A nonlinear truck trailer system fuzzy control method under a networked environment

Abstract

The application provides a nonlinear truck trailer system fuzzy control method in a networked environment, comprising: modeling a nonlinear truck trailer system as a piecewise T-S fuzzy model, and designing a piecewise fuzzy state feedback controller with state adaptive saturation, and giving a controller design condition; designing a new piecewise event triggering mechanism, wherein an event triggering rule follows different space region information of state variables of the system model, and researching an event triggering fuzzy control scheme; the application gives a new event triggering control scheme, which can guarantee system stability in the case that the system is affected by outliers, and overcomes the problem that the event triggering mechanism and the controller need to be designed coordinately in the prior application; finally, the effectiveness of the technical method of the application is verified through an actual truck trailer system.

Description

Technical Field

[0001] This invention relates to the field of robust control of networked fuzzy systems, and particularly to a fuzzy control method for a nonlinear truck trailer system in a networked environment. Background Technology

[0002] The truck-trailer reversing control problem is a classic control problem, with the objective of controlling both the truck and trailer to a designated position by reversing the preceding truck. However, the multivariable and nonlinear characteristics of the system model make it difficult to obtain an accurate mathematical model, thus complicating the control problem for truck-trailer systems. To address this issue, scholars both domestically and internationally have proposed various solutions over the past few decades, among which the TS fuzzy model has received widespread attention due to its ability to accurately approximate nonlinear characteristics under certain conditions. Furthermore, the TS fuzzy model is composed of several linear system models weighted by membership functions, and linear system control theory is also applicable to the TS fuzzy model, which greatly simplifies the control problem for nonlinear systems. Therefore, research on the TS fuzzy control problem for nonlinear truck-trailer systems has significant practical implications.

[0003] In recent years, with the development and widespread adoption of internet technology, traditional communication mechanisms, which rely on fixed-period data collection and transmission, have become inadequate due to information redundancy and wasted network resources. A new communication mechanism, the event-triggered mechanism, has been proposed. This mechanism achieves efficient utilization of network resources by setting data transmission conditions. Therefore, the control problem of event-triggered systems has attracted extensive research from numerous scholars. Notable invention patents include: "A Fuzzy Control Method for a Nonlinear Truck-Trailer System Based on an Event-Triggered Mechanism" (CN201810044342.1), "An Adaptive Event-Triggered Control Method for Nonlinear Uncertain Systems" (CN201910871451.5), "A Control Method for a TS Fuzzy Network System Based on Event Triggering" (CN201810858012.6), and "A Networked TS Fuzzy Control Method for Event Triggering in Generalized Systems." ∞ The control method (CN201911246449.5) studied the control problem of TS fuzzy systems under an event-triggered communication mechanism. However, it should be noted that the fuzzy controller and the event-triggered mechanism in the aforementioned invention patent need to be designed collaboratively, which increases the complexity of the control process. Therefore, how to design the controller and the event-triggered mechanism separately is an unsolved problem, and no relevant invention exists yet; a design solution is urgently needed.

[0004] Furthermore, in a networked environment, data signals are subject to interference from various factors during transmission, leading to data anomalies and consequently deteriorating or even destabilizing system performance. Therefore, processing abruptly changing data signals is particularly important, and many scholars have conducted active research on this issue, but most studies have focused on linear systems. How to handle outliers in nonlinear control systems has become another pressing problem to be solved. Summary of the Invention

[0005] The purpose of this invention is to provide a fuzzy controller design method for a nonlinear truck trailer system in a networked environment, so as to solve the control problem of the nonlinear truck trailer system, and at the same time, ensure the stability of the control system and achieve the ideal performance requirements under the conditions of limited network resources and abnormal transmission signals.

[0006] The technical solution of the present invention:

[0007] A fuzzy control method for a nonlinear truck-trailer system in a networked environment includes the following:

[0008] First, a dynamic mathematical model of the truck trailer system is established.

[0009] Then, a piecewise fuzzy state feedback controller with state adaptive saturation is designed, and the controller gain is solved by linear matrix inequality technique.

[0010] Secondly, construct a segmented event triggering mechanism and design an event triggering control scheme.

[0011] Finally, the segmented fuzzy controller u(t) transmits the control signal to the system actuator to achieve the control objective.

[0012] The beneficial effects of this invention are as follows: This invention provides a fuzzy controller design for a nonlinear truck-trailer system in a networked environment, which ensures ideal control performance of the system even when subjected to outlier disturbances, while improving the utilization efficiency of network resources. Furthermore, the proposed solution overcomes the limitations of event-triggered mechanisms and the need for co-design of the fuzzy controller. Attached Figure Description

[0013] Figure 1 This is a flowchart of the method steps of the present invention.

