A preset performance-based adaptive backstepping sliding mode control method for networked control systems

Abstract

The application belongs to the field of automation control, and particularly relates to a preset performance based adaptive backstepping sliding mode control method for a network control system, comprising the following steps: converting a nonlinear network control system model with uncertain time delay into a system model without uncertain time delay; defining a system tracking error index and a preset performance trajectory, and converting the constrained system tracking error index into a new unconstrained error index; defining a new system state error containing an intermediate virtual control signal, and performing coordinate conversion on the system model; designing a sliding mode function and a Lyapunov function, and estimating network disturbance by using an adaptive neural network function to obtain a system input signal control rate; the application effectively solves the time delay problem of the network control system without limiting the upper limit of the time delay or the time delay derivative by using the network disturbance concept, and completes the control of the system by designing a preset performance index, so that the dynamic and steady state performance of the system is ensured.

Description

Technical Field

[0001] This invention belongs to the field of automation control technology, specifically relating to an adaptive inversion sliding mode control method based on preset performance for network control systems. Background Technology

[0002] A networked control system is a real-time closed-loop control system formed by sensors, controllers, and actuators connected through a communication network. Due to this characteristic, networked control systems have broad application prospects in many fields, such as space and land exploration, access to hazardous areas and related operations, factory automation, remote diagnostics and troubleshooting, experimental equipment, home robots, and aircraft operations. However, the latency of the communication link significantly degrades the system's performance, limiting the application of networked control systems in real-world environments.

[0003] Regarding network latency issues, current network latency control methods generally suffer from the following problems: they require upper limits on network latency or restrictions on the rate of change of latency. This is unacceptable for systems with high network latency or in situations with changing network environments. Furthermore, regarding tracking error control in network control systems, current control algorithms often have the following problems: they ignore the dynamic control performance of the system; and they cannot accurately limit the steady-state tracking error range of the system. Summary of the Invention

[0004] To address the technical problems existing in the prior art, the present invention aims to provide an adaptive inversion sliding mode control method based on preset performance for network control systems, which effectively solves the problems of network delay compensation and good tracking error control performance in network control systems.

[0005] An adaptive inversion sliding mode control method based on preset performance for networked control systems, the method comprising:

[0006] S1: Construct a nonlinear network control system model with uncertain time delay, and transform the nonlinear network control system model with uncertain time delay into a nonlinear network control system model without uncertain time delay;

[0007] S2: Define the tracking error index of the network control system and design a preset performance trajectory; transform the constrained system tracking error index into an unconstrained error index based on the preset performance trajectory.

[0008] S3: Define a new system state error that includes intermediate virtual control signals. Based on the new system state error, perform coordinate transformation on the nonlinear network control system model without uncertain time delay to obtain a new nonlinear network control system model.

[0009] S4: Set the sliding mode function and Lyapunov function of the new nonlinear network control system model, and obtain the control law of the intermediate virtual control signal and the system input signal;

[0010] S5: Set an adaptive neural network function, use the adaptive neural network function to estimate the network interference of the system, and improve the control rate of the system input signal based on the estimation results.

[0011] Preferably, the process of transforming a nonlinear network control system model with uncertain time delay into a nonlinear network control system model without uncertain time delay includes:

[0012] S11: Define the total time delay t of a nonlinear network control system model with uncertain time delay. z = t1 + t2; where t1 represents the control channel delay and t2 represents the feedback channel delay;

[0013] S12: Based on the concept of network interference, the time delay t z All the negative impacts on the system can be summarized as network interference T d In the middle, we obtained

[0014] S13: Define a new system state vector And design the local terminal control signal T l = -f(X); where f(X) is a known system function, n is the system order, and T is the transpose marker;

[0015] S14: Based on network interference and the new system state vector, the nonlinear network control system model with uncertain time delay is transformed into a nonlinear network control system model without uncertain time delay; the expression of the transformed model is:

[0016]

[0017] Where A is a constant matrix, B is a constant vector, and T c This is a remote control signal.

