncertain discrete-time system in the case of device failure keeps robust stability.

Technical scheme：A kind of algorithm based on sliding mode prediction fault tolerant control method for time_varying delay control system actuator failures, according to System output errors have obtained the system algorithm based on sliding mode prediction model with time varying characteristic, the model energy using pole-assignment design Enough while sliding mode asymptotically stability is ensured, dynamic improves the motion qualities of system；Consider that time lag system is subject to simultaneously in The influence of portion's Parameter Perturbation and external disturbance, it is proposed that a kind of new discrete sliding mode prediction reference track, the reference locus are not Only ensure that the state of system has good robustness and quick convergence, Er Qieneng during convergence sliding-mode surface It is enough significantly to suppress sliding formwork chattering phenomenon；Using multi-agent particle swarm algorithm improvement rolling optimization process, can either be quickly accurate Control law really is solved, the premature convergence problem of conventional particle group's algorithm can be prevented effectively from again, be used to contain time-varying for a class The robust Fault-Tolerant Control of the uncertain discrete-time system of time lag, comprises the following specific steps that：

Step 1) determine uncertain discrete-time system model and its parameter：

Step 1.1) determine that the uncertain discrete-time system with actuator failures and Time-varying time-delays is formula (1), wherein, x (k) ∈RⁿIt is system mode, u (k) ∈ R^pFor system is input into, y (k) ∈ R^qFor system is exported, Δ A, Δ B and Δ A_dRespectively system is joined Number perturbation, A, B, A_d, C and E be appropriate dimension real matrix, v (k) ∈ RⁿIt is external disturbance, f (k) is failure function, τ (k) ∈ R⁺It is Time-varying time-delays；

Step 1.2) system (1) is rewritten as formula (2), wherein, d (k)=Δ Ax (k)+Δ Bu (k)+Δ A_dx(k-τ(k)) + v (k)+Ef (k), and d (k) meets | d (k)-d (k-1) |≤d₀And d_L≤|d(k)|≤d_U；

Step 2) forecast model design：

Step 2.1) definition system output errors be formula (3), wherein, y_rK () is desired output, y (k) is reality output；

E (k)=y (k)-y_r(k) (3)

Step 2.2) using linear sliding mode face s (k)=σ e (k), σ=[σ₁, σ₂..., σ_q] can be set by Method of Pole Placement Meter, then it is (4) that can obtain the algorithm based on sliding mode prediction model based on system output errors (3)；

S (k+1)=σ e (k+1) (4)

Step 2.3) according to nominal system x (k+1)=Ax (k)+Bu (k)+A of system (2)_dX (k- τ (k)) can be obtained Prediction of the forecast model at (k+P) moment exports (5) and its vector form (6)；

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

Wherein, P is prediction time domain, and M is control time domain, and meets M≤P, and controlled quentity controlled variable u (k+j) keeps in M-1≤j≤P U (k+M-1) is constant；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=[(σ CA)^T, (σ CA² )^T..., (σ CA^P)^T]^T；Y_r(k)=[y_r(k+1), y_r..., y (k+2)_r(k+P)]^T；

Step 3) reference locus design：

Step 3.1) design such as the reference locus of formula (7)：

Wherein, ζ (k)=σ d (k)=σ [Δs Ax (k)+Δ Bu (k)+Δ A_dX (k- τ (k))+v (k)+Ef (k)] represent system Influence of the equivalent total disturbance to sliding formwork output valve,s₀For Design constant, by selecting suitable s₀, control signal amplitude can be coordinated excessive and converge to s (k)=0 speed excessively slow two Relation between person；There is the interference of uncertain and failure due to system, AF panel means embedded in the reference locus, By using ζ₁Compensation ζ (k), its influence to systematic function is offset to greatest extent, when | s (k) | be when smaller s (k) gradually During into quasisliding mode, compensated due to existing, can causedSo as to effectively suppress sliding formwork Buffet；

Step 3.2) approximately tried to achieve by formula (8) One-step delay estimation techniqueCan be completed in the case where d (k) is unknown To s_ref(k+1) solution, s_ref(k+1) vector form meets (9), wherein

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

Step 4) feedback compensation design：

Step 4.1) calculate the k moment predicated error be formula (10), wherein s (k) for k moment forecast models reality it is defeated Go out, and s (k | k-P) prediction for (k-P) moment to the k moment is exported, and meet formula (11)；

e_s(k)=s (k)-s (k | k-P) (10)

