CN113885335B - Fault-tolerant control method for networked system with partial decoupling disturbance - Google Patents
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Abstract
The invention discloses a networked system fault-tolerant control method with partial decoupling disturbance, belonging to the field of networked systems; firstly, the original system is converted into a state augmentation system equivalent to the original system through model conversion; then under the condition that the random loss of measured data is considered, constructing an unknown input observer to realize the joint estimation of the system state and the fault, and designing a fault-tolerant control law based on signal compensation to realize the active fault-tolerant control of the original system based on the on-line estimation values of the state and the fault. In the fault-tolerant control algorithm, the existence conditions of the observer and the controller gain can be obtained by utilizing Lyapunov stability theory to carry out random analysis on an error system, and corresponding estimator and controller parameters can be obtained by solving matrix inequality with convex constraint on line. Finally, the effectiveness of the proposed fault-tolerant control method is verified by means of a simulation example of a jet engine model.
Description
Technical Field
The invention belongs to the field of networked systems, and relates to a fault-tolerant control method of a networked system with partial decoupling disturbance.
Background
With the improvement of the industrial automation degree and the development of the technology in the intelligent manufacturing field, the trend of the high integration of the control system and the communication network is more obvious. The Network Control System (NCSs) is a closed loop feedback control system formed by highly integrated interaction of network units and controlled objects through a shared network, and has the advantages of low cost, simple installation, convenient maintenance and the like, and is recently and continuously focused by students at home and abroad, and widely applied to a plurality of practical engineering fields.
However, in practical application, the introduction of the communication network increases the flexibility and the extension convenience of the system, and simultaneously brings new challenges to the analysis and design of the system, such as data packet loss, transmission delay, quantization error, network attack, and the like. On the other hand, due to the increasing size and complexity of modern industrial systems, the probability of system failure is also increasing. Any minor or potential failure of such complex large systems, if not diagnosed and handled effectively in time, can trigger a chain reaction until the system crashes, even with catastrophic consequences. The common method for solving the series of problems is to construct a proper fault-tolerant control law so as to ensure that the system can still stably run under the fault condition.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a fault-tolerant control method of a networked system with partial decoupling disturbance. Aiming at the joint estimation and fault-tolerant control problems of the state and the fault of a discrete time networked control system with actuator faults and partial decoupling disturbance. In the case of random loss of measurement data, joint estimation of system state and fault is realized by constructing an unknown input observer. And then, based on the result of fault estimation, adopting a fault-tolerant control strategy based on signal compensation to reduce the influence of the fault on the system performance.
The technical scheme of the invention is as follows:
a networked system fault-tolerant control method with partial decoupling disturbance comprises the following steps:
1) A model of a discrete-time networked system of the type shown below is built:
wherein:
represented as a state vector, input vector and measurable output of the system, respectively, < >>
Is a bounded unknown input vector that may be caused by disturbances or modeling errors; />
For measuring noise of the system, w (k) εl 2 [0,∞),l 2 [0, +.E) is expressed as a space consisting of square integrable measurable functions,
let Δf (k) =f (k+1) -f (k) be the actuator fault signal to be estimated, here let Δf (k) be bounded, i.e. the rate of change of f (k) is moderate; />
Are constant matrices of the system, E is a faultA component matrix of the signal; furthermore, the->
Wherein assume d 1 (k) Is unknown but can be decoupled, and d 2 (k) Is not decoupled, B and B d1 Are all in a full rank matrix; n is the dimension of the system state vector, m is the dimension of the input vector, p is the dimension of the measurable measurement output, q is the dimension of the measurement noise, l d For the dimension of the unknown input vector, l f For the dimension of the fault signal>
Decoupling the dimension of the partial vector for unknown inputs, +.>
The dimensionality of the partial vector cannot be decoupled for unknown inputs, +.>
Representing the real number domain;
under the condition of random packet loss, the input signals received by the unknown input observer are as follows:
wherein:
the random variable beta (k) satisfies Bernoulli distribution and is used for representing the possible packet loss phenomenon of the system in a network channel; when beta (k) =1, it indicates that no data packet is lost in the system, and when beta (k) =0, it indicates that all data packets are lost in the system, and the probability of packet loss is expressed as
Expressed as packet loss rate;
2) Modeling of augmentation systems