[0018] Preferably, step S2 includes the following specific steps:

[0019] S21: Define the system tracking error e1; its expression is:

[0020] e1 = yy d ,

[0021] Among them, y d Given the system tracking trajectory;

[0022] S22: Set a preset performance trajectory, the expression of which is:

[0023] ρ1(t)=(ρ 10 -ρ 1∞ )e -lt +ρ 1∞

[0024] Where, ρ 10 Let ρ be the initial error bound. 1∞ For the final error bound, e -lt Let ρ1(t) be the convergence rate, and l be the convergence rate parameter;

[0025] S23: Constrain the system tracking error according to the preset performance trajectory. The expression for the constraint is:

[0026] -σρ1(t) <e1<σρ1(t)

[0027] Where σ is a constant greater than 0 and less than or equal to 1;

[0028] S24: Define a smooth, strictly increasing function S1 (∈1). Transform the system tracking error e1 according to the smooth, strictly increasing function. Calculate the new unconstrained error index ∈1 based on the transformed system tracking error. Its expression is:

[0029]

[0030] in, It is the reciprocal of a smooth, strictly increasing function.

[0031] Preferably, step S3 includes the following specific steps:

[0032] S31: Define a new system state error e that includes intermediate virtual control signals. i Its expression is:

[0033]

[0034] Where, α i (t), i = 1, 2, ..., n-1 are intermediate virtual control signals;

[0035] S32: Calculate based on preset performance trajectory The calculation formula is:

[0036]

[0037] α0(t)=y d

[0038] in, Let ρ represent the i-th new system state vector value. i (t) represents the i-th preset performance trajectory, S i(.) denotes a smooth, strictly increasing function, α i-1 (t) represents the intermediate virtual control signal of the (i-1)th state vector, ∈ i This represents the i-th unconstrained error index;

[0039] S33: For the i-th new system state vector index Taking the derivative, we get:

[0040]

[0041] S34: According to A coordinate transformation is performed on the nonlinear network control system model without uncertain time delay to obtain an unconstrained error index ∈ i A new nonlinear network control system model where i = 1, 2, ..., n is the system state vector. The expression for the new nonlinear network control system model is as follows:

[0042]

[0043] in, Let ρ represent the reciprocal vector of the i-th new unconstrained error index. i+1 (t) represents the (i+1)th preset performance trajectory, S i+1 (.) represents a smooth, strictly increasing function for the (i+1)th system state vector, ∈ i+1 The unconstrained error index represents the (i+1)th system state vector. Let f(X) represent the input signal of the new system, and let T represent the known system function. d This indicates network interference.

[0044] Furthermore, the intermediate virtual control signal α i The expression for (t) is:

[0045]

[0046] Where, k si This indicates the control parameters.

[0047] Preferably, the expression for the sliding mode function s is:

[0048]

[0049]

[0050] Where, ∈=∈1+∈2+…+∈ n k is the sliding mode variable. n1 ,k n2 , It is a positive number, and Represents a symbolic function.

[0051] Preferably, the expression for the control law of the system input signal is:

[0052]

[0053] Where, ρ n (t) represents the preset performance trajectory of the nth system state vector, ∈ n The unconstrained error index represents the state vector of the nth system. Let μ represent the reciprocal vector of the i-th new unconstrained error index, where μ is a positive constant.

[0054] The preferred and improved expression for the control law of the system input signal is:

[0055]

[0056] Preferably, the expression for the weights of the adaptive neural network function is:

[0057]

[0058] in, This represents the adaptive law for the weight estimates of a neural network. Represents radial basis functions. This represents the state vector of the new system. This represents the estimated weights of the neural network.