Step 4.2) add correction after, P step prediction output and its vector form be respectively (12), (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_pIt is correction coefficient, typically takes h₁=1,1 ＞ h₂＞ h₃ ＞ ... ＞ h_P＞ 0, i.e., with the increase of prediction step number, the effect of feedback compensation gradually weakens；

Step 5) rolling optimization design：

Step 5.1) design the k moment optimality criterion be formula (14), wherein, β_i、γ_iIt is non-negative weights, β_iIt is sampling The shared proportion in performance indications of moment error；γ_iIt is the limitation to input weight；Its vector form is formula (15)；

Wherein,

Step 5.2) determine population scale L, particle i position be u_i=(u_i1, u_i2..., u_iM), speed is v_i= (v_i1, v_i2..., v_iM), the span of weight coefficient w, maximum iteration t_max, Studying factors c₁、c₂, Particle Environment scope δ；

Step 5.3) optimality criterion J (k) is taken as value function Ψ is adapted to, according to proximate particle information, more new particle Position；Assuming that n in the proximate particle of particle i to possess the particle of optimal adaptation value, if adaptation of the adaptive value of particle i better than n Value, then keep the position of particle i constant；Otherwise, according to the position of formula (16) more new particle i, wherein ξ is random for [- 1,1] Number；The proximate particle of particle i is taken as position positioned at { (n_i1, n_i2..., n_iM)| |n_ij-u_ij|≤δ, j=1,2 ..., M } in not All particles including particle i；

u_i'=u_n+ξ(u_i-u_n) (16)

Step 5.4) according to the renewal equation of formula (17), position, the speed of iteration more new particle obtain the optimal position of population Put；

Wherein, history desired positions are p_i=(p_i1, p_i2..., p_iM), r₁、r₂It is the random number between [0,1], g =(g₁, g₂..., g_M) it is total optimization position；

Step 5.5) when maximum iteration is reached, optimizing terminates, and implements current controlled quentity controlled variable, and make k+1 → k return to step It is rapid 2).

Beneficial effect：A kind of algorithm based on sliding mode prediction fault tolerant control method for time_varying delay control system actuator failures, according to System output errors have obtained the system algorithm based on sliding mode prediction model with time varying characteristic, the model energy using pole-assignment design Enough while sliding mode asymptotically stability is ensured, dynamic improves the motion qualities of system；Consider that time lag system is subject to simultaneously in The influence of portion's Parameter Perturbation and external disturbance, it is proposed that a kind of new discrete sliding mode prediction reference track, the reference locus are not Only ensure that the state of system has good robustness and quick convergence, Er Qieneng during convergence sliding-mode surface It is enough significantly to suppress sliding formwork chattering phenomenon；Using multi-agent particle swarm algorithm improvement rolling optimization process, can either be quickly accurate Control law really is solved, the premature convergence problem of conventional particle group's algorithm can be prevented effectively from again, be used to contain time-varying for a class The robust Fault-Tolerant Control of the uncertain discrete-time system of time lag.With following specific advantage：

1. the algorithm based on sliding mode prediction model of system, the model have been obtained using pole-assignment design according to system output errors With time varying characteristic, and while sliding mode asymptotically stability is ensured, can dynamically improve the motion qualities of system；

2. a kind of novel Discrete sliding formwork reference locus influenceed with external disturbance while consideration inner parameter perturbs, can not only Enough ensure the state of system has good robustness and quick convergence during convergence sliding-mode surface, and can be bright Suppress sliding formwork chattering phenomenon aobviously；

3. using the rolling optimization process of multi-agent particle swarm algorithm improvement, compared to traditional method of derivation, can not only It is enough rapidly and accurately to solve the control law for meeting condition, while conventional particle group's algorithm can be prevented effectively from searching process Easily it is absorbed in the problem of Local Extremum.

Institute's extracting method of the present invention is as a kind of for the uncertain discrete-time system containing actuator failures and Time-varying time-delays Robust Fault-Tolerant Control method, with certain application value, it is easy to accomplish, real-time is good, and accuracy is high, can effectively improve control Security of system processed and workable, it is time-consuming, it is in hgher efficiency, can be widely applied to holding for uncertain discrete control system In the control of row device failure tolerant.

