A high-precision indirect signal reconstruction-based fault-tolerant control method for wheeled robot systems

Abstract

The application discloses a kind of high-precision indirect signal reconstruction-based wheeled robot system fault-tolerant control method.This method under the interference of external noise, establishes the wheeled robot system containing unknown system state and actuator fault, gives its system output function, constructs indirect variable based on unknown system state and actuator fault, obtains estimation error system.In addition, a distributed fault-tolerant controller containing estimated state and fault is designed to act on the continuous time of system, to ensure that estimation error system is uniformly ultimately bounded, to realize the synchronization of error system.

Description

Technical Field

[0001] This invention relates to a fault-tolerant control method, specifically a high-precision indirect signal reconstruction method based on a wheeled robot system. Background Technology

[0002] Many dynamic models used in wheeled robot control systems are built only under conditions where the system state and actuator failures are known. However, in practical applications, the actual system state and the actual values ​​of actuator failures are unknown. Furthermore, the information interaction topology between the wheeled robot system and its subsystems needs to change its interaction structure for self-repair under different failure conditions. Therefore, discussing the synchronization of switching wheeled robot systems is crucial for ensuring system stability. Based on this idea, researchers have conducted extensive research on the synchronization of switching wheeled robot systems in continuous time and have achieved a series of results. Summary of the Invention

[0003] The purpose of this invention is to propose a fault-tolerant control method for wheeled robot systems based on high-precision indirect signal reconstruction, which can effectively improve the performance of wheeled robot systems.

[0004] The specific technical solution of the present invention is as follows: A fault-tolerant control method for a wheeled robot system based on high-precision indirect signal reconstruction, comprising the following steps:

[0005] Using the Kronecker product technique to obtain data on a wheeled robot system containing unknown system states and actuator fault signals, an indirect signal is constructed to estimate the actual value of the system fault.

[0006] Design a distributed fault-tolerant controller that includes state estimation and fault reporting.

[0007] We propose a consistent final bounded condition based on Lyapunov's stability theorem and Young's inequality to realize the synchronization state.

[0008] Under the interference of external noise, for a wheeled robot system model containing unknown system states and actuator failures:

[0009]

[0010] f(x) = 1.5tanh(x), α 1 =1.2, α 2 =0.4, L=[9.9041 179.3490 9.9041],

[0011] L I =[3.6010 3.6010 3.6010],

[0012]

[0013]

[0014] In the formula, p represents the number of nodes, ζ(t) represents the known system state, and x p (t) represents the unknown state of the p-th node, x j f(t) represents the unknown state of the j-th node, A, B, C, G, D represent known parameter matrices, f(ζ(t)) represents the composite function with ζ(t) as the independent variable, and f(x) represents the unknown state of the j-th node. p (t) represents x p (t) is a composite function of the independent variable, u p (t) represents the control input, r p (t) represents an unknown system fault, τ p (t) represents the external input, ɑ σ(t) >0 indicates coupling strength. Γ represents the external coupling matrix. σ(t) Denotes the inner coupling matrix; for t∈[t i , t i+1 The system switching signal σ(t) = ω: [0, +∞) → Z is defined by ω (ω represents the system mode, Z represents an integer), where ( Let (representing a natural number) be the instant of mode switching, whose switching time sequence satisfies t0 < t1 < t2 < ..., and for any ... ( (representing positive integers) t i+1 -t i ≥μ1>0;

[0015] Assume time t∈[t i , t i+1 When ), the mode of the corresponding switching signal is σ(t)=ω, and the variable is defined. And T i，h =[t i，h , t i，h+1 ), where h∈{0,1,2,...,H-1},H∈N + ;

[0016] Define e p (t)=x p (t)-ζ(t) gives the error system.

[0017]

[0018] Where e j (t) represents the synchronization error of the j-th node, F(e p (t))=f(xp (t))-f(ζ(t)).

[0019] In addition, its output system is given:

[0020] y p (t)=De p (t)

[0021] Where D is a known matrix;

[0022] Using the Kronecker product, the system can be further written as:

[0023]

[0024] In the formula, e(t) is the error variable e p In matrix form of (t), G σ(t) External coupling matrix The matrix form of F(e(t)) is F(e p The matrix form of u(t) is given, where u(t) is the control input u. p R(t) is in matrix form, where R(t) represents the unknown system fault r. p The matrix form of τ(t), where τ(t) is the external input τ. p The matrix form of y(t) is given, where y(t) is the system output y. p Matrix form of (t)

[0025] Because x p If (t) is an unknown state, then the error variable e p (t) is also unknown; to solve this problem, an indirect signal is introduced;

[0026]

[0027] Where L R It is an estimate of the gain.