[0059] The beneficial effects of this invention are:

[0060] Compared with many existing control methods for networked control systems, the adaptive inversion sliding mode control method based on preset performance proposed in this invention can effectively solve two key problems of networked control systems simultaneously: network delay compensation and good dynamic and steady-state control performance. This invention utilizes the concept of network interference to summarize all the negative impacts of time delay on the system into a single network interference and compensate for it, without requiring upper limits on network delay or the rate of change of delay, making it easy to apply in engineering. At the same time, this invention also considers the dynamic and steady-state control performance of the networked control system. The designed adaptive inversion sliding mode control method based on preset performance not only accurately controls the steady-state tracking error, but also limits the transient tracking error within a preset range. Attached Figure Description

[0061] Figure 1 This is a flowchart of the adaptive inversion sliding mode control method based on preset performance for network control systems according to the present invention;

[0062] Figure 2This is a position tracking curve diagram in an embodiment of the present invention;

[0063] Figure 3 This is a tracking error trajectory curve diagram in an embodiment of the present invention. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] An adaptive inversion sliding mode control method based on preset performance for networked control systems, such as... Figure 1 As shown, the method includes: First, based on the concept of network interference, the nonlinear network control system model with uncertain time delay is transformed into a system model without uncertain time delay; Second, a system tracking error index is defined, and a preset performance trajectory is designed to transform the constrained system tracking error index into a new unconstrained error index; Third, according to the inversion control principle, a new system state error including intermediate virtual control signals is defined, and the system model obtained in the first step is transformed again to obtain a new nonlinear network control system model; Fourth, a sliding mode function and a Lyapunov function are designed to obtain the control rates of the intermediate virtual control signals and the system input signals; Fifth, an adaptive neural network function is designed to estimate network interference and obtain an improved system input signal control rate.

[0066] A specific implementation of an adaptive inversion sliding mode control method based on preset performance for networked control systems, the method comprising:

[0067] S1: Construct a nonlinear network control system model with uncertain time delay, and transform the nonlinear network control system model with uncertain time delay into a nonlinear network control system model without uncertain time delay. Specific steps include:

[0068] S11: Determine the model of the nonlinear network control system with uncertain time delay, its expression is:

[0069]

[0070]

[0071] Where X = [X1 X2…X] n-1 X n ] TLet be the system state vector, T be the transpose label, n be the system order, y be the system output signal, and f(X) be the known system function. T is the system input signal. c Input signals to the system, For a control signal that has been delayed by the control channel, T l For local control signals, constant matrix The constant vector B = [0 0…0 1] T t1 is the control channel delay; t2 is the feedback channel delay; e is the base of the natural exponent; and s is the Laplace frequency domain transform symbol.

[0072] S12: Define the total time delay t of a nonlinear network control system model with uncertain time delay. z =t1+t2; Based on the concept of network interference, the time delay t z All the negative impacts on the system can be summarized as network interference T d In the middle, we obtained

[0073] S13: Define the new system state vector And design the local terminal control signal T l = -f(X), where f(X) is a known system function, n is the system order, and T is the transpose marker.

[0074] S14: Based on network interference, the new system state vector, and the new system input signal, the nonlinear network control system model with uncertain time delay is transformed into a nonlinear network control system model without uncertain time delay; the expression of the transformed model is:

[0075]

[0076] S2: Define the system tracking error metric and design a preset performance trajectory; based on the preset performance trajectory, transform the constrained system tracking error metric into an unconstrained error metric. Specific steps include:

[0077] S21: Define the system tracking error e1; its expression is:

[0078] e1 = yy d

[0079] Among them, y d Given the system tracking trajectory, y represents the system output;

[0080] S22: Set a preset performance trajectory, the expression of which is:

[0081] ρ1(t)=(ρ 10 -ρ 1∞ )e -lt+ρ 1∞

[0082] Where, ρ 10 Let ρ be the initial error bound. 1∞ For the final error bound, e -lt Let ρ1(t) be the convergence rate, and l be the convergence rate parameter;

[0083] S23: Constrain the system tracking error according to the preset performance trajectory. The expression for the constraint is:

[0084] -σρ1(t) <e1<σρ1(t)

[0085] Where σ is a constant greater than 0 and less than or equal to 1;

[0086] S24: Define a smooth, strictly increasing function S1(∈1), transform the system tracking error e1 according to the smooth, strictly increasing function, and calculate a new unconstrained error index ∈1 based on the transformed system tracking error.