Brief description of the drawings

Fig. 1 is the flow chart of the inventive method；

What Tu2Shi Quanser companies developed is used to study the rotations of experimental provision Qball-X4 tetra- of four-rotor helicopter control Wing helicopter；

Fig. 3 is Qball-X4 four-rotor helicopter X-axis position curve figures；

Fig. 4 is Qball-X4 four-rotor helicopter X-direction speed curve diagrams；

Fig. 5 is Qball-X4 four-rotor helicopter Actuator dynamic curve maps；

Fig. 6 is control law curve map；

Fig. 7 is the control law curve map that part is amplified.

Specific embodiment

The present invention is done below in conjunction with the accompanying drawings further is explained.

As shown in figure 1, a kind of algorithm based on sliding mode prediction fault tolerant control method for time_varying delay control system actuator failures, according to System output errors have obtained the system algorithm based on sliding mode prediction model with time varying characteristic, the model energy using pole-assignment design Enough while sliding mode asymptotically stability is ensured, dynamic improves the motion qualities of system；Consider that time lag system is subject to simultaneously in The influence of portion's Parameter Perturbation and external disturbance, it is proposed that a kind of new discrete sliding mode prediction reference track, the reference locus are not Only ensure that the state of system has good robustness and quick convergence, Er Qieneng during convergence sliding-mode surface It is enough significantly to suppress sliding formwork chattering phenomenon；Using multi-agent particle swarm algorithm improvement rolling optimization process, can either be quickly accurate Control law really is solved, the premature convergence problem of conventional particle group's algorithm can be prevented effectively from again, be used to contain time-varying for a class The robust Fault-Tolerant Control of the uncertain discrete-time system of time lag, comprises the following specific steps that：

Step 1) determine uncertain discrete-time system model and its parameter：

Step 1.1) determine that the uncertain discrete-time system with actuator failures and Time-varying time-delays is formula (1), wherein, x (k) ∈RⁿIt is system mode, u (k) ∈ R^pFor system is input into, y (k) ∈ R^qFor system is exported, Δ A, Δ B and Δ A_dRespectively system is joined Number perturbation, A, B, A_d, C and E be appropriate dimension real matrix, v (k) ∈ RⁿIt is external disturbance, f (k) is failure function, τ (k) ∈ R⁺It is Time-varying time-delays；

Step 1.2) system (1) is rewritten as formula (2), wherein, d (k)=Δ Ax (k)+Δ Bu (k)+Δ A_dx(k-τ(k)) + v (k)+Ef (k), and d (k) meets | d (k)-d (k-1) |≤d₀And d_L≤|d(k)|≤d_U；

Step 2) forecast model design：

Step 2.1) definition system output errors be formula (3), wherein, y_rK () is desired output, y (k) is reality output；

E (k)=y (k)-y_r(k) (3)

Step 2.2) using linear sliding mode face s (k)=σ e (k), σ=[σ₁, σ₂..., σ_q] can be set by Method of Pole Placement Meter, then it is (4) that can obtain the algorithm based on sliding mode prediction model based on system output errors (3)；

S (k+1)=σ e (k+1) (4)

Step 2.3) according to nominal system x (k+1)=Ax (k)+Bu (k)+A of system (2)_dX (k- τ (k)) can be obtained Prediction of the forecast model at (k+P) moment exports (5) and its vector form (6)；

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

Wherein, P is prediction time domain, and M is control time domain, and meets M≤P, and controlled quentity controlled variable u (k+j) keeps in M-1≤j≤P U (k+M-1) is constant；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=[(σ CA)^T, (σ CA² )^T..., (σ CA^P)^T]^T；Y_r(k)=[y_r(k+1), y_r..., y (k+2)_r(k+P)]^T；

Step 3) reference locus design：

Step 3.1) design such as the reference locus of formula (7)：

Wherein, ζ (k)=σ d (k)=σ [Δs Ax (k)+Δ Bu (k)+Δ A_dX (k- τ (k))+v (k)+Ef (k)] represent system Influence of the equivalent total disturbance to sliding formwork output valve,s₀For Design constant, by selecting suitable s₀, control signal amplitude can be coordinated excessive and converge to s (k)=0 speed excessively slow two Relation between person；There is the interference of uncertain and failure due to system, AF panel means embedded in the reference locus, By using ζ₁Compensation ζ (k), its influence to systematic function is offset to greatest extent, when | s (k) | be when smaller s (k) gradually During into quasisliding mode, compensated due to existing, can causedSo as to effectively suppress sliding formwork Buffet；