[0028] So

[0029]

[0030] Based on the above formula, the actual values ​​of the system state and faults are estimated as follows:

[0031]

[0032] Where L R and L I To estimate the gain, I N identity matrix

[0033] make Then the estimation error system can be obtained

[0034]

[0035] Therefore, the control input u(t) is constructed as

[0036]

[0037] in

[0038]

[0039] At this point, the error system can be rewritten as

[0040]

[0041] This control scheme can guarantee the uniform and bounded stability of the system. The proof is as follows:

[0042] C001: Select the energy function in the following form:

[0043] V σ(t) (t)=V1(t)+V2(t)+V3(t)

[0044] C002: In the formula, the selected energy functions V1(t), V2(t), and V3(t) are expressed as follows:

[0045]

[0046] C003: Among them

[0047]

[0048] C004: When t∈T j，h When σ(t) = ω, calculate the first derivative of V1(t):

[0049]

[0050] C005: According to C003 regarding... From the definition, we can obtain:

[0051]

[0052] C006: Using Young's inequality, we can obtain...

[0053]

[0054] C007: Taking the derivatives of V2(t) and V3(t) yields...

[0055]

[0056] C008: Similar to C006, it can be obtained

[0057]

[0058] C009: Combining C003-C008, we can obtain...

[0059]

[0060] C010: Among them

[0061]

[0062] C011: Based on Lyapunov stability theory, if... have

[0063] C012: When t∈[t] i，H , t i+1 When σ(t) = ω, combining C003 and C008, we can obtain

[0064]

[0065] C013: Among them

[0066]

[0067] C014: Based on Lyapunov stability theory, if... have

[0068] C015: Due to V σ(t) (t) in [t i , t i+1 If the function is continuous, then from C011 and C014 we can obtain...

[0069]

[0070] C016: Suppose that for t∈[t] i-1 ,t i )satisfy So when hour, Represents time t i Left-continuous, C002 can be redescribed as

[0071]

[0072] C017: Among them

[0073]

[0074] C018: When hour, Represents time t i Right continuum, B002 can be redescribed as

[0075] V σ(t) (t i )=V1(t i )+V2(t i )+V3(t i )

[0076] C019: Among them

[0077]

[0078] C020: According to the definition in C002, we can obtain

[0079]

[0080] C021: Combining C017 and C019, we can obtain

[0081]

[0082] C022: So when the condition is... At the time of its establishment, there were Therefore, the closed-loop system achieves consistent and eventually bounded synchronization. Attached Figure Description

[0083] Figure 1-2 Two topological diagrams for followers;

[0084] Figure 3-7 A dynamic trajectory diagram of unknown error and tracking error;

[0085] Figure 8-12 Dynamic trajectory diagrams of unknown fault signals and tracked fault signals; Detailed Implementation

[0086] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0087] A fault-tolerant control method for a wheeled robot system based on high-precision indirect signal reconstruction includes the following steps:

[0088] Step 1: Set the various system parameters;

[0089] Step 2: Construct indirect signals based on the unknown state and unknown actuator fault;

[0090] Step 3: Provide the actual values ​​for the corresponding unknown states and unknown actuator faults;

[0091] Step 4: Set up the estimation error system;

[0092] Step 5: Set distributed control inputs at continuous intervals;

[0093] Step 6: Verify whether the estimation error system achieves consistent eventual boundedness.

[0094] Step 7: Verify whether the error system achieves synchronization at continuous and switching times respectively.

[0095] An embodiment of the present invention is described below:

[0096] Consider a wheeled robot system based on high-precision indirect signal reconstruction, whose corresponding dynamic models are as follows:

[0097]

[0098] f(x) = 1.5tanh(x), α 1 =1.2, α 2 =0.4, L=[9.9041 179.3490 9.9041],

[0099] L I =[3.6010 3.6010 3.6010],

[0100]

[0101]

[0102] The two topologies of the follower are shown in Figure 1-2. The dynamic trajectories of the unknown error and tracking error under high-precision indirect signal reconstruction are as follows: Figure 3-7 As shown, the dynamic trajectories of the unknown fault signal and the tracked fault signal under high-precision indirect signal reconstruction are as follows: Figure 8-12 As shown.

