Distributed fault-tolerant tracking control method for interconnected nonlinear system under sensor fault condition

Abstract

The invention belongs to the field of fault-tolerant control of a strong interconnection nonlinear system, and discloses a distributed fault-tolerant tracking control method of the strong interconnection nonlinear system under a sensor fault condition, which comprises the following steps of: taking the strong interconnection nonlinear system under the condition of unknown sensor fault as a research object, and performing coordinate transformation to obtain a distributed fault-tolerant tracking control model of the strong interconnection nonlinear system; a backstepping method control technology is utilized to design a virtual controller containing an estimated square term obtained after fault amplification, an adaptive law and an actual controller so as to process unknown sensor faults of a controlled system. The distributed fault-tolerant tracking control method provided by the invention can effectively process the adverse effect of unknown sensor faults on a closed-loop control system. The method is suitable for a strong interconnection nonlinear system under a sensor fault condition, and the practicability and effectiveness of a control scheme are verified through numerical simulation research.

Description

Technical Field

[0001] The present invention belongs to the field of fault-tolerant control of strongly interconnected nonlinear systems, and specifically relates to a distributed fault-tolerant tracking control method in the case of sensor failure in this field. Background Art

[0002] With the rapid development of information technology, strongly interconnected nonlinear systems are increasingly being used in various fields. These systems achieve real-time monitoring and control of complex environments by closely integrating computing, networking, and physical processes. Typical applications of strongly interconnected nonlinear systems include intelligent public transportation systems. Sensors are key components for the system to obtain external information. Their failures may cause data distortion, which in turn affects the controller design and closed-loop stability analysis of the controlled system. At present, although some decentralized control methods have been proposed for faults in interconnected nonlinear systems:

[0003] (1) Li Jun. Research on fault-tolerant technology of interconnected nonlinear systems based on distributed control [D]. A distributed fault-tolerant tracking control problem of pure feedback nonlinear interconnected systems with actuator failures is proposed.

[0004] (2) Chinese invention patent CN202310692361.6[P] proposes a distributed fault-tolerant control method for solving actuator failures in the field of distributed control of interconnected nonlinear systems.

[0005] Although the above methods can effectively solve the faults in interconnected nonlinearity, there are still some problems:

[0006] The research on fault-tolerant tracking control of strongly interconnected nonlinear systems is still not perfect. The decentralized fault-tolerant control method proposed above cannot solve the problem of unknown sensor failures, and there are almost no results in the decentralized fault-tolerant asymptotic tracking control method considering sensor failure. Summary of the invention

[0007] The purpose of this invention is to solve the problem of unknown sensor failure in strongly interconnected nonlinear systems and propose a distributed fault-tolerant tracking control method. This method designs a virtual controller and an adaptive law containing the estimated square term obtained after fault amplification for strongly interconnected nonlinear systems with sensor failures, and gives an actual controller to eliminate the adverse effects of unknown sensor failures on closed-loop control systems. Finally, through simulation experiments and research, the practicality and effectiveness of the control scheme are verified.

[0008] In order to achieve the above object, the present invention proposes a distributed fault-tolerant tracking control method for a strongly interconnected nonlinear system under sensor failure conditions, which is implemented by the following steps:

[0009] Step 1: Consider the strongly interconnected nonlinear system under the following sensor failure conditions. The general mathematical model of the system is:

[0010]

[0011] Among them, u i (t) and y i They represent the control input and system output of the system, respectively, i,j (i=1,2,...,N,j=1,2,...,n i ) represents the system status, where N is the subsystem number, n i is the order of the subsystem; the state variables are represented by the vector x i ,j =[x i，1 , x i，2 , ..., x i,j ] T Give, special, The unknown function of the system is f i，j (x i ), the interaction between the subsystems is h i,j (x), all state variables are combined in the vector x = [x1, x2, ..., x N ] T d i，j (t) is a bounded external perturbation that satisfies the condition in is an unknown scalar.

[0012] The actual control input formula for sensor failure is as follows:

[0013]

[0014] Among them, α i，j (t) represents the failure factor, T i,f >0 is the failure time, y i To measure system variables, is the measured output of the sensor. In particular, if α i,j If (t) = 1, it can be said that there is no unknown sensor failure in the system.

[0015] Step 2: Perform coordinate transformation as follows:

[0016]

[0017] Among them, z i，1 and z i,k is the new tracking error, and is the measured output of the sensor, y i，d is the reference signal, γi,k-1 is the virtual control input.