To obtain estimates of both system state and failure, the system (1) is augmented to the form:
wherein, 
by constructing a suitable observer, the state estimation value of the augmentation system can be obtained
The state of the original system and the estimated value of the fault can be obtained respectively according to the following formulas;
3) Designing an unknown input observer:
wherein:
to augment the state estimate of the system, +.>
Is the state vector of the unknown input observer, +.>
For being designed forA gain matrix;
defining an estimated error vector as
Further calculation may be made of:>
to ensure that the estimated error value is as small as possible due to the presence of random numbers, both sides of equation (6) are expected simultaneously, with the following result:
the dynamic estimation error can be written as:
in the process, let
Using it to represent the augmented state value of previous moment and k > 1;
4) The error dynamic system (8) is an input-state stable and sufficient condition for unknown input observer presence is:
wherein:
η(k)＝e(k+1)-e(k),/>
L 1 ＝P -1 Y,L 2 ＝RH，/>
* Representing a transpose of the symmetric position matrix, 0 being a zero matrix;
all are unknown matrixes to be determined; alpha is a given constant, +.>
γ δ > 0 is a given system performance index, +.>
And->
The dimensions of the corresponding identity matrices of the 5 th row 5 column and the 6 th row 6 column in the formula (9) are respectively represented;
given constant
And +.>
γ δ The system performance index is more than 0, the LMI tool box in MATLAB is utilized to solve the formula (9), when a positive definite matrix P and a matrix Y exist to enable the formula (9) to be established, the system is stable in input-state, and an accurate estimated value of the augmentation state of the system (3) can be obtained, namely, the step 5) can be carried out; when the unknown variable is not available, the system is not stable in input-state, and an accurate estimated value of the augmentation state of the system (3) cannot be obtained, and step 5) cannot be performed;
5) Networked system fault tolerant control with partial decoupling disturbance
The system is arranged in a normal running state of the system, namely, in the case of no fault, a static output feedback controller exists in the system in advance, and the static output feedback controller comprises the following forms:
the task is then to design a suitable feedback gain K to maintain a gradual steady performance of the system (1) and to meet specific performance criteria.
When obtaining the estimated value of the system actuator fault, the compensation can be performed by giving an additional signal, and ensuring that the system still has good input-state stable performance, and the compensation signal of the system can be designed as follows
Wherein the method comprises the steps of
Expressed as matrix->
Is a generalized inverse matrix of (2);
thus, a fault tolerant control law based on signal compensation can be designed in the form of:
bringing a new control law (10) into the system (1) to establish a new closed-loop system with fault tolerance, as follows:
wherein A is δ ＝A+β(k)BKC,
B e ＝EJ 2 ,/>
Obtaining a residual signal e (k) of an unknown input observer by a formula (8), and then obtaining an estimated value of the system state by a formula (4)
And the estimated value f (k) of the fault, finally adopting the fault-tolerant control law of the formula (10) to eliminate the influence of the fault on the system and ensure the input-state stability of the system.
Further, in the step 5), a suitable feedback gain K is designed to enable the system (1) to maintain progressive stability performance and meet specific performance indexes, and the following quadratic form indexes for maintaining performance control are selected as follows:
wherein Q and M are given symmetric positive definite matrixes with proper dimensions, the Lyapunov stability theory is utilized, the existence condition of a conservation-state feedback control law is utilized, and the feedback gain K is easily obtained by solving a linear matrix equation.
The method has the beneficial effects that the method considers the design method of the unknown input observer under the conditions of system executor faults, random packet loss and partial decoupling disturbance existing in the networked system, realizes joint estimation of the system state and faults through the design of the unknown input observer, still accurately and effectively estimates the faults occurring in the system under the conditions of random packet loss and partial decoupling disturbance, and effectively reduces the influence of the faults and external disturbance on the stability performance of the system through an active fault-tolerant control strategy based on signal compensation.
Drawings
FIG. 1 is a flow chart of a networked system fault-tolerant control method in the presence of a partially decoupled disturbance.
FIG. 2 is a graph of five state components of a networked system compared to corresponding estimates of actuator faults. Wherein a is x1, b is x2, c is x3, d is x4, e is x5, and f is f (k);
fig. 3 is a diagram of a first system state component comparison for three different situations.
Fig. 4 is a comparison of the second system state components for three different situations.
Fig. 5 is a diagram of a third system state component comparison for three different situations.
Fig. 6 is a fourth system state component comparison plot for three different cases.
Fig. 7 is a diagram of a fifth comparison of system state components for three different situations.
Detailed Description
The following describes the embodiments of the present invention further with reference to the drawings.