Step 3.2) approximately tried to achieve by formula (8) One-step delay estimation techniqueCan be completed in the case where d (k) is unknown To s_ref(k+1) solution, s_ref(k+1) vector form meets (9), wherein

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

Step 4) feedback compensation design：

Step 4.1) calculate the k moment predicated error be formula (10), wherein s (k) for k moment forecast models reality it is defeated Go out, and s (k | k-P) prediction for (k-P) moment to the k moment is exported, and meet formula (11)；

e_s(k)=s (k)-s (k | k-P) (10)

Step 4.2) add correction after, P step prediction output and its vector form be respectively (12), (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_pIt is correction coefficient, typically takes h₁=1,1 ＞ h₂＞ h₃ ＞ ... ＞ h_P＞ 0, i.e., with the increase of prediction step number, the effect of feedback compensation gradually weakens；

Step 5) rolling optimization design：

Step 5.1) design the k moment optimality criterion be formula (14), wherein, β_i、γ_iIt is non-negative weights, β_iIt is sampling The shared proportion in performance indications of moment error；γ_iIt is the limitation to input weight；Its vector form is formula (15)；

Wherein,

Step 5.2) determine population scale L, particle i position be u_i=(u_i1, u_i2..., u_iM), speed is v_i= (v_i1, v_i2..., v_iM), the span of weight coefficient w, maximum iteration t_max, Studying factors c₁、c₂, Particle Environment scope δ；

Step 5.3) optimality criterion J (k) is taken as value function Ψ is adapted to, according to proximate particle information, more new particle Position；Assuming that n in the proximate particle of particle i to possess the particle of optimal adaptation value, if adaptation of the adaptive value of particle i better than n Value, then keep the position of particle i constant；Otherwise, according to the position of formula (16) more new particle i, wherein ξ is random for [- 1,1] Number；The proximate particle of particle i is taken as position positioned at { (n_i1, n_i2..., n_iM)| |n_ij-u_ij|≤δ, j=1,2 ..., M } in not All particles including particle i；

u_i'=u_n+ξ(u_i-u_n) (16)

Step 5.4) according to the renewal equation of formula (17), position, the speed of iteration more new particle obtain the optimal position of population Put；

Wherein, history desired positions are p_i=(p_i1, p_i2..., p_iM), r₁、r₂It is the random number between [0,1], g =(g₁, g₂..., g_M) it is total optimization position；

Step 5.5) when maximum iteration is reached, optimizing terminates, and implements current controlled quentity controlled variable, and make k+1 → k return to step It is rapid 2).

The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should It is considered as protection scope of the present invention.

Below with the validity of real case emulation explanation embodiment.

Made using the Qball-X4 four-rotor helicopters actuator of flight control system developed by Canadian Quanser companies It is application study object.Qball-X4 subjects such as Fig. 2.There are six dimension variables in Qball-X4 four-rotor helicopters, system That is (X, Y, Z, ψ, θ, φ), wherein X, Y, Z are location variable, and ψ is yaw angle, and θ is the angle of pitch, and φ is roll angle.Present case is imitated True selection X-axis direction of advance channel signal is used as research object.

Motion of the body on X-axis is influenceed by gross thrust and roll angle φ/pitching angle theta.Assuming that yaw angle ψ is 0, that The dynamical equation of X-axis is described as follows：

Wherein M_gIt is body quality, X is X-direction position.F is the thrust that rotor is produced：

Wherein, K_gIt is that, on the occasion of gain, ω is actuator bandwidth.Definition v is Actuator dynamic：

Its state-space expression is：

In X-axis position control model, pitching angle theta is coupled with it, and overall control can be divided into two stages, One is the angle of pitch control stage, waits the angle of pitch to control to after preset value, is put into second stage --- the position control stage. When position reaches setting position, pitching angle theta is zeroed by angle of pitch control passage.In the case of θ is less, by linear Change is obtained：

Assuming that in the X-axis position control stage, the angle of pitch has been scheduled on 2 ° of ≈ 0.035rad, it is considered to which external disturbance, parameter are taken the photograph Dynamic, network delay and actuator failures, introduce the related disturbance of Actuator dynamic, perturbation, time lag and failure, each in system (1) The value of matrix is as follows：