[0087] The expression for a smooth, strictly increasing function is:

[0088]

[0089] The formula for converting the system tracking error e1 is:

[0090] e1=ρ1(t)S1(∈1)

[0091] The formula for calculating the new unconstrained error index ∈1 is:

[0092]

[0093] in, It is the reciprocal of a smooth, strictly increasing function.

[0094] S3: Define a new system state error including intermediate virtual control signals according to the inversion control principle. Perform coordinate transformation on the nonlinear network control system model without uncertain time delay based on the new system state error to obtain a new nonlinear network control system model. Specific steps include:

[0095] S31: Define a new system state error e that includes intermediate virtual control signals. i Its expression is:

[0096]

[0097] Where, α i (t), i = 1, 2, ..., n-1 are intermediate virtual control signals;

[0098] S32: Calculate based on preset performance trajectory The calculation formula is:

[0099]

[0100] α0(t)=y d

[0101] in, Let ρ represent the i-th new system state vector value. i (t) represents the preset performance trajectory of the i-th state vector, S i (.) denotes a smooth, strictly increasing function, α i-1 (t) represents the intermediate virtual control signal of the (i-1)th state vector;

[0102] S33: For the formula in step S32 Taking the derivative, we get Its expression is:

[0103]

[0104] S34: According to A coordinate transformation is performed on the nonlinear network control system model without uncertain time delay to obtain an unconstrained error index ∈ i A new nonlinear network control system model where i = 1, 2, ..., n is the system state vector. The expression for the new nonlinear network control system model is as follows:

[0105]

[0106] in, Let α represent the reciprocal vector of the i-th new unconstrained error index. i (t) represents the intermediate virtual control signal, ρ i+1 (t) represents the (i+1)th preset performance trajectory, S i+1 (.) denotes the smooth, strictly increasing function of the (i+1)th system, ∈ i+1 The unconstrained error index represents the (i+1)th system state vector. Let f(X) represent the input signal of the new system, and let T represent the known system function. d This indicates network interference.

[0107] S4: Set the sliding mode function and Lyapunov function for the new nonlinear network control system model, and obtain the control laws of the intermediate virtual control signal and the system input signal. The specific process includes:

[0108] The Lyapunov function for the i = 1, 2, ..., n-1 step in the inversion control method is designed as follows: The obtained intermediate virtual control signal α i The control rate of (t) is:

[0109]

[0110] Where, k si For control parameters, satisfy k si >0.

[0111] The sliding mode function for the nth step in the design inversion control method is expressed as follows:

[0112]

[0113]

[0114] Where, ∈=∈1+∈2+…+∈ n k is the sliding mode variable. n1 ,k n2 , It is a positive number, and Represents a symbolic function.

[0115] Design a Lyapunov function with the following expression:

[0116]

[0117] Calculate the system input signal T based on the sliding mode function and Lyapunov function. c The formula for the control rate is:

[0118]

[0119] Where, ρ n (t) represents the preset performance trajectory of the nth system state vector, ∈ n S represents the unconstrained error index of the nth system state vector. n (.) denotes a smooth, strictly increasing function for the nth system state vector, T d Let μ represent network interference, μ be a positive constant, and s represent the sliding membrane function.