[0014] Figure 2 This is a schematic diagram of a truck trailer system model according to an embodiment of the present invention.

[0015] Figure 3 This is a schematic diagram of the system state response without state adaptive saturation in an embodiment of the present invention.

[0016] Figure 4This is a schematic diagram of the system state response with state adaptive saturation added in an example of the present invention.

[0017] Figure 5 This is a schematic diagram of the controller control output according to an embodiment of the present invention.

[0018] Figure 6 Parameters of the embodiments of the present invention The trajectory.

[0019] Figure 7 This is a schematic diagram illustrating the data transmission process of the event triggering device according to an embodiment of the present invention. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0021] like Figure 1 As shown, the present invention provides a fuzzy control method for a nonlinear truck trailer system in a networked environment, comprising the following steps:

[0022] Step 1: Establish a dynamic mathematical model of the truck-trailer system, as shown below:

[0023]

[0024]

[0025]

[0026] In the formula, x1(t), x2(t), and x3(t) represent the angle between the truck and trailer's running directions, the horizontal angle between the trailer's current position and the ideal position, and the vertical distance to the ideal position, respectively; u(t) is the control input; v represents the constant reversing speed; L represents the trailer length; t0 represents the system's initial time; and l represents the truck length. Indicates the sampling time.

[0027] First, the above nonlinear truck-trailer system is modeled as a TS fuzzy system model, as shown below:

[0028]

[0029]

[0030] Where x(t) is the system state vector, ω(t) represents the bounded disturbance signal, z(t) is the measurement output, ∑ represents the summation symbol, and h m (x(t)), m=(1,2,...,r) represents the fuzzy membership function, r represents the total number of fuzzy rules, A m B m D m and Em This is the system matrix.

[0031] Then, the TS fuzzy system model is established as a piecewise TS fuzzy model, as shown below:

[0032]

[0033] z(t) = E l x(t)

[0034] Where l represents different partitions of the system state space. All are system matrices. This represents the set of parameters for the system's state space region.

[0035] Step 2: Design of a piecewise fuzzy state feedback controller with state adaptive saturation.

[0036] (2.1) Design a piecewise fuzzy state feedback controller with the following structure:

[0037] u(t) = K s Sat σ(t) (x(t))

[0038] Among them, K s Let be the gain matrix of the fuzzy controller, and s represent the different partitions in which the controller is located. σ(t) (x(t)) is a symmetric vector saturation function, σ(t) is a variable nonnegative saturation bound, and satisfies the following equation:

[0039]

[0040]

[0041] Where λ>0 and R>0 represent the control parameter and adjustment matrix for adaptive saturation, respectively, w k >0, (k=1,2,...,m) represents the k-th diagonal element of matrix W, where W is given in step 2 (2.3), and m is a positive integer. σ k (t) represents the saturation boundary of the saturation function at a certain time. The above refers to σ k The equation for (t) always holds true. yes The derivative of .

[0042] Based on the piecewise TS fuzzy model of the truck-trailer system in step 1 and the designed piecewise fuzzy state feedback controller, a closed-loop model of the truck-trailer system can be established, as shown below:

[0043]

[0044] z(t) = E l x(t)

[0045] in,

[0046]

[0047] B ls =B l K s

[0048] A ls =A l +B l K s

[0049] (2.2) Construct a Lyapunov function with the following structure and analyze the system stability:

[0050]

[0051] Where matrix P is a Lyapunov matrix, and the parameters are... ε>0 is a sufficiently small scalar. This indicates taking the maximum value between the two.

[0052] (2.3) Design conditions for piecewise fuzzy controllers:

[0053] For a given parameter λ>0, if there exist scalars β1>0, β2≥0, Lyapunov matrix P>0, matrix Y>0, diagonal matrix U>0, diagonal matrix W>0, and adjustment matrix R>0, satisfying the following inequalities:

[0054]

[0055]

[0056]

[0057]

[0058] Where He(*)=* T +, * denote any matrix, and I denotes the identity matrix. Matrix P -1 Let w represent the inverse of matrix P. k Y represents the k-th element on the diagonal of matrix W. k This represents the k-th row of matrix Y.

[0059] Then the truck trailer system can achieve stability and meet the ideal performance requirements.

[0060] (2.4) Solve for the gain of the piecewise fuzzy state feedback controller with state adaptive saturation.

[0061] Define matrix X s =K s P -1 Matrix P and X are obtained by solving the linear matrix inequality in step (2.3). s Finally, the gain of the fuzzy controller is obtained as K. s =X s P.

[0062] Step 3: Construct a segmented event triggering mechanism and design an event triggering control scheme.