Referring to fig. 1, a fault-tolerant control method for a networked system with a partial decoupling disturbance includes the following steps:
step 1, establishing a model of a discrete time networking system shown as follows
The model of the networked system with actuator failure, external interference and random packet loss is given by formula (12):
disturbance decomposition can better mitigate the adverse effects of interference. It is therefore desirable to achieve as complete decoupling of the disturbance as possible. For systems that are subject to disturbances that cannot be completely decoupled, optimization techniques are typically employed to decouple some of the disturbance components while attenuating the disturbance components that cannot be decoupled.
For bounded unknown input vectors, possibly caused by disturbances or modeling errors,/for example>
Wherein assume d 1 (k) Is unknown but can be decoupled, and d 2 (k) Is not decoupled;
because the bandwidth of the network is limited, a random packet loss phenomenon may occur in the signal transmission process of the system, so that a certain amount of estimator input data is lost, and under the condition that random packet loss exists, an input signal received by an unknown input observer is:
wherein:
the random variable beta (k) satisfies Bernoulli distribution and is used for representing the possible packet loss phenomenon of the system in a network channel; when beta (k) =1, it indicates that no data packet is lost in the system, and when beta (k) =0, it indicates that all data packets are lost in the system, and the probability of packet loss is expressed as
Expressed as packet loss rate;
hypothesis 1. Matrix
And->
Satisfies the following formula:
suppose 2. For Re (z). Gtoreq.0, the following equation holds:
To obtain estimates of both system status and faults, the system (12) is augmented as follows:
wherein, 
lemma 1 if the system satisfies hypothesis 1, then a matrix exists
So that the following equation holds:
proof that formula (18) can be written as
Due to
And->
Is a column full order matrix, i.e.)>
Let go of combination hypothesis 1>
Thus, formula (19) is solved, proving complete, wherein a special solution is
2, if the system meets assumption 2, the system
Is observable, i.e. satisfies the following equation for an arbitrary complex z whose real part is non-negative:
wherein, 
it is demonstrated that any complex z with a non-negative real part, equation (21) can be converted into the following form:
further calculations may result in that when z=1, the above formula (22) may be equivalent to
When z.noteq.1, formula (22) may be equivalent to
Wherein Re (z) is equal to or greater than 0, and is proved to be finished because the system meets the assumption 2.
Step 3, designing an unknown input observer
Wherein:
to augment the state estimate of the system, +.>
Is the state vector of the unknown input observer, +.>
An unknown input observer gain matrix to be designed;
defining a residual error signal:
based on the lemma 1 and the lemma 2, the following equation can be made to hold:
taking the formulas (1), (3), (25) and (27) together, a dynamic estimation error systematic formula (18) can be obtained:
in the process, let
Which is defined as the augmented state value of the previous instant and k > 1;
from the above, d 1 (k) Can be completely decoupled by introducing H to satisfy the condition, and d 2 (k) Still present. The next task is therefore to design a reasonable observer gain such that the error vector e is estimated(k) Remain stable and reduce d as much as possible 2 (k) Influence on e (k).
Definition 1 (i) if there is a function γ:
satisfying the condition of continuous, strictly increasing, and γ (0) =0, then it can be called a K function; when γ is a K function, and when s.fwdarw.infinity, γ(s). Fwdarw.infinity, γ is called K ∞ A function.
(ii) Function of
The K function is decreased in any interval that s is more than or equal to 0. Then for any interval where t is greater than or equal to 0, σ (s, t) is equal to 0 when t→infinity, at which time the function σ may be referred to as the Kl function.
Primer 3 ream
As a continuous function, the system (12) may be said to be input-state stable if it satisfies the following two conditions. Wherein, the euclidean norm or matrix spectral norm of the corresponding vector is denoted.