[0120] S5: Set the adaptive neural network function, and use the adaptive neural network function to deal with the system network interference T. d An estimate is performed, and the control rate of the system input signal is improved based on the estimation result. The expression for the improved control rate of the system input signal in step S5 is:

[0121]

[0122] in, These are the weight estimates for the neural network. Let be the radial basis function. And the adaptive law for the neural network weight estimate is:

[0123]

[0124] In this embodiment, the adaptive inversion sliding mode control method based on preset performance proposed in this invention for networked control systems is applied to a van der Bohr oscillator system with input and output delays. The control method is simulated and verified in Matlab / Simulink software. The van der Bohr oscillator system model with input and output delays is represented as follows:

[0125]

[0126] f(X)=(1-x1 2 )x2-x1

[0127] The network delays t1 and t2 of the input and output channels are selected as values ​​randomly distributed in the interval [0.05, 0.25].

[0128] The various control parameters for the simulation experiment are set as follows: The given tracking trajectory is: y d =0.4sin(0.6t), the preset performance curve is: ρ i (t)=(0.5-0.01)e -lt +0.01, where i = 1, 2, ρ i0 =0.5 is the initial error bound, ρ i∞ =0.01 is the final error bound, and the convergence rate parameter l = 0.5. Parameter σ = 1. The network delays of the input and output channels are selected as values ​​randomly distributed in the interval [0.05, 0.25]. Control parameter k si =3,k n1 =1.2,k n2 =1.5, μ = 5.

[0129] By selecting various control parameters, the position tracking curve and tracking error curve obtained are as follows: Figure 2 As shown in Figure 3. Figure 2 The figure shows the position tracking curve, where the dashed line represents the given tracking trajectory and the solid line represents the actual tracking curve. As can be seen from the figure, the actual position curve is well controlled by the invented method to track the given trajectory. Figure 3The dynamic and steady-state tracking error curves of the trajectory are displayed. As can be seen from the graphs, the dynamic tracking error is always confined within the preset performance trajectory, ensuring the dynamic control performance of the system. Furthermore, the tracking error quickly reaches a steady state, essentially converges, and remains at zero. In summary, the results demonstrate the effectiveness of the proposed adaptive inversion sliding mode control method based on preset performance for networked control systems. It not only effectively compensates for the adverse effects of network delay but also achieves precise position tracking of the networked control system, ensuring both dynamic and steady-state control performance.

[0130] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An adaptive inversion sliding mode control method based on preset performance for networked control systems, characterized in that, include: S1: Construct a nonlinear network control system model with uncertain time delay, and transform the nonlinear network control system model with uncertain time delay into a nonlinear network control system model without uncertain time delay; S2: Define the tracking error index of the network control system and design a preset performance trajectory; transform the constrained system tracking error index into an unconstrained error index based on the preset performance trajectory. S3: Define a new system state error that includes intermediate virtual control signals. Based on the new system state error, perform coordinate transformation on the nonlinear network control system model without uncertain time delay to obtain a new nonlinear network control system model. S4: Set the sliding mode function and Lyapunov function of the new nonlinear network control system model, and obtain the control law of the intermediate virtual control signal and the system input signal; S5: Set an adaptive neural network function, use the adaptive neural network function to estimate the network interference of the system, and improve the control rate of the system input signal based on the estimation result; The improved expression for the control law of the system input signal is: ； in, This represents the preset performance trajectory of the nth system state vector. The unconstrained error index represents the state vector of the nth system. The function representing the smooth, strictly increasing state vector of the nth system is... Let i represent the reciprocal vector of the i-th new unconstrained error index. This indicates network interference. For positive integers, Represents a symbolic function. For positive integers, Represents the sliding membrane function. Represents radial basis functions. This represents the estimated weights of the neural network. The expression for the weights of the adaptive neural network function is: ； in, This represents the adaptive law for the weight estimates of a neural network. Represents the sliding membrane function. Represents radial basis functions. This represents the state vector of the new system. This represents the estimated weights of the neural network.

2. The adaptive inversion sliding mode control method for networked control systems based on preset performance, as described in claim 1, is characterized in that... The expression for the model of a nonlinear network control system with uncertain time delay is: ； ； in, Let be the system state vector. For transpose, Let the system order be . For system output signals, It is a constant matrix. A constant vector, Given the system function, Input signals to the system, For remote control signals, The control signal is delayed by the control channel. For local control signals, The base of the natural index is . To control channel delay, The Laplace frequency domain transform symbol is used. This is due to a delay in the feedback channel.