C=[1 0 0],Δ A=0.1A, Δ B=0.1B, Δ A_d=0.1A_d, x (0)=[1 1 1]^T, f (k)=1.5+ [0.2sin (2k) of 0.3sin (6k) 0] x (k), v K the element in () takes the white Gaussian noise that average is zero, sliding-mode surface coefficient matrix σ is taken as σ=[1].Population Studying factors c₁ =2, c₂=2, weight coefficient w_min=0.2, w_max=0.9, population scale is L=20, maximum iteration t_max=50, ring Border scope δ=6.What optimization time domain P was represented is that to approach the output that following P walk desired value at the k moment interested, optimizes time domain P The major part of controlled device dynamic effects should be covered.Practice have shown that, increasing P, system rapidity reduction, the stability of a system increases By force；Reduce P, then contrast.So present case emulation selection takes into account the prediction time domain P=4 of rapidity and stability.During control Domain M represents the change number of following controlled quentity controlled variable to be determined, and increase reduces influences of the M to system and P contrasts, for dynamic Step response is not that sufficiently complex system M is typically chosen as 1~2, therefore present case Simulation Control time domain elects M=2 as.Emulation time domain K=1000 is taken, wherein, organism parameter value is K=120N, ω=15rad/s, M=1.4kg.Control input PWM may bring Time lag, and and then have influence on vertical direction acceleration dynamic and produce time lag.Because time lag size is uncertain, sheet Simulation case Time-varying time-delays take the random integers between [1,3].

Simulation result shows that the designed fault tolerant control method of present case emulation is not true to the time lag with actuator failures Determining system has stronger robustness and it can be made quickly to tend towards stability.Compared with traditional sliding-mode control, four rotors Helicopter body, by Fig. 3-Fig. 5, is not difficult to find out X-axis position, X-axis in the presence of the designed control method of present case emulation Position and speed and Actuator dynamic change curve are more gentle, and whole flight course body will not occur apparent shake.Together When, control law Fast Convergent and larger fluctuation will not be produced, after convergence in the absence of obvious buffeting, such as Fig. 6.Although using this Simulation case method is still present certain buffeting, but buffeting amplitude has been cut in nearly half, such as Fig. 7.In general, for containing There is the actuator failures system of Parameter Perturbation, external disturbance and Time-varying time-delays, the control method of present case emulation is effective 's.

Claims (1)

1. a kind of algorithm based on sliding mode prediction fault tolerant control method for time_varying delay control system actuator failures, it is characterised in that：According to System output errors have obtained the system algorithm based on sliding mode prediction model with time varying characteristic, the model energy using pole-assignment design Enough while sliding mode asymptotically stability is ensured, dynamic improves the motion qualities of system；Consider that time lag system is subject to simultaneously in The influence of portion's Parameter Perturbation and external disturbance, it is proposed that a kind of new discrete sliding mode prediction reference track, the reference locus are not Only ensure that the state of system has good robustness and quick convergence, Er Qieneng during convergence sliding-mode surface It is enough significantly to suppress sliding formwork chattering phenomenon；Using multi-agent particle swarm algorithm improvement rolling optimization process, can either be quickly accurate Control law really is solved, the premature convergence problem of conventional particle group's algorithm can be prevented effectively from again, be used to contain time-varying for a class The robust Fault-Tolerant Control of the uncertain discrete-time system of time lag, comprises the following specific steps that：

Step 1) determine uncertain discrete-time system model and its parameter：

Step 1.1) determine that the uncertain discrete-time system with actuator failures and Time-varying time-delays is formula (1), wherein, x (k) ∈ Rⁿ It is system mode, u (k) ∈ R^pFor system is input into, y (k) ∈ R^qFor system is exported, Δ A, Δ B and Δ A_dRespectively systematic parameter is taken the photograph It is dynamic, A, B, A_d, C and E be appropriate dimension real matrix, v (k) ∈ RⁿIt is external disturbance, f (k) is failure function, τ (k) ∈ R⁺For Time-varying time-delays；

$\left\{\begin{array}{c}x(k+1)=(A+\mathrm{\Δ}A)x\left(k\right)+(B+\mathrm{\Δ}B)u\left(k\right)+(A_d+{\mathrm{\ΔA}}_d)x(k-\mathrm{\τ}(k\left)\right)+v\left(k\right)+Ef\left(k\right)\\ y\left(k\right)=Cx\left(k\right)\end{array}\right.---\left(1\right)$

