Two-degree-of-freedom helicopter predefined time fault-tolerant tracking control method

Abstract

The invention discloses a two-degree-of-freedom helicopter predefined time fault-tolerant tracking control method, which comprises the following steps of: establishing a two-degree-of-freedom helicopter dynamical model containing external disturbance and actuator faults, constraining a system state by constructing a time-varying Barrier Lyapunov function, and fusing optimization control based on reinforcement learning into backstepping control, so that the two-degree-of-freedom helicopter is subjected to time-varying fault-tolerant tracking control. The method comprises the steps of designing an optimal virtual controller, designing an optimal tracking controller by adopting a control method based on a mixed zero-sum game theory aiming at an actuator fault and composite disturbance, and relieving communication burden by adopting a dual-channel event triggering mechanism comprising a controller-actuator and a sensor-controller. The controller designed by the invention can ensure that all signals of the whole two-degree-of-freedom helicopter are bounded within the preset time, and ensure that the two-degree-of-freedom helicopter can still quickly and accurately track a reference trajectory within the preset time under the constraint of actuator faults and states.

Description

Technical Field

[0001] This invention relates to the field of two-degree-of-freedom helicopter control technology, and in particular to a two-degree-of-freedom helicopter predefined time-tolerant fault-tracking control method based on hybrid zero-sum game theory. Background Technology

[0002] Unmanned helicopters, with their unique advantages such as vertical takeoff and landing, low environmental dependence, and hovering capabilities, are widely used in transportation, maritime surveillance, and battlefield reconnaissance. It is important to clarify that precise flight along a reference trajectory is fundamental for a two-degree-of-freedom (DOF) helicopter to accomplish these complex tasks. However, as a multi-input multi-output (MIMO) system, a DDF helicopter is inevitably affected by its strong coupling, uncertainties, and external unknown disturbances. Furthermore, as a physically structured system, its state must be constrained for flight safety. Considering the possibility of actuator failures further complicates the design of its tracking controller; failure to achieve the expected tracking accuracy can lead to serious economic and safety incidents. Patent application CN 115357005 A proposes an active fault-tolerant control method for sensor failures in DDF helicopters, but it does not consider the uncertainties inherent in DDF helicopters. Patent application CN 114578696 A proposes an adaptive neural network quantization fault-tolerant control method for DDF helicopters, but it does not consider the transient performance of the system's tracking error. Application publication number CN 118732509 A proposes a predetermined time tracking control method for a two-degree-of-freedom helicopter, but does not consider the control problem of the system state under constrained conditions.

[0003] Therefore, there is an urgent need to design a fault-tolerant tracking controller to improve the steady-state performance of a two-degree-of-freedom helicopter, and to accurately track the reference trajectory within a predetermined time under state constraints and actuator failures. Summary of the Invention

[0004] The purpose of this invention is to provide a design method for a two-degree-of-freedom helicopter predefined time-tolerant tracking controller based on hybrid zero-sum game theory, which can solve the above-mentioned problems.

[0005] To achieve the above objectives, the present invention is implemented according to the following technical solution:

[0006] This invention discloses a two-degree-of-freedom helicopter predefined time-tolerant fault-tolerant tracking control method, characterized by comprising the following steps:

[0007] Step 1: Establish a two-degree-of-freedom helicopter system model, which comprehensively considers internal uncertainties, external disturbances, and actuator failures.

[0008] Step 2: Based on the backstepping control method, decompose the two-degree-of-freedom helicopter system model into a cascaded first-stage subsystem and a second-stage subsystem;

[0009] Step 3: Construct a time-varying Barrier Lyapunov function to constrain the system state, and design a dual-channel event triggering mechanism to reduce communication burden;

[0010] Step 4: Design a virtual controller for the first-level subsystem using reinforcement learning strategies. and its corresponding execution-judgment learning law ; and construct a Lyapunov function that includes the time-varying Barrier Lyapunov function. Take its derivative to obtain ;

[0011] Step 5: For the second-level subsystem, model actuator failure, control input, and combined disturbance as three participants in a hybrid zero-sum game. , and By combining reinforcement learning strategies, we can solve for the game strategies of the three participants and their corresponding execution-evaluation learning laws. And design adaptive laws Construct a Lyapunov function that includes the time-varying BarrierLyapunov function. Take its derivative to obtain ;

[0012] Step 6: Based on the Lyapunov function and Construct the global Lyapunov function And by taking its derivative, we get By ensuring that the overall Lyapunov function satisfies the predefined time stability condition, the gain parameters of the controller to be designed are calculated through inequality scaling and simplification.