[0063] (3.1) The conditions for triggering segmented events are as follows:

[0064]

[0065] Where inf represents the infimum; t k and t k+1 τ represents the current and next sampling times, where k is a positive integer; ls >0 represents the parameter to be determined; x e (t)=x s (t)-x(t) represents the sampled signal x s The difference between (t) and the sampled signal x(t); Indicates the threshold of the event triggering mechanism, ∈ ls >0 indicates the given event trigger parameter.

[0066] (3.2) Based on the established segmented event triggering mechanism, the segmented fuzzy controller designed in step 2 is re-presented as follows:

[0067] u s (t)=K s Sat σ(t) (x s (t))

[0068] The control output signal is only triggered at times t0, t1, ..., t k Update: For any k≥0, t k ≤t k+1 And there is x s (t)=x(t k ).

[0069] Based on the established segmented event triggering mechanism, a new closed-loop system model is presented as follows:

[0070]

[0071] z(t) = E l x(t)

[0072] (3.3) Determine the gain of the segmented event triggering mechanism

[0073] The piecewise fuzzy controller designed in step 2 is still applicable in step 3, realizing the separate design of the event triggering mechanism and the controller. The gain of the piecewise event triggering mechanism is as follows:

[0074] If there exist constant parameters β1>0, β2≥0, Lyapunov matrix P, matrix K s Choose constant parameter ∈ ls If >0, we can obtain:

[0075]

[0076] Where 0 < ρ < 1 represents a given constant parameter, λ min (P) represents the smallest eigenvalue of matrix P, and γ>0 is a specified parameter.

[0077] Define τ ls >0 is taken as a solution to φ(t)=1, where the ordinary differential equation is as follows:

[0078]

[0079] Where, σ k ω represents the upper bound of the saturation function, ω0 represents the upper bound of the disturbance, and other parameters have been given in steps 1, 2, and 3. The relevant parameters of the segmented event triggering mechanism can be obtained by solving the above formula. and τ ls .

[0080] Step 4: The segmented fuzzy controller u(t) transmits the control signal to the system actuator to achieve the control objective.

[0081] The objective of this invention is to ensure that the designed piecewise fuzzy controller can effectively control a truck-trailer model when the system is affected by outliers. Furthermore, the proposed method allows for the separate design of the event-triggered mechanism and the controller, ensuring that the controller established without introducing event-triggered conditions is still applicable to control systems after the introduction of an event-triggered mechanism.

[0082] The effectiveness of the control strategy in this invention for controlling a nonlinear truck trailer system is verified through specific examples below.

[0083] Non-linear truck trailer systems in Figure 2 The dynamic model is given below:

[0084]

[0085]

[0086]

[0087] Wherein, the model parameter v = -1.0 m / s 2 , L=5.5m, t0=0.5s, l=2.8m,

[0088] The above model is modeled as the piecewise TS fuzzy system model in step 1, with the following parameters:

[0089]

[0090]

[0091]

[0092] E1 = [1 0 0], E2 = [1 0 0]

[0093] Choose relevant parameters λ = 1, β1 = 0.1, ∈ 11 =∈ 12 =∈ 21 =∈ 22 =0.001, γ=1, ρ=0.5, initial system state x0=[-0.2-0.20.1] T By solving the linear matrix inequality in step (2.3) and the equation in step (3.3), the fuzzy controller gain in this example is obtained as follows:

[0094] K1 = [5.8813 -8.2897 1.1590]

[0095] K2 = [5.8813 -8.2897 1.1590]

[0096] The time interval between adjacent triggers is τ 11 =τ 12 =2.0366e-06, τ 21 =τ 22 =1.9417e-06, the event trigger threshold is The system control performance parameter is β2 = 10.9086.

[0097] Considering the periodic perturbation ω(t) = 0.4sin(0.2t), ω0 = 0.4, t0 = 0, and based on the above parameters, the simulation results can be obtained by performing steps 2 and 3. The details are as follows:

[0098] (1) Figure 3 and Figure 4The figure illustrates the impact of adaptive saturation of the state on the state signal of the truck-trailer system. As shown in the figure, the proposed piecewise fuzzy controller effectively addresses the impact of outlier signals on system stability, while existing methods perform poorly.

[0099] (2) Figure 5 The output is controlled by an adaptive saturated piecewise fuzzy state feedback controller representing the state of existence.

[0100] (3) Figure 6 Indicates parameters The trajectory.

[0101] (4) Figure 7 This indicates the time and interval at which the event-triggered mechanism releases data. The signal of the event-triggered fuzzy controller will be updated at different trigger times and will remain until the next trigger time.

[0102] Therefore, the simulation results show that the design method disclosed in this invention is effective.