Step 1.2) system (1) is rewritten as formula (2), wherein, d (k)=Δ Ax (k)+Δ Bu (k)+Δ A_dx(k-τ(k))+v(k) + Ef (k), and d (k) meets | d (k)-d (k-1) |≤d₀And d_L≤|d(k)|≤d_U；

$\left\{\begin{array}{c}x(k+1)=Ax\left(k\right)+Bu\left(k\right)+A_{d}x(k-\mathrm{\τ}(k\left)\right)+d\left(k\right)\\ y\left(k\right)=Cx\left(k\right)\end{array}\right.---\left(2\right)$

Step 2) forecast model design：

Step 2.1) definition system output errors be formula (3), wherein, y_rK () is desired output, y (k) is reality output；

E (k)=y (k)-y_r(k) (3)

Step 2.2) using linear sliding mode face s (k)=σ e (k), σ=[σ₁, σ₂..., σ_q] can be designed by Method of Pole Placement, then It is (4) that the algorithm based on sliding mode prediction model based on system output errors (3) can be obtained；

S (k+1)=σ e (k+1) (4)

Step 2.3) according to nominal system x (k+1)=Ax (k)+Bu (k)+A of system (2)_dX (k- τ (k)) can obtain predicting mould Prediction of the type at (k+P) moment exports (5) and its vector form (6)；

$\begin{array}{c}s(k+P)=\mathrm{\σ}e(k+P)=\mathrm{\σ}\[y(k+P)-y_r(k+P)\]=\mathrm{\σ}Cx(k+P)-y_r(k+P)\\ =\mathrm{\σ}C\[A^{P}x\left(k\right)+\underset{i=1}{\overset{P}{\mathrm{\Σ}}}{A}^{i-1}{A}_{d}x(k+P-i-\mathrm{\τ}(k+P-i\left)\right)\\ +\underset{i=1}{\overset{M-1}{\mathrm{\Σ}}}{A}^{P-i}Bu(k+i-1)+\underset{i=1}{\overset{P-M}{\mathrm{\Σ}}}{A}^{i}Bu(k+M-1)\]-{\mathrm{\σy}}_r(k+P)\end{array}---\left(5\right)$

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

Wherein, P is prediction time domain, and M is control time domain, and meets M≤P, and controlled quentity controlled variable u (k+j) keeps u (k+ in M-1≤j≤P M-1 it is) constant；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=[(σ CA)^T, (σ CA²)^T..., (σCA^P)^T]^T；Y_r(k)=[y_r(k+1), y_r..., y (k+2)_r(k+P)]^T；

Step 3) reference locus design：

Step 3.1) design such as the reference locus of formula (7)：

$\left\{\begin{array}{c}{s}_{ref}(k+1)=(1-\frac{s_0}{s_0+\left|s\left(k\right)\right|})s_{ref}\left(k\right)-\mathrm{\ζ}\left(k\right)+{\mathrm{\ζ}}_1\\ s_{ref}\left(k\right)=s\left(k\right)\end{array}\right.---\left(7\right)$

Wherein, ξ (k)=σ d (k)=σ [Δs Ax (k)+Δ Bu (k)+Δ A_dX (k- τ (k))+v (k)+Ef (k)] represent that system is equivalent The influence to sliding formwork output valve is always disturbed,s₀It is design Constant, by selecting suitable s₀, can coordinate control signal amplitude it is excessive and converge to s (k)=0 speed excessively it is slow both it Between relation；There is the interference of uncertain and failure due to system, AF panel means are embedded in the reference locus, pass through Using ζ₁Compensation ξ (k), offsets its influence to systematic function, when | s (k) | is that s (k) is progressed into when smaller to greatest extent During quasisliding mode, compensated due to existing, can causedBuffeted so as to effectively suppress sliding formwork；

Step 3.2) approximately tried to achieve by formula (8) One-step delay estimation techniqueCan complete right in the case where d (k) is unknown s_ref(k+1) solution, s_ref(k+1) vector form meets (9), wherein J=1,2 ..., P；

$\begin{array}{c}\hat{d}\left(k\right)=d(k-1)=x\left(k\right)-Ax(k-1)-A_{d}x(k-1-\mathrm{\τ}(k-1\left)\right)\\ -Bu(k-1)\end{array}---\left(8\right)$