[0013] As a further description of the above technical solution, the equations for a two-degree-of-freedom helicopter system, including actuator failure and combined disturbances, are as follows:

[0014]

[0015] In the formula: , , and These represent the pitch and yaw angles of a two-degree-of-freedom helicopter, respectively. , Represents pitch angle angular velocity, Represents yaw angle angular velocity; , This represents the voltage of the pitch propeller motor. This represents the voltage of the yaw propeller motor; , Indicates an unknown failure factor. This indicates an unknown bias fault. Indicates a compound fault. Represents the control input to be designed; , For an unknown smooth nonlinear function vector, External disturbance; represent transpose; and This is the gain matrix for a two-degree-of-freedom helicopter system model. Specifically, it is represented as follows:

[0016]

[0017]

[0018] in, and These represent the thrust gain of the pitch propeller acting on the pitch axis and yaw axis, respectively. and These represent the thrust gain of the yaw propeller acting on the pitch and yaw axes, respectively. The total mass of a two-degree-of-freedom helicopter; It is the acceleration due to gravity; and These represent the sine and cosine functions, respectively. The distance from the system's center of mass to the helicopter's fixed support point; and These represent the friction damping coefficients present during pitch and yaw rotations, respectively. and These represent the moments of inertia of the pitch axis and the yaw axis, respectively.

[0019] As a further description of the above technical solution, the time-varying Barrier Lyapunov function is:

[0020]

[0021] In the formula: , and For the time-varying constraints of the design, and Indicates the system tracking error. It is a logarithmic function.

[0022] As a further description of the above technical solution, the dual-channel event triggering mechanism is as follows:

[0023]

[0024]

[0025] In the formula: and For the first The actual execution signal of each control input; and To trigger at the time Updated ideal control signal; , respectively The first control input Second and third Next trigger time It is a positive integer; These are the weighting coefficients. ; and For error signals, , For positive integers, , This is the control input to be designed.

[0026] As a further description of the above technical solution, the virtual controller Execution-Judgment Learning Law , They are respectively:

[0027] ,

[0028] ,

[0029] In the formula: , , To track the desired trajectory Time derivative, , , , for Time derivative, , , , Represents the hyperbolic tangent function. ,and The control parameters to be designed, and , For the scheduled time of the design, and For weight estimation, For input The basis function vector.

[0030] As a further description of the above technical solution, the three participants in the hybrid zero-sum game , and Execution-Judgment Learning Law Design Adaptive Law They are respectively:

[0031]

[0032]

[0033]

[0034]

[0035] In the formula: , , The system gain matrix The inverse matrix, To control the gain and satisfy , , , for Time derivative, , , , and For weight estimation, For input basis function vectors, For input basis function vectors, , and These are the control parameters for the design.

[0036] The beneficial effects of this invention are:

[0037] 1) Unlike existing finite-time and fixed-time control methods, the predefined-time tracking controller based on the method of this invention can ensure that all signals of the entire two-degree-of-freedom helicopter attitude system are predefined-time bounded. In addition, by adding a hyperbolic tangent function to the recursive control framework, the predefined time stability is ensured, while eliminating the singularity problem that occurs in the derivation process, so that the tracking error converges within the predefined time.

[0038] 2) By introducing a time-varying Barrier Lyapunov function, the system state is constrained within a specified region; actuator faults, control inputs, and compound disturbances are treated as three participants, and a control method based on hybrid zero-sum game theory is adopted. A reinforcement learning strategy is introduced to establish a predefined time-tolerant tracking controller with an execution-evaluation structure.

[0039] 3) The dual-channel event triggering mechanism is incorporated into the design of the predefined time tracking controller, so that the control signal is updated intermittently according to the pre-planned triggering conditions. This effectively avoids continuous updates of the system control signal, reduces the update frequency of the control signal and the wear of the actuator, and ensures that the two-degree-of-freedom helicopter can still accurately track the reference trajectory even when the control signal is updated intermittently. Attached Figure Description

[0040] Figure 1 This is a simplified model diagram of a two-degree-of-freedom helicopter;

[0041] Figure 2 This is a flowchart of the adaptive fault-tolerant control system for a two-degree-of-freedom helicopter.

[0042] Figure 3 It is a trajectory diagram of a two-degree-of-freedom helicopter tracking the desired angle under constraints in its pitch angle.

[0043] Figure 4 It is a trajectory diagram of a two-degree-of-freedom helicopter tracking the desired angle under constraints at the yaw angle.

[0044] Figure 5 This is a trajectory tracking response diagram for a two-degree-of-freedom helicopter with angular error.