[0018] Step 3: Design a virtual controller i,m , Adaptive Law and the actual controller u i (t) are as follows:

[0019] Virtual Controllers¶ i，m for:

[0020]

[0021] Adaptive Law for:

[0022]

[0023] Actual controller u i (t) is:

[0024]

[0025] in, and is a positive design parameter, is the estimated square term after fault amplification, n and r are positive integers, satisfying n≤2r, 0<c<1 is a constant value, δ i (t) is the introduced integral bounded function. The symbolic function sgn(.) in the virtual controller enhances the signal processing function of the controller, reduces the amount of calculation, and avoids the problem of variable algebraic paradox.

[0026] The main control objective of the present invention is to design a distributed fault-tolerant tracking control method for strongly interconnected nonlinear systems under sensor failure conditions, so that all signals of the closed-loop system are bounded convergent, and the output of each subsystem can still asymptotically track the reference signal before and after the system fails.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1) The existing distributed fault-tolerant tracking control lacks a method to solve the problem of sensor failure. The present invention designs a virtual controller and adaptive law that are different from the mathematical forms in previous literature and provides an actual controller. The structure and implemented functions of the proposed controller are different from those of the existing similar ones, which can eliminate the adverse effects of unknown sensor failures on the closed-loop control system.

[0029] (2) Interconnected nonlinear systems involve more complex situations than single nonlinear systems, have a wider range of applications, and are more adaptable to actual production and life requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1is a control flow chart;

[0031] Figure 2 It is a simplified model diagram of a strongly interconnected nonlinear system;

[0032] Figure 3 is the output of the subsystem and the tracking reference signal diagram;

[0033] Figure 4 is the tracking error graph of the subsystem;

[0034] Figure 5 is the virtual controller diagram of the subsystem;

[0035] Figure 6 is the adaptive law diagram of the subsystem;

[0036] Figure 7 is the actual controller diagram of the subsystem; DETAILED DESCRIPTION

[0037] The specific implementation of the present invention is now described in further detail in conjunction with the accompanying drawings. In order for those skilled in the art to better understand the implementation of the present invention, the present invention also provides simulation verification results using MatlabR2023b software.

[0038] Step 1: Consider the strongly interconnected nonlinear system under the following sensor failure conditions. The general mathematical model of the system is:

[0039]

[0040] Among them, u i (t) and y i They represent the control input and system output of the system, respectively, i,j (i=1,2,...,N, j=1,2,...,n i ) represents the system status, where N is the subsystem number, n i is the order of the subsystem; the state variables are represented by the vector x i ，j =[x i,1 ,x i,2 ,...,x i,j ] T Give, special, The unknown function of the system is f i,j (x i ), the interaction between the subsystems is h i，j (x), all state variables are combined in the vector x = [x1, x2, ..., x N ] T d i,j (t) is a bounded external perturbation that satisfies the condition in is an unknown scalar.

[0041] The actual control input formula for sensor failure is as follows:

[0042]

[0043] Among them, α i,j (t) represents the failure factor, T i，f >0 is the failure time, y i To measure system variables, is the measured output of the sensor. In particular, if α i,j If (t) = 1, it can be said that there is no unknown sensor failure in the system.

[0044] Step 2: Perform coordinate transformation as follows:

[0045]

[0046] Among them, z i，1 and z i，k is the new tracking error, and is the measured output of the sensor, y i，d is the reference signal, γ i,k-1 is the virtual control input.

[0047] Step 3: Design a virtual controller i，m , Adaptive Law and the actual controller u i (t) are as follows:

[0048] Virtual Controllers¶ i,m for:

[0049]

[0050] Adaptive Law for:

[0051]

[0052] Actual controller u i (t) is:

[0053]

[0054] in, and is a positive design parameter, is the estimated square term after fault amplification, n and r are positive integers, satisfying n≤2r, 0<c<1 is a constant value, δ i(t) is the introduced integral bounded function. The symbolic function sgn(.) in the virtual controller enhances the signal processing function of the controller, reduces the amount of calculation, and avoids the problem of variable algebraic paradox.

[0055] The main control objective of the present invention is to design a distributed fault-tolerant tracking control method for strongly interconnected nonlinear systems under sensor failure conditions, so that all signals of the closed-loop system are bounded convergent, and the output of each subsystem can still asymptotically track the reference signal before and after the system fails.