(i) Presence of K ∞ Function psi 1 Sum phi 2 Satisfies the following formula:
(ii) Presence of K ∞ Function psi 3 And K function ψ 4 So that the following is true
Wherein h (x, v) is expressed as a binary function with x and v as independent variables, and v is a new independent variable;
step 4. Dynamic estimation of error System input-State stabilization and sufficient conditions for unknown input observer to exist
Step 4.1 dynamic estimation error System input-sufficient Condition for State stabilization
Selecting the Lyapunov function in the following form:
V(e(k))＝e T (k)Pe(k) (31)
it is obvious that
λ min (P)||e(k)|| 2 ≤V(e(k))≤λ max (P)||e(k)|| 2 (32)
Equation (31) shows that V (e (k)) satisfies condition (29) in lemma 3. Wherein, psi is 1 (||e(k)||)＝λ min (P)||e(k)|| 2 ,ψ 2 (||e(k)||)＝λ max (P)||e(k)|| 2 ,λ min Representing the minimum eigenvalue, lambda, of a real symmetric matrix max Representing the maximum eigenvalue of the real symmetric matrix;
definition η (k) =e (k+1) -e (k), obtainable from formula (28)
As can be seen from the equation (30), let e (k+1) =h (x (k), v (k)), then
ΔV(e(k))＝V(e(k+1))-V(e(k))＝V(h(x , v))-V(x)
And obtaining the sufficient conditions of the input-state stability of the error system formula (18) and the existence of an unknown input observer by using a Lyapunov stability theory and a linear matrix inequality analysis method. The method comprises the following steps:
assuming that expression (33) holds:
wherein:
L 1 ＝P -1 Y,L 2 ＝RH,/>
* Representing a transpose of the symmetric position matrix, 0 being a zero matrix; />
All are unknown matrixes to be determined; alpha is a given constant, +.>
γ δ > 0 is a given system performance index, +.>
And->
The dimensions of the corresponding identity matrices of the 5 th row 5 column and the 6 th row 6 column in the formula (9) are respectively represented;
the Lyapunov function (31) is biased along the trajectory of the system as follows:
by the transformation of the equation, the right side of equation (34) can be equivalent to equation (35)
Wherein, 
LMI (25) shows that Ω < 0, as known from formula (27), is->
Y＝PL 1 ；
Further calculate and get
Because-alpha V (e (k))isless than or equal to-alpha lambda min (P)||e(k)|| 2 Formula (36) may be written as follows:
equation (37) means that the original system satisfies condition (30) in lemma 3, where ψ 3 (||e(k)||)＝αλ min (P)||e(k)|| 2 ,
The error dynamic system (28) is input-state stable;
if positive definite matrices P > 0 and Y exist such that equation (33) holds, the system is input-state stable. When the dynamic estimation error system obtained in the step 4.1 is stable in input-state, executing the step 4.2; if the dynamic estimation error system obtained in step 4.1 is not input-state stable, step 4.2 cannot be performed;
step 4.2. Unknown sufficient conditions for the input observer to exist
To establish a sufficient condition for the existence of an unknown input observer, assuming that equation (9) is established, a constant is given according to Lyapunov stability theory
And +.>
γ δ Solving formula (9) by using LMI toolbox in MATLAB, and existence of positive definite matrix P and matrix Y, so that the system satisfies input-state stability, and the intermediate observer parameter is L 1 ＝P -1 Y and can be calculated by formula (27), i.e. step 5) can be performed; when the above unknown variables have no feasible solution, the system is not input-state stable and cannot obtain unknown input observer parameters, cannot proceed to step 5)
Step 5, networked system fault-tolerant control with partial decoupling disturbance
The system is arranged in a normal running state of the system, namely, in the case of no fault, a static output feedback controller exists in the system in advance, and the static output feedback controller comprises the following forms:
the task is then to design a suitable feedback gain K to maintain a gradual steady performance of the system (1) and to meet specific performance criteria. For example, the following quadratic index of the performance control may be selected:
wherein, Q and M are given symmetric positive definite matrixes with proper dimensions, and the feedback gain K is easily obtained by solving a linear matrix equation by using the Lyapunov stability theory and the existence condition of the protection performance state feedback control law, which is not described herein in detail in view of the limitation of the space.
When obtaining the estimated value of the system actuator fault, the compensation can be performed by giving an additional signal, and ensuring that the system still has good input-state stable performance, and the compensation signal of the system can be designed as follows
Wherein the method comprises the steps of
Expressed as matrix->
Is a generalized inverse matrix of (2);
thus, a fault tolerant control law based on signal compensation can be designed in the form of:
bringing a new control law (39) into the system (1) to establish a new closed loop system with fault tolerance as follows:
wherein A is δ ＝A+β(k)BKC,
B e ＝EJ 2 ,/>
Applying the method to design a Lyapunov function for a new closed loop system to enable the Lyapunov function to meet the conditions (29) and (30) in the quotients 3, and assuming that the function form is
Then
To demonstrate that the new closed loop system still has good input-state stability performance, the following Lyapunov function is selected:
wherein epsilon is more than 0,
is of the order of LyaThe punov function satisfies a positive definite matrix of the satisfaction condition.