[0045] Figure 6 This is a control input curve diagram of a two-degree-of-freedom helicopter system;

[0046] Figure 7 This is the execution-evaluation weighted trajectory diagram of a two-degree-of-freedom helicopter system;

[0047] Figure 8 This is a diagram showing the trigger intervals for the control inputs of a two-degree-of-freedom helicopter system. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0049] like Figure 1 and Figure 2 As shown: This invention provides a two-degree-of-freedom helicopter predefined time-tolerant fault-tolerant tracking control method based on hybrid zero-sum game theory, including the following steps:

[0050] Step 1, according to Figure 1 The simplified diagram of the two-degree-of-freedom helicopter system shown is used to construct the following dynamic model:

[0051]

[0052] In the formula: and The pitch and yaw angles represent the pitch and yaw angles of a two-degree-of-freedom helicopter. and They represent pitch angles respectively. Angular acceleration and angular velocity; and They represent yaw angles respectively Angular acceleration and angular velocity; This indicates the voltage of the pitch propeller motor. Production and effect The thrust, and satisfying , This indicates the voltage of the yaw propeller motor. Production and effect The thrust, and satisfying ; and These represent the thrust gain of the pitch propeller acting on the pitch axis and yaw axis, respectively. and These represent the thrust gain of the yaw propeller acting on the pitch and yaw axes, respectively. The total mass of a two-degree-of-freedom helicopter; It is the acceleration due to gravity; and These represent the sine and cosine functions, respectively. The distance from the system's center of mass to the helicopter's fixed support point; and These represent the friction damping coefficients present during pitch and yaw rotations, respectively. and These represent the moments of inertia of the pitch axis and the yaw axis, respectively.

[0053] Detailed system parameters are shown in Table 1:

[0054] Table 1: Model Parameters of a Two-Degree-of-Freedom Helicopter System

[0055]

[0056] definition , , , represent Furthermore, considering actuator failures and combined disturbances, the two-degree-of-freedom helicopter system model is expressed as follows:

[0057]

[0058] In the formula: , Indicates an unknown failure factor. This indicates an unknown bias fault. Indicates a compound fault. Represents the control input to be designed; , For an unknown smooth nonlinear function vector, External disturbance; represent transpose; and The gain matrices for the two-degree-of-freedom helicopter system model are as follows:

[0059]

[0060]

[0061] Step 2: Based on the system equations obtained in Step 1, construct the following coordinate transformation using the backstepping control method:

[0062]

[0063] In the formula: and Represents tracking error. As a virtual controller, the two-degree-of-freedom helicopter system model is decomposed into two-level subsystems, and error variables are introduced. , These are used as tracking error variables for the first-level subsystem and the second-level subsystem, respectively.

[0064] Step 3: Based on the coordinate transformation in Step 2, construct a time-varying Barrier Lyapunov function and design the following dual-channel event triggering mechanism:

[0065]

[0066]

[0067]

[0068]

[0069] In the formula: , and For the time-varying constraints of the design, and Indicates the system tracking error. It is a logarithmic function. and For the first The actual execution signal of each control input; and To trigger at the time Updated ideal control signal; , respectively The first control input Second and third Next trigger time It is a positive integer; These are the weighting coefficients. ; and For error signals, , For positive integers, , This is the control input to be designed.

[0070] Step 4: Based on the Barrier Lyapunov function and event triggering mechanism obtained in Step 3, construct the optimal performance function for the first-stage subsystem of the two-degree-of-freedom helicopter system. :

[0071]

[0072] In the formula: and It is a positive number, and . This represents the set of all allowed control inputs. The ideal and optimal virtual controller.

[0073] Furthermore, the Hamilton-Jacobi-Bellman equation is obtained as follows:

[0074]

[0075] In the formula: express right The partial derivative, Indicates the modulus length. for The derivative with respect to time. Then, using the stability condition. We can obtain:

[0076]

[0077] Furthermore, it can be obtained

[0078]

[0079]

[0080] Where: auxiliary cost function for:

[0081]

[0082] In the formula: , , To track the desired trajectory Time derivative, , , , for Time derivative, , , , Let represent the hyperbolic tangent function, and , The scheduled time for the design.

[0083] because Since the information is unknown but continuous, we choose a radial basis function neural network for approximate estimation:

[0084]

[0085] In the formula: For ideal weights, Indicates that the input is basis function vectors, This is the approximate error vector.

[0086] Furthermore, a reinforcement learning strategy is introduced to design an execution-evaluation adaptive law. and and optimal virtual controller :

[0087]

[0088]

[0089]

[0090] In the formula: ,and For the control parameters to be designed, and This is for weight estimation.