[0056] In this example, the above method is used to simulate and verify using MatlabR2023b software. The verification process and results are as follows: A typical intelligent public transportation system in a strongly interconnected nonlinear system can be simplified into a cart inverted pendulum connected by two springs, with a bounded distance l2(t)-l1(t). The position of the spring δ(t) can change along the length l0 of the pendulum. The dynamics of the cart inverted pendulum can be modeled as follows:

[0057]

[0058] Among them, y1 and y2 are the swing angles, u1 and u2 are the control torques, Δ1(t) and Δ2(t) are bounded perturbations, k is the connected spring constant, m1 and m2 are the masses of the inverted pendulum ends, m1=3, m2=3+0.01sin(t), l1(t)=0.1sin(12t), l2(t)=0.1(2+sin(15t)), d1(t)=0.01sin(3t), d2(t)=0.01sin(2t), l0=0.2, g=9.81, k=1, θ i (t) = [Q1, Q2, Q 3,i ] T ,

[0059] Therefore, the model of the cart inverted pendulum can be rewritten as:

[0060]

[0061] in, l1(t)-l2(t)] T ,h 1,2 =Q4y2,h 2,2 =Q4y1,d i,2 (t) = d i (t). The reference signal is selected as: y 1,d = sin(t)+sin(0.5t), y 2,d=0.5sin(t)+sin(0.5t), select the integral bounded function as: δ 1,2 (t) = δ 2,2 (t) = 0.5e -0.1t δ1(t)=δ2(t)=e -0.1t , neural network Contains 25 nodes: The center spacing is: [-1, 1], the width is κ s =4(s=1,2,...,l), Sensor failures are only considered to occur after the 5th and 10th seconds, and the parameters are:

[0062]

[0063] The design parameters and initial settings were chosen through a trial-and-error process: θ 1，1 =θ 1,2 =θ 2,1 =θ 2，2 =20, c 1，1 =c 1，2 =c 2，1 =c 2，2 =0.9,

[0064] Figure 1 is a control flow chart, Figure 2 is a simplified model diagram of the selected strongly interconnected nonlinear system. Figure 3 It can be seen that the output of the subsystem can track the reference signal very well; Figure 4 It can be seen that the tracking error fluctuates significantly at the fault location and converges to 0 asymptotically; Figure 5 is the virtual controller curve; Figure 6 is an adaptive law curve, and it can be seen that its convergence is bounded; Figure 7 It can be seen that the actual controller has obvious fluctuations at the fault location.

[0065] The parts of the present invention that are not described in detail are common knowledge to those skilled in the art. The above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A distributed fault-tolerant tracking control method for interconnected nonlinear systems under sensor failure conditions, including the use of neural network technology to identify unknown external disturbances, the use of event triggering mechanism to solve the problem of limited network communication, and the introduction of hyperbolic tangent function and integral bounded function to construct a practical controller, characterized by The following steps are involved: Step 1: Consider a strongly interconnected nonlinear system under a sensor failure scenario, and establish its general mathematical model and sensor failure model; Step 2: perform coordinate transformation and design a new tracking error signal; Step 3: Using the backstepping control technique, design a virtual controller, adaptive law and actual controller containing the estimated square term obtained after fault amplification.

2. According to step 1 in claim 1, consider the strongly interconnected nonlinear system under the following sensor failure situation, the general mathematical model of the system is: in, u i (t) and y i They represent the control input and output of the system, respectively, i,j (i=1,2,...,N,j=1,2,...,n i ) represents the system status, where N is the subsystem number, n i is the order of the subsystem; The state variables are represented by the vector x i，j =[x i,1 ,x i,2 , ..., x i，j ] T Give, special, The unknown function of the system is f i,j (x i ), the interaction between the subsystems is h i，j (x), all state variables are combined in the vector x = [x1, x2, ..., x N ] T d i，j (t) is a bounded external perturbation that satisfies the condition in is an unknown scalar.

3. According to step 1 in claim 1, the actual control input formula for sensor failure is as follows: in, α i,j (t) represents the failure factor, T i,f >0 is the failure time, y i To measure system variables, is the measured output of the sensor. In particular, if α i,j If (t) = 1, it can be said that there is no unknown sensor failure in the system.

4. According to step 2 in claim 1, coordinate transformation is performed as follows: in, z i，1 and z i，k is the new tracking error, and is the measured output of the sensor, y i，d is the reference signal, γ i,k-1 is the virtual control input.

5. According to step 3 of claim 1, design a virtual controller γ i,m , Adaptive Law and the actual controller u i (t) are as follows: Virtual Controllers¶ i,m for: Adaptive Law for: Actual controller u i (t) is: in, c i，m , and is a positive design parameter, is the estimated square term after fault amplification, n and r are positive integers, satisfying n≤2r, 0<c<1 is a constant value, δ i (t) is an introduced integral bounded function, and the symbolic function sgn(.) in the virtual controller enhances the signal processing function of the controller, reduces the amount of calculation, and avoids the problem of variable algebraic paradox. The main control goal of the present invention is to design a distributed fault-tolerant tracking control method for strongly interconnected nonlinear systems under sensor failure conditions, so that all signals of the closed-loop system are bounded convergent, and before and after the system fails, the output of each subsystem can still asymptotically track the reference signal.

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