Motor high-performance control method and system based on fixed time adaptive fuzzy control

Abstract

The invention discloses a motor high-performance control method and system based on fixed time adaptive fuzzy control. The method comprises the following steps: constructing a motor system dynamic model containing state constraint; combining the preset time performance function with the obstacle Lyapunov function to generate a tracking expected trajectory; a composite disturbance observer is introduced into a motor system dynamics model, unknown disturbance existing in motor operation is estimated and compensated, and a fuzzy adaptive controller with fixed time and preset performance is designed; the Lyapunov stability theory is used for proving that the controller enables the motor system to be stable within preset fixed time; the method can be applied to the fields of industrial automation, electric automobiles, automatic production lines and the like, motor tracking control can be ensured to meet preset performance indexes within fixed time, the speed of the motor is ensured to be within a limited speed range, and the running performance and stability of the motor are improved.

Description

Technical Field

[0001] This invention relates to control methods and systems, specifically to a high-performance motor control method and system based on fixed-time adaptive fuzzy control. Background Technology

[0002] As a core actuator, the electric motor is widely used in many fields such as industrial automation, robotics, electric vehicles, and precision manufacturing. Its core function is to accurately convert received electrical signals into angular displacement or angular velocity output of the shaft. The performance of the motor control system directly determines the dynamic response, positioning accuracy, operating efficiency, and stability of the entire equipment. However, in actual operation, motors often encounter load variations, which adversely affect their operating performance and stability.

[0003] Traditional motor control methods include torque control, position control, and speed control. While these methods can meet different motion control requirements to some extent, they often struggle to adjust control strategies quickly and accurately when faced with complex and variable load conditions, such as sudden load changes or nonlinear disturbances. This can lead to decreased control performance or even system instability.

[0004] Therefore, to improve the response speed and disturbance rejection performance of motors, a novel control method is urgently needed that can proactively adapt to the unknown dynamics of the system, achieve stable convergence within a fixed time, and effectively handle nonlinear disturbances. Simultaneously, it is also necessary to ensure that specific process constraints are not violated during the control process to guarantee the safety and reliability of system operation. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a high-performance motor control method based on fixed-time adaptive fuzzy control to ensure that the motor tracking control meets the preset performance indicators within a fixed time, while ensuring that the motor speed is within the limited speed range, thereby improving the motor's operating performance and stability. On the other hand, this invention also provides a high-performance motor control system based on fixed-time adaptive fuzzy control.

[0006] Technical solution: The high-performance motor control method of the present invention includes the following steps:

[0007] S1. Construct a dynamic model of the motor system including state constraints;

[0008] S2. Combine the preset time performance function with the obstacle Lyapunov function to generate the desired tracking trajectory within a preset fixed time.

[0009] S3. Introduce a composite disturbance observer into the dynamic model of the motor system containing state constraints to estimate and compensate for unknown disturbances that exist in the operation of the motor.

[0010] S4. Construct the Lyapunov function and apply the Lyapunov stability theory to prove that the controller makes the motor system stable within a preset fixed time, and obtain a stable result.

[0011] Preferably, the formula for the motor system dynamics model including state constraints described in S1 is as follows:

[0012]

[0013] Where x1 represents the position of the motor rotor, and x2 represents the speed of the motor. Let J represent the rotational acceleration of the motor, B represent the moment of inertia of the system load referred to the motor, u represent the viscous damping coefficient of the system referred to the motor, f(x1,x2) represent the nonlinear friction function, d(t) represent the unknown disturbance, and k represent the rotational acceleration of the motor. x1 k x2 This represents the state constraint boundary.

[0014] Preferably, the formula combining the preset time performance function and the obstacle Lyapunov function in S2 is as follows:

[0015]

[0016] Where φ1=z1-δ1, z1=x1-y d To track error variables, δ1 and δ2 are compensation signals. The estimated value of the fuzzy parameter θ. Let y be the observation error value of the composite disturbance. d This is the desired tracking signal.

[0017] Preferably, the fuzzy adaptive controller in S3 is as follows:

[0018]

[0019] Where α1 is the input of the first-order filter, i.e., the virtual control variable to be designed. The derivative of the desired tracking signal, For the adaptive law, φ1=z1-δ d τ1=φ1 / (λ1) 2 -φ1 2 ), τ2=φ2 / (λ2) 2 -φ2 2 ), m1, m2, σ1, σ2, b 11 b 12 b 21 b 22 , where a is a positive parameter For fuzzy parameter estimation, ξ is the radial basis function vector, 0 <k d <2, k1>0, k2>0, 1 / 2 <M<1,N> 1.

[0020] The high-performance motor control system of the present invention includes:

[0021] The modeling module is used to construct a dynamic model of an electric motor system that includes state constraints.

[0022] The performance constraint module is used to combine a preset time performance function and a barrier Lyapunov function to output the expected tracking trajectory within a preset fixed time.