Thus, the process is carried out,
the condition (29) in the lemma 3 is satisfied, wherein, < ->
Obtainable from (37)
E{ΔV(x(k))}＜E{-α e ||e(k)|| 2 +γ e ||v(k)|| 2 } (43)
Wherein alpha is e ＝αλ min (P),
The combination of (35), (42) and (43) can be pushed out
Wherein alpha is c 、γ c 、ε e 、ε d And epsilon x Are all positive scalar quantities, and the total number of the two scalar quantities is equal,
select->
Combinations of (43) and (44) are available
Wherein, 
β xe ＝max{εγ e ,γ c +ε d }. Because ofThe closed loop system (39) satisfies conditions (29) and (30) in the quotation 3, that is, the system is input-state stable.
Examples:
by adopting the networked system fault-tolerant control method with partial decoupling disturbance, the dynamic estimation error system (28) is stable in input-state under the condition of considering external disturbance and faults. The specific implementation method is as follows:
jet gas turbine engines can be essentially described as a thermodynamic model that uses the atmosphere as a working medium to produce propulsion thrust and mechanical power, and because of its highly nonlinear dynamic structure, are modeled herein at some set point as a linearized 17-stage system, with system variables including pressure, absolute temperature, static pressure, shaft speed, air and gas mass flow rate. The 17 th order model may be reduced to a 5 th order jet engine model of the form (1), N, for simplicity of operation and ease of implementation L 、N H Respectively the low-pressure valve core speed and the high-pressure valve core speed, T 7 、T 29 Respectively measuring the temperature of the tail gas and the outlet temperature of the combustion chamber, P 6 For the nozzle pressure, M f For the fuel flow of the host, A J Is the area of the tail gas nozzle.
Selecting
The system parameters are given as%>
To reflect the effect of an unknown input observer, it is assumed that the actuator fault signal f= [ f a f a f a f a ],E＝[B 0 5×2 ]；
Meanwhile, in the system (9), a disturbance input is given, and in the actual system, the disturbance input is always present, assuming that the disturbance input is a random signal ranging in amplitude from-0.001 to 0.001; h can be solved by using equation (15), α= -5 is selected,
γ δ =0.78, packet loss rate +.>
Then solving the formula (25) by using an LMI tool box to obtain parameters P and Y, and respectively solving a gain matrix T and L of the UIO according to the formula (17) 1 ,L 2 And R.
The fault tolerant controller based on signal compensation used herein is in the form of:
wherein, 
J 2 ＝[0 4× 5 I 4 ]。
the data required herein can be obtained by simulation with MATLAB software, wherein the specific simulation patterns are shown in fig. 2-7.
Fig. 1 shows the state of the closed loop system and its estimated value, the blue solid line represents the state value of the system, and the red dashed line represents the estimated value of the state of the system. In this example, the fault types considered by the networked system include a gradual fault and a constant fault, and as can be seen from fig. 1, the observer provided herein can obtain a better estimation effect no matter what fault type is affected. Therefore, an efficient estimation of the networked system can be achieved with the proposed UIO-based fault estimation strategy.
Fig. 2-6 show five state components in three cases, namely a state in the absence of a fault, a state in the presence of a fault, and a state after fault tolerance has been implemented. As can be seen from the figure, the fault-tolerant control law designed herein can effectively reduce the influence of faults on the system state under the condition of data packet loss and external interference.
In summary, according to simulation results, under the condition that random packet loss and partial decoupling disturbance exist, the designed unknown input observer can effectively obtain the state of the system and the estimated value of the fault, and in the networked system, the fault-tolerant control mode based on signal compensation is adopted to effectively reduce the influence of the fault on the stability of the system, so that the problem of various fault and disturbance forms can be well solved by adopting the unknown input strategy, and meanwhile, the fault-tolerant control method of the networked system with partial decoupling disturbance provided by the invention is also effective.