3. The adaptive inversion sliding mode control method for networked control systems based on preset performance, as described in claim 1, is characterized in that... The process of transforming a nonlinear network control system model with uncertain time delay into a nonlinear network control system model without uncertain time delay includes: S11: Define the total time delay of a nonlinear network control system model with uncertain time delay. ;in, This is represented as control channel delay. This indicates a delay in the feedback channel; S12: Time delay based on the concept of network interference. All the negative impacts on the system can be attributed to network interference. In the middle, we obtained ; S13: Define a new system state vector Design local control signals ;in, Given the system function, Let the system order be . This is a transpose marker; S14: Based on network interference and the new system state vector, the nonlinear network control system model with uncertain time delay is transformed into a nonlinear network control system model without uncertain time delay; the expression of the transformed model is: ； in, It is a constant matrix. A constant vector, This is a remote control signal.

4. The adaptive inversion sliding mode control method for networked control systems based on preset performance, as described in claim 1, is characterized in that... The specific steps of step S2 include: S21: Define system tracking error Its expression is: ； in, Given the system tracking trajectory; S22: Set a preset performance trajectory, the expression of which is: ； in, As the initial error bound, For the final error bound, for The convergence rate, It is the convergence rate parameter; S23: Constrain the system tracking error according to the preset performance trajectory. The expression for the constraint is: ； in, A constant that is greater than 0 and less than or equal to 1; S24: Define a smooth, strictly increasing function Based on the smooth, strictly increasing function, the system tracking error is... Perform the transformation, and calculate the new unconstrained error index based on the transformed system tracking error. Its expression is: ； in, It is the reciprocal of a smooth, strictly increasing function.

5. The adaptive inversion sliding mode control method for networked control systems based on preset performance, as described in claim 1, is characterized in that... The specific steps of step S3 include: S31: Define a new system state error that includes intermediate virtual control signals. Its expression is: ； in, This is an intermediate virtual control signal; S32: Calculate based on preset performance trajectory The calculation formula is: ； ； in, This represents the i-th new system state vector value. This represents the preset performance trajectory of the i-th state vector. This represents a smoothly strictly increasing function. The intermediate virtual control signal is represented as the (i-1)th state vector. This represents the i-th unconstrained error index; S33: For the i-th new system state vector index Taking the derivative, we get: ； S34: According to A coordinate transformation is performed on the nonlinear network control system model without uncertain time delay to obtain an unconstrained error index. A new nonlinear network control system model for system state vectors The expression for the new nonlinear network control system model is as follows: ； in, Let i represent the reciprocal vector of the i-th new unconstrained error index. This represents the (i+1)th preset performance trajectory. The function representing the smooth, strictly increasing state vector of the (i+1)th system is... The unconstrained error index represents the (i+1)th system state vector. This represents the input signal of the new system. Represents a known system function. This indicates network interference.

6. The adaptive inversion sliding mode control method for networked control systems based on preset performance, as described in claim 5, is characterized in that... Intermediate virtual control signal The expression is: ； in, This indicates the control parameters.

7. The adaptive inversion sliding mode control method for networked control systems based on preset performance, as described in claim 1, is characterized in that... Sliding mode function The expression is: ； ； in, For sliding mode variables; It is a positive number, and ; Represents a symbolic function.

8. The adaptive inversion sliding mode control method for networked control systems based on preset performance, as described in claim 1, is characterized in that... The expression for the control law of the system input signal is: ； in, This represents the preset performance trajectory of the nth system state vector. The unconstrained error index represents the state vector of the nth system. The function representing the smooth, strictly increasing state vector of the nth system is... Let i represent the reciprocal vector of the i-th new unconstrained error index. This indicates network interference. For positive integers, Represents a symbolic function. For positive integers, This represents the sliding membrane function.

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