[0023] The disturbance observation module is used to introduce a composite disturbance observer into the dynamic model of a motor system with state constraints, to estimate and compensate for unknown disturbances in motor operation, and to design a fuzzy adaptive controller with predetermined performance at a fixed time.

[0024] The stability proof module is used to construct the Lyapunov function and apply Lyapunov stability theory to prove that the controller makes the motor system stable within a preset fixed time, thus obtaining a stable result.

[0025] Preferably, the disturbance observation module includes an introduction of a fuzzy logic system to approximate the unknown nonlinear friction function, thereby eliminating the influence of the nonlinear friction function.

[0026] Preferably, the fuzzy logic system is combined with an adaptive control method to dynamically update the adaptive rate and approximate the changes in nonlinear friction in real time.

[0027] Preferably, the disturbance observation module includes an introduction of a command filter to avoid high-order derivative calculations and reduce complexity.

[0028] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0029] 1. Through the fusion of multiple strategies, precise control of the motor under complex operating conditions is achieved. By combining the preset time performance function and the obstacle Lyapunov function, it can not only ensure that the motor output accurately tracks the desired trajectory within a preset fixed time, but also achieve the preset adjustment time and steady-state accuracy by adjusting the parameters.

[0030] 2. By introducing a composite nonlinear disturbance observer to estimate unknown disturbances in real time, and combining it with a fuzzy logic system to approximate unknown nonlinear functions, the total disturbance can be quickly identified and dynamically compensated. This can significantly improve the anti-disturbance capability of the motor system, strictly constrain motor speed and other state variables within the safe operating range, and solve problems such as convergence time depending on the initial state and difficulty in guaranteeing state constraints in traditional control. It balances high precision and high safety of control and can effectively address unknown disturbances and nonlinear friction problems that exist during operation.

[0031] 3. By introducing a command filtering method, the complexity of the control algorithm can be significantly reduced and the implementation efficiency in practical engineering can be improved by avoiding repeated calculation of the higher-order derivatives of the tracking signal. The introduction of an adaptive control strategy can realize online parameter updates, enhance the adaptability of the motor system to changes in unknown parameters, and ensure that the control system can remain stable in complex operating environments.

[0032] 4. By utilizing the fixed-time convergence characteristic, the system can be dynamically adjusted within a set time without relying on the initial state, thereby enhancing the system's response speed and real-time performance.

[0033] 5. This invention can effectively cope with complex scenarios such as limited motor speed and position disturbance. With its advantages of fixed-time high precision, strong robustness and state constraint guarantee, it significantly improves the operating performance of the equipment and the reliability of the system, and has important engineering application value. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the motor system control of the present invention;

[0035] Figure 2 This is a schematic diagram of the motor system of the present invention;

[0036] Figure 3 This is a schematic diagram of the fuzzy control process of the present invention. Detailed Implementation

[0037] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0038] A high-performance motor control method based on fixed-time adaptive fuzzy control includes the following steps:

[0039] S1. Construct a dynamic model of the motor system including state constraints, as shown below:

[0040]

[0041] Where x1 represents the position of the motor rotor, and x2 represents the speed of the motor. Let J represent the rotational acceleration of the motor, B represent the moment of inertia of the system load referred to the motor, u represent the viscous damping coefficient of the system referred to the motor, f(x1,x2) represent the nonlinear friction function, d(t) represent the unknown disturbance, and k represent the rotational acceleration of the motor. x1 k x2 Represents the state constraint boundary.

[0042] S2. Combine the preset time performance function with the obstacle Lyapunov function.

[0043] S21. The preset time performance function is as follows:

[0044]

[0045] Where λ(t) represents a preset performance function that monotonically decreases with time to a threshold, achieving dual control over tracking accuracy and convergence time; κ and Γ represent positive parameters; and λ f Indicates steady-state accuracy; And T s =κ / Γ represents the set time, from which we can know that λ(t) at t=T s It converges to λ in time f And it remains constant thereafter. Because T s =κ / Γ can reveal the set time T s It is only related to the design parameters κ and Γ, therefore, the desired settling time can be obtained by adjusting these two parameters. Furthermore, the desired accuracy can be achieved by selecting the parameter λ(t).

[0046] Therefore, as long as the tracking error is confined within the performance function boundary within a fixed time, the desired settling time and steady-state accuracy can be achieved simultaneously.

[0047] S22, The barrier Lyapunov function (BLF) is shown below:

[0048]

[0049] Where φ1=z1-δ1, z1=x1-y d Let y represent the tracking error variable. d δ1 represents the desired tracking signal, and δ1 represents the command filter compensation signal.

[0050] The combination of the predetermined performance function and the barrier Lyapunov function can guarantee that the tracking error satisfies |φ|≤λ(t) within a fixed time.