Claims (2)
1. A networked system fault tolerant control method with partial decoupling disturbance, comprising the steps of:
1) A model of a discrete-time networked system of the type shown below is built:
wherein:
represented as a state vector, input vector and measurable output of the system, respectively, < >>
Is a bounded unknown input vector that may be caused by disturbances or modeling errors; />
For measuring noise of the system, w (k) εl 2 [0,∞)，l 2 [0, +.E) is expressed as a space consisting of square integrable measurable functions, and (2)>
Let Δf (k) =f (k+1) -f (k) be the actuator fault signal to be estimated, here let Δf (k) be bounded, i.e. the rate of change of f (k) is moderate; />
The constant matrix of the system is adopted, and E is the component matrix of the fault signal; furthermore, the->
Wherein d is provided with 1 (k) Is unknown but can be decoupled, and d 2 (k) Is not decoupled, B and +>
Are all in a full rank matrix; n is the dimension of the system state vector, m is the dimension of the input vector, p is the dimension of the measurable measurement output, q is the dimension of the measurement noise, l d For the dimension of the unknown input vector, l f For the dimension of the fault signal>
Decoupling the dimension of the partial vector for unknown inputs, +.>
The dimensionality of the partial vector cannot be decoupled for unknown inputs, +.>
Representing the real number domain;
under the condition of random packet loss, the input signals received by the unknown input observer are as follows:
wherein:
the random variable beta (k) satisfies Bernoulli distribution and is used for representing the possible packet loss phenomenon of the system in a network channel; when beta (k) =1, it indicates that no packet is lost in the system, and when beta (k) =0, it indicates that all packets are lost in the system, and the probability of packet loss is expressed as +.>
Expressed as packet loss rate;
2) Modeling of augmentation systems
To obtain estimates of both system state and failure, the system (1) is augmented to the form:
wherein, 
i is an identity matrix;
obtaining state estimates for an augmentation system by constructing appropriate observers
The state of the original system and the estimated value of the fault can be obtained respectively according to the following formulas; />
3) Designing an unknown input observer:
wherein:
to augment the state estimate of the system, +.>
Is the state vector of the unknown input observer,
a gain matrix to be designed;
defining an estimated error vector as
Further calculations may be:
to ensure that the estimated error value is as small as possible due to the presence of random numbers, both sides of equation (6) are expected simultaneously, with the following result:
the dynamic estimation error can be written as:
in the process, let
Using it to represent the augmented state value of previous moment and k > 1;
4) The error dynamic system (8) is an input-state stable and sufficient condition for unknown input observer presence is:
wherein:
η(k)＝e(k+1)-e(k)，/>
L 1 ＝P -1 Y，L 2 ＝RH，/>
* Representing a transpose of the symmetric position matrix, 0 being a zero matrix; />
All are unknown matrixes to be determined; alpha is a given constant, +.>
γ δ > 0 is a given system performance index, +.>
And->
The dimensions of the corresponding identity matrix of the 5 th row and 5 th column and the 6 th row and 6 th column in the formula (9) are respectively represented;
given a constant alpha,
And +.>
γ δ The system performance index is more than 0, the LMI tool box in MATLAB is utilized to solve the formula (9), when a positive definite matrix P and a matrix Y exist to enable the formula (9) to be established, the system is stable in input-state, and an accurate estimated value of the augmentation state of the system (3) can be obtained, namely, the step 5) can be carried out; when the unknown variable is not available, the system is not stable in input-state, and an accurate estimated value of the augmentation state of the system (3) cannot be obtained, and step 5) cannot be performed;
5) Networked system fault tolerant control with partial decoupling disturbance
The system is arranged in a normal running state of the system, namely, in the case of no fault, a static output feedback controller exists in the system in advance, and the static output feedback controller comprises the following forms:
the task is then to design a suitable feedback gain K to maintain the system (1) progressively stable and meet specific performance criteria;
when obtaining the estimated value of the system actuator fault, the compensation can be performed by giving an additional signal, and ensuring that the system still has good input-state stable performance, and the compensation signal of the system can be designed as follows
Wherein the method comprises the steps of
Expressed as matrix->
Is a generalized inverse matrix of (2);
thus, a fault tolerant control law based on signal compensation can be designed in the form of:
bringing a new control law (10) into the system (1) to establish a new closed-loop system with fault tolerance, as follows:
wherein A is δ ＝A+β(k)BKC，
B e ＝EJ 2 ，/>
Obtaining a residual signal e (k) of an unknown input observer by a formula (8), and then obtaining an estimated value of the system state by a formula (4)
And the estimated value f (k) of the fault, finally adopting the fault-tolerant control law of (10) to eliminate the influence of the fault on the system and ensure the input-state stability of the systemCan be used.
2. The fault-tolerant control method of a networked system with partial decoupling disturbance according to claim 1, wherein in step 5), a suitable feedback gain K is designed to maintain progressive stability of the system (1) and meet specific performance criteria, and the quadratic criteria for the following performance criteria are selected as follows:
wherein Q and M are given symmetric positive definite matrixes with proper dimensions, the Lyapunov stability theory is utilized, the existence condition of a conservation-state feedback control law is utilized, and the feedback gain K is easily obtained by solving a linear matrix equation.
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