Claims

1. A fuzzy control method for a nonlinear truck trailer system in a networked environment, characterized in that: The steps are as follows: Step 1: Establish a dynamic mathematical model of the truck-trailer system, as shown below: In the formula, x1(t), x2(t), and x3(t) represent the angle between the truck and trailer's running directions, the horizontal angle between the trailer's current position and the ideal position, and the vertical distance to the ideal position, respectively; u(t) is the control input; v represents the constant reversing speed; L represents the trailer length; t0 represents the system initial time; l represents the truck length; and t represents the sampling time. First, the above nonlinear truck-trailer system is modeled as a TS fuzzy system model, as shown below: Where x(t) is the system state vector, ω(t) represents the bounded disturbance signal, z(t) is the measurement output, ∑ represents the summation symbol, and h m (x(t)), m=1,2,...,r represents the fuzzy membership function, r represents the total number of fuzzy rules, A m B m D m and E m For the system matrix; Then, the TS fuzzy system model is established as a piecewise TS fuzzy model, as shown below: z(t)=E l x(t) Where l represents different partitions of the system state space. All are system matrices. A set of parameters representing the state space region of the system; Step 2: Design of a piecewise fuzzy state feedback controller with state adaptive saturation; (2.1) Design a piecewise fuzzy state feedback controller with the following structure: u(t)=K s Sat σ(t) (x(t)) Among them, K s Sat represents the gain matrix of the fuzzy controller, where s denotes the different partitions in which the controller is located. σ(t) (x(t)) is a symmetric vector saturation function, σ(t) is a variable nonnegative saturation bound, and satisfies the following equation: Where λ>0 and R>0 represent the control parameter and adjustment matrix for adaptive saturation, respectively, w k >0,k=1,2,...,m represents the k-th element on the diagonal of matrix W, where m is a positive integer; σ k (t) represents the saturation boundary of the saturation function at a certain time. The above refers to σ k The equation for (t) always holds true. yes The derivative; Based on the piecewise TS fuzzy model of the truck-trailer system in step 1 and the designed piecewise fuzzy state feedback controller, a closed-loop model of the truck-trailer system is established, as shown below: z(t)=E l x(t) in, B ls =B l K s A ls =A l +B l K s (2.2) Construct a Lyapunov function with the following structure and analyze the system stability: Where matrix P is a Lyapunov matrix, and the parameters are... ε>0 is a sufficiently small scalar. This indicates taking the maximum value between the two. (2.3) Design conditions for piecewise fuzzy controllers: For a given parameter λ>0; if there exist scalars β1>0, β2≥0, Lyapunov matrix P>0, matrix Y>0, diagonal matrix U>0, diagonal matrix W>0, and adjustment matrix R>0, satisfying the following inequalities: Where He(*)=* T +* and * denote any matrix, and I denotes the identity matrix; Matrix P -1 Let w represent the inverse of matrix P. k Y represents the k-th element on the diagonal of matrix W. k This represents the k-th row of matrix Y; Then the truck trailer system can achieve stability and meet the ideal performance requirements; (2.4) Solve for the gain of the piecewise fuzzy state feedback controller with state adaptive saturation; Define matrix X s =K s P -1 Matrix P and X are obtained by solving the linear matrix inequality in step (2.3). s Finally, the gain of the fuzzy controller is obtained as K. s =X s P; Step 3: Construct a segmented event triggering mechanism and design an event triggering control scheme; (3.1) The conditions for triggering segmented events are as follows: Where inf represents the infimum; t k and t k+1 τ represents the current and next sampling times, where k is a positive integer; ls >0 represents the parameter to be determined; x e (t)=x s (t)-x(t) represents the sampled signal x s The difference between (t) and the sampled signal x(t); Indicates the threshold of the event triggering mechanism, ∈ ls >0 indicates the given event trigger parameter; (3.2) Based on the established segmented event triggering mechanism, the segmented fuzzy controller designed in step 2 is re-presented as follows: u s (t)=K s Sat σ(t) (x s (t)) The control output signal is only triggered at times t0, t1, ..., t k Update: For any k≥0, t k ≤t k+1 And there is x s (t)=x(t k ); Based on the established segmented event triggering mechanism, a new closed-loop system model is presented as follows: z(t)=E l x(t) (3.3) Determine the gain of the segmented event triggering mechanism If there exist constant parameters β1>0, β2≥0, Lyapunov matrix P, matrix K s Choose constant parameter ∈ ls >0, resulting in: Where 0 < ρ < 1 represents a given constant parameter, λ min (P) represents the smallest eigenvalue of matrix P, and γ>0 is a specified parameter; Define τ ls >0 is taken as a solution to φ(t)=1, where the ordinary differential equation is as follows: Where, σ k The upper bound of the saturation function is represented by ω, and the upper bound of the disturbance is represented by ω0. The relevant parameters of the piecewise event triggering mechanism are obtained by solving the above formula. and τ ls ; Step 4: The segmented fuzzy controller u(t) transmits the control signal to the system actuator to achieve the control objective.

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