[0091] For the first-stage subsystem of a two-degree-of-freedom helicopter system model, a Lyapunov function is constructed.

[0092]

[0093] In the formula: and , Represents the trace of a matrix.

[0094] Furthermore, the Lyapunov function Taking the derivative with respect to time, we get:

[0095]

[0096] The optimal virtual controller designed Execution-evaluation adaptive law and Substitute into the formula By simplifying the inequality, we can obtain:

[0097]

[0098] Step 5: The second-level subsystem of the two-degree-of-freedom helicopter system model is:

[0099]

[0100] In the formula: Indicates virtual signal The derivative with respect to time, for nonlinear terms Introducing radial basis neural networks

[0101]

[0102] In the formula: For ideal weights, Indicates that the input is basis function vectors, Let be the approximate error vector, and satisfy . , .

[0103] For the second-level subsystem of a two-degree-of-freedom helicopter system model, actuator failure, control input, and combined disturbances are considered as three players. Combining a hybrid game strategy, the cost functions for the three players are defined as follows:

[0104]

[0105] In the formula: , and To formulate the optimal control strategy that achieves Nash equilibrium. To control the gain and satisfy .

[0106] Furthermore, based on Leibniz's formula and differential calculus, the Bellman equation can be obtained, expressed in terms of Hamiltonian functions as follows:

[0107]

[0108] In the formula: express right The partial derivative, for The derivative with respect to time. Then, using the stability condition. , and We can obtain:

[0109]

[0110] Furthermore, we have

[0111]

[0112]

[0113]

[0114]

[0115] In the formula, the auxiliary cost function for:

[0116]

[0117] In the formula: , , The system gain matrix The inverse matrix, , , for Time derivative, , , This is for weight estimation.

[0118] because Since the information is unknown but continuous, we choose a radial basis function neural network for approximate estimation:

[0119]

[0120] In the formula: For ideal weights, Indicates that the input is basis function vectors, This is the approximate error vector.

[0121] Furthermore, the execution-evaluation adaptive law is obtained by approximating the execution-evaluation structure. and and mixed zero-sum game participants , and And adaptive law :

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128] In the formula: and for The estimated value, , and These are the parameters to be designed.

[0129] Constructing Lyapunov functions for the second-stage subsystem of a two-degree-of-freedom helicopter system model :

[0130]

[0131] In the formula: , and .

[0132] Furthermore, the Lyapunov function Taking the derivative with respect to time, we get:

[0133]

[0134] The designed mixed zero-sum game participants , and Adaptive law Execution-evaluation adaptive law and Substitute into the formula By simplifying the inequality, we can obtain:

[0135]

[0136] Step 6: Verify the results obtained in Step 5, and construct the global Lyapunov function for the two-degree-of-freedom helicopter system model. And by differentiating it with respect to time, we get:

[0137]

[0138] In the formula: , , , , , , , , .

[0139] According to the formula Design a virtual controller Adaptive law Execution-evaluation adaptive law and Mixed zero-sum game participants , and This ensures that all signals in a two-degree-of-freedom helicopter closed-loop system are bounded by a predefined time, and that the upper bound of its settling time is [not specified]. Its stability error can be converged to a sufficiently small region, that is:

[0140]

[0141] Furthermore, regarding the self-triggering mechanism and ,have:

[0142]

[0143] In the formula: and It is a constant, determined by the initial conditions. get Then we can further obtain:

[0144]

[0145] Therefore, the time interval between the two triggers This effectively avoids the Zeno effect.

[0146] To illustrate the control effect of the method of the present invention in detail, a simulation experiment will be conducted in MATLAB, with the reference trajectory set as follows. Unknown disturbance set to The initial system conditions are set as follows: , , The actuator failure model is described as follows:

[0147]

[0148] The selected controller gains are shown in Table 2.

[0149] Table 2: Controller Gain

[0150] symbol numerical values symbol numerical values symbol numerical values 2 1 8 / 9 0.001 0.1 0.2 1 2 3 3 10

[0151] The following results were obtained through simulation experiments using MATLAB. Figure 3 It is a trajectory diagram of a two-degree-of-freedom helicopter tracking the desired angle under constraints in its pitch angle. Figure 4 It is a trajectory diagram of a two-degree-of-freedom helicopter tracking the desired angle under constraints at the yaw angle. Figure 5 This is a trajectory tracking response diagram for a two-degree-of-freedom helicopter with angular error. Figure 6 The diagram shows the control input curves of a two-degree-of-freedom helicopter system. The simulation results show that the invented tracking controller effectively avoids continuous updates of the control signal, alleviates the burden of network communication, and reduces the wear of the actuator. Figure 7It is a weight trajectory diagram of the execution-evaluation neural network for a two-degree-of-freedom helicopter system; Figure 8 The trigger interval of the control input for the two-degree-of-freedom helicopter system effectively avoids the Zeno effect. Simulation results show that the predefined time tracking control method proposed in this invention ensures the predefined time stability of the two-degree-of-freedom helicopter closed-loop system; the tracking error converges within a given time, and even in the event of actuator failure, the two-degree-of-freedom helicopter can still accurately track the reference trajectory.