Claims

1. A fault-tolerant control method for a wheeled robot system based on high-precision indirect signal reconstruction, characterized in that, Includes the following steps: The Kronecker product technique is used to obtain data on a wheeled robot system containing unknown system states and actuator fault signals. An indirect signal is constructed to estimate the actual value of the system fault. The specific process is as follows: The model of a wheeled robot system containing unknown states and actuator malfunctions under the influence of external noise is as follows: In the formula This represents the number of nodes, and can be 1, 2, 3, 4, or 5. Indicates a known system state. Indicates the first The unknown state of each node Indicates the first The unknown state of each node , , , , Represents a known parameter matrix. Indicates A composite function of the independent variable. Indicates For a composite function of the independent variable, Indicates control input, Indicates an unknown system failure. Indicates external input. Represents the coupling strength, where Indicates a system switching signal; for Switching signals pass Defined Let Z represent the system modes, where Z is an integer. It is the moment of modal switching. Let the natural numbers be represented, and their switching time series satisfy the following conditions: And for any have , Represents positive integers; Represents the external coupling matrix. Represents the inner coupling matrix; All the above symbols specifically represent switching signals. When, coupling strength Switching signals When, coupling strength ; , ， ， ， ， ， ， ， ， ， ， ， Assuming time When, the mode of the corresponding switching signal is Define variables as well as ,in , ; Definition of the first The synchronization error of each node is Then the error system can be obtained. in For the first Synchronization error of each node ; In addition, its output system is given: in Given a matrix, For system output; With the help of the Kronecker integrator The system can be further written as In the formula For error variables In matrix form, External coupling matrix In matrix form, for In matrix form, To control input In matrix form, Unknown system failure In matrix form, For external input In matrix form, For system output Matrix form; because If it is an unknown state, then the error variable It is also unknown; to solve this problem, an indirect signal is introduced. in It is to estimate the gain; Due to error variables and system failure Since it is unknown, we need to design a system that includes synchronization error estimation. and fault estimation Distributed fault-tolerant controller ， in For error variables The estimated value, Unknown fault The estimated value, , ; In the aforementioned controller Based on this, a consistent final bounded condition for a wheeled robot closed-loop system based on Lyapunov's stability theorem and Young's inequality is given, and the proof is as follows: B001: Select the energy function in the following form: ， B002: Selected energy function , , They are respectively represented as ， ， ， Among them when Sometimes, , , ;when Sometimes, , , ; The estimation error for the synchronization error is, The estimation error is for the indirect signal. This represents the error in estimating unknown faults. B003: When hour, Calculate at this time First derivative: B004: According to B002 regarding... From the definition, we can obtain: B005: Using Young's inequality, we can obtain B006: Yes and Taking the derivative, we can obtain B007: Similar to B005. B008: Combining B003-B007, we can obtain in B009: Based on Lyapunov stability theory, if... ,have ; B0010: When hour, Combining B002 and B008, we can obtain: in B0011: Based on Lyapunov stability theory, if... ,have ; B0012: Due to exist The above is a continuous function, so from B009 and B0011 we can obtain ， B0013: Assuming for satisfy ; then when hour, Indicates time Left-continuous, B002 can be redescribed as in B0014: When hour, Indicates time Right continuum, B002 can be redescribed as in B0015: According to the definition in B002, we can obtain ， ， ， ， ， ， B0016: Combining B0013 and B0014, we can obtain ， B0017: So when the conditions are... At the time of its establishment, there were Therefore, the closed-loop system achieves consistent and eventually bounded synchronization.

2. The fault-tolerant control method for a wheeled robot system based on high-precision indirect signal reconstruction according to claim 1, characterized in that, The indirect signal The estimation subsystem is constructed by the following steps: For indirect signals Taking the derivative, we have Based on the above formula, the synchronization error and fault are estimated as follows: in For observer gain, It is the identity matrix. For error variables The estimated value, Indirect signal The estimated value, Unknown fault The estimated value, For system output The estimated value; It is an integral term; Let the synchronization error estimation error be The estimation error of the intermediate variables is The fault estimation error is The output estimation error is Then the estimation error system can be obtained 。

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