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

Step 4) feedback compensation design：

Step 4.1) calculate the k moment predicated error be formula (10), wherein s (k) for k moment forecast models reality output, s (k | k-P) prediction for (k-P) moment to the k moment is exported, and meet formula (11)；

e_s(k)=s (k)-s (k | k-P) (10)

$\begin{array}{c}s\left(k\right|k-P)=\mathrm{\σ}C\[A^{P}x(k-P)+\underset{i=1}{\overset{P}{\mathrm{\Σ}}}{A}^{i-1}{A}_{d}x(k-i-\mathrm{\τ}(k-i\left)\right)\\ +\underset{i=1}{\overset{M-1}{\mathrm{\Σ}}}{A}^{P-i}Bu(k-P+i-1)+\underset{i=1}{\overset{P-M}{\mathrm{\Σ}}}{A}^{i}Bu(k-P+M-1)\]-{\mathrm{\σy}}_r\left(k\right)\end{array}---\left(11\right)$

Step 4.2) add correction after, P step prediction output and its vector form be respectively (12), (13)；

$\tilde{s}(k+P)=s(k+P)+h_P{e}_s\left(k\right)---\left(12\right)$

${\hat{S}}_{PM}\left(k\right)=S_{PM}\left(k\right)+H_P{E}_s\left(k\right)---\left(13\right)$

Wherein,

E_S(k)=[s (k)-s (k | k-1), s (k)-s (k | k-2) ..., s (k)-s (k | k-P)]^T, h_pIt is correction coefficient, typically Take h₁=1,1 ＞ h₂＞ h₃＞ ... ＞ h_P＞ 0, i.e., with the increase of prediction step number, the effect of feedback compensation gradually weakens；

Step 5) rolling optimization design：

Step 5.1) design the k moment optimality criterion be formula (14), wherein, β_i、γ_lIt is non-negative weights, β_iIt is sampling instant The shared proportion in performance indications of error；γ_lIt is the limitation to input weight；Its vector form is formula (15)；

$j\left(k\right)=\underset{i=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\β}}_i{\[s_{ref}(k+i)-\tilde{s}(k+1)\]}^2+\underset{l=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\γ}}_l{\[u(k+l-1)\]}^2---\left(14\right)$

$J\left(k\right)={\[S_{ref}\left(k\right)-{\tilde{S}}_{PM}\left(k\right)\]}^{T}Q\[S_{ref}\left(k\right)-{\tilde{S}}_{PM}\left(k\right)\]+{\[U\left(k\right)\]}^{T}R\[U\left(k\right)\]---\left(15\right)$

Wherein,

Step 5.2) determine population scale L, particle i position be u_i=(u_i1, u_i2..., u_iM), speed is v_i=(v_i1, v_i2..., v_iM), the span of weight coefficient w, maximum iteration t_max, Studying factors c₁、c₂, Particle Environment scope δ；

Step 5.3) optimality criterion J (k) is taken as value function Ψ is adapted to, according to proximate particle information, update particle position； Assuming that n in the proximate particle of particle i to possess the particle of optimal adaptation value, if adaptive value of the adaptive value of particle i better than n, Keep the position of particle i constant；Otherwise, according to the position of formula (16) more new particle i, wherein ξ is the random number of [- 1,1]；Particle The proximate particle of i is taken as position positioned at { (n_i1, n_i2..., n_iM)||n_ij-u_ij|≤δ, j=1,2 ..., M } in not include particle All particles of i；

u_i'=u_n+ξ(u_i-u_n) (16)

Step 5.4) according to the renewal equation of formula (17), position, the speed of iteration more new particle obtain population optimal location；

$\left\{\begin{array}{c}{v}_i^{t+1}={\mathrm{wv}}_i^t+c_1{r}_1(p_i-u_i^t)+c_2{r}_2(g-u_i^t)\\ u_i^{t+1}=u_i^t+v_i^{t+1}\\ w=w_{\min }+\[(t_{\max }-t)(w_{\max }-w_{\min })\]/t_{\max }\end{array}\right.---\left(17\right)$

Wherein, history desired positions are p_i=(p_i1, p_i2..., p_iM), r₁、r₂It is the random number between [0,1], g=(g₁, g₂..., g_M) it is total optimization position；

Step 5.5) when maximum iteration is reached, optimizing terminates, and implements current controlled quentity controlled variable, and make k+1 → k return to step 2)。