[0152] The technical solutions of the present invention are not limited to the specific embodiments described above. Any technical modifications made in accordance with the technical solutions of the present invention fall within the protection scope of the present invention.

Claims

1. A two-degree-of-freedom helicopter predefined time-tolerant fault-tolerant tracking control method, characterized in that, Includes the following steps: Step 1: Establish a two-degree-of-freedom helicopter system model, which comprehensively considers internal uncertainties, external disturbances, and actuator failures. Step 2: Based on the backstepping control method, decompose the two-degree-of-freedom helicopter system model into a cascaded first-stage subsystem and a second-stage subsystem; Step 3: Construct a time-varying Barrier Lyapunov function to constrain the system state, and design a dual-channel event triggering mechanism to reduce communication burden; Step 4: For the first-level subsystem, design a virtual controller and its corresponding execution-evaluation learning law by combining reinforcement learning strategies. ; and construct a Lyapunov function that includes the time-varying Barrier Lyapunov function. Take its derivative to obtain ; Step 5: For the second-level subsystem, model the actuator failure, control input, and combined disturbance as three participants in a hybrid zero-sum game; combine reinforcement learning strategies to solve for the game strategies of the three participants and their corresponding execution-evaluation learning laws. And design an adaptive law; construct a Lyapunov function containing the time-varying Barrier Lyapunov function. Take its derivative to obtain ; Step 6: Based on the Lyapunov function and Construct the global Lyapunov function And differentiate it; By ensuring that the overall Lyapunov function satisfies the predefined time stability condition, the gain parameters of the controller to be designed are calculated through inequality scaling and simplification.

2. The two-degree-of-freedom helicopter predefined time-tolerant fault-tolerant tracking control method according to claim 1, characterized in that, The two-degree-of-freedom helicopter system model established in step 1 is specifically as follows: In the formula: , , and These represent the pitch and yaw angles of a two-degree-of-freedom helicopter, respectively. , Represents pitch angle angular velocity, Represents yaw angle angular velocity; , This represents the voltage of the pitch propeller motor. This represents the voltage of the yaw propeller motor; , Indicates an unknown failure factor. This indicates an unknown bias fault. Indicates a compound fault. Represents the control input to be designed; , For an unknown smooth nonlinear function vector, External disturbance; represent transpose; and This is the gain matrix of a two-degree-of-freedom helicopter system model.

3. The two-degree-of-freedom helicopter predefined time-tolerant fault-tolerant tracking control method according to claim 1, characterized in that, The time-varying Barrier Lyapunov function constructed in step 3 is as follows: In the formula: , and For the time-varying constraints of the design, and Indicates the system tracking error. It is a logarithmic function.

4. The two-degree-of-freedom helicopter predefined time-tolerant fault-tolerant tracking control method according to claim 1, characterized in that, The dual-channel event triggering mechanism in step 3 is as follows: In the formula: and For the first The actual execution signal of each control input; and To trigger at the time Updated ideal control signal; , respectively The first control input Second and third Next trigger time It is a positive integer; These are the weighting coefficients. ; and For error signals, , For positive integers, , This is the control input to be designed.

5. The two-degree-of-freedom helicopter predefined time-tolerant fault-tolerant tracking control method according to claim 1, characterized in that, In step 4, the virtual controller and the execution-evaluation learning law are used. , They are respectively: In the formula: For virtual controllers; , , To track the desired trajectory Time derivative, , , , for Time derivative, , , , Represents the hyperbolic tangent function. ,and The control parameters to be designed, and , For the scheduled time of the design, and For weight estimation, For input The basis function vector.

6. The two-degree-of-freedom helicopter predefined time-tolerant fault-tolerant tracking control method according to claim 1, characterized in that, In step 5, the three participants in the mixed zero-sum game perform a performance-judgment learning law. The adaptive laws are designed as follows: In the formula: , and For the three participants, actuator failure, control input, and combined disturbance; The adaptive law for the design; , , The system gain matrix The inverse matrix, To control the gain and satisfy , , , for Time derivative, , , , and For weight estimation, For input basis function vectors, For input basis function vectors, , and These are the control parameters for the design.

Images