[0051] S23. The design combines the predetermined performance function with the barrier Lyapunov function as follows:

[0052]

[0053] Where φ1=z1-δ1, z1=x1-y d To track error variables, δ1 and δ2 are compensation signals. The estimated value of the fuzzy parameter θ. Let y be the observation error value of the composite disturbance. d This is the desired tracking signal.

[0054] S3. Design a fixed-time, predetermined-performance fuzzy adaptive controller. The specific steps are as follows:

[0055] S31. In the dynamic model of the motor system containing state constraints, a composite nonlinear disturbance observer is introduced for real-time estimation and compensation of the total disturbance. This observer estimates and compensates for unknown disturbances existing during motor operation. The composite nonlinear disturbance observer is as follows:

[0056]

[0057] in, Let represent the estimated value of the composite disturbance D, and v represent the auxiliary variable, which is the estimation error of the composite nonlinear disturbance observer for the system's composite disturbance. It converges to the neighborhood of the origin within a fixed time, and the convergence rate is determined by the observer gain parameter k. d Adjustment; 0 <k d <2, k1>0, k2>0, 1 / 2 <M<1,N> 1.

[0058] S32. In order to eliminate the influence of the nonlinear friction function, a fuzzy logic system is used to estimate this unknown function. The fuzzy logic system is used to approximate the unknown nonlinear function.

[0059] S33. Combining fixed-time command filters and adaptive control methods, a fixed-time predetermined performance fuzzy adaptive controller is designed. Adaptive control dynamically updates the adaptive rate to approximate changes in nonlinear friction in real time, improving the system's robustness to parameter drift. The command filter avoids high-order derivative calculations, reducing complexity. Therefore, the dynamic system model of the motor can be modified as follows:

[0060]

[0061] Where D=d+ε * ε represents the composite of the neural network approximation error and the unknown perturbation. * It is the approximation error of the neural network. For fuzzy parameter estimation, ξ is the radial basis function vector, and W *T These are the weights of the neural network.

[0062] Fixed-time command filter:

[0063] (1) Define z1 = x1 - y d z2=x2-α 1c , where α 1c This is the output signal of the instruction filter.

[0064] (2) The fixed-time command filter is designed as follows:

[0065]

[0066] Where μ=α 1c -α1, l1, l2, and m are positive parameters.

[0067] (3) Filtering error compensator:

[0068]

[0069] Where δ1 and δ2 are compensation signals, and b1 and b2 are positive parameters.

[0070] S34. The fuzzy adaptive controller is designed as follows:

[0071]

[0072] Where α1 is the input of the first-order filter, i.e., the virtual control variable to be designed. The derivative of the desired tracking signal, For the adaptive law, φ1=z1-δ d τ1=φ1 / (λ1) 2 -φ1 2 ), τ2=φ2 / (λ2) 2 -φ2 2 ), m1, m2, σ1, σ2, b 11 b 12 b 21 b 22 , where a is a positive parameter For fuzzy parameter estimation, ξ is the radial basis function vector;

[0073] 0 <k d <2, k1>0, k2>0, 1 / 2 <M<1,N> 1.

[0074] S4. Construct the Lyapunov function and apply Lyapunov stability theory to prove that the designed fuzzy adaptive controller can stabilize the motor closed-loop control system, ensuring that the motor closed-loop control system remains stable within a fixed time t ≤ T. s (T s It indicates that the system is stable within a preset fixed time period, and all system variables are bounded, achieving fixed-time convergence and high-precision tracking performance indicators.

[0075] Differentiating the Lyapunov function in S23 and substituting the virtual controller and adaptive law into the simplified form, we obtain:

[0076]

[0077] Where Δ is a bounded constant, according to the fixed-time stability theorem, we know that:

[0078] When 1 / 2 is satisfied <M<1,N> 1,0 <k d <2, and for all t≥T c hour, Established;

[0079] Convergence time This demonstrates that the convergence time is independent of the initial conditions of the system.

[0080] Furthermore, for any given position tracking error ε1, the parameter is adjusted so that λ f +μ1≤ε1 holds true;

[0081] Where |α 1c -α1|≤μ1, where μ1 is an integer real number, λ f If the final convergence boundary of the predetermined performance function is given, then the motor rotor position x1 at a fixed time T... c Internal strict tracking of the desired signal y d And the tracking error z1=x1-y d At time T c It converges within a given error ε1; the estimation error of the composite nonlinear disturbance observer for the total system disturbance D. The convergence rate to the neighborhood of the origin within a fixed time can be determined by the observer gain parameter k. d adjust.

[0082] A high-performance motor control system based on fixed-time adaptive fuzzy control includes:

[0083] The modeling module is used to construct a dynamic model of an electric motor system that includes state constraints.

[0084] The performance constraint module is used to combine a preset time performance function and a barrier Lyapunov function to output the expected tracking trajectory within a preset fixed time.

[0085] The disturbance observation module is used to introduce a composite disturbance observer into the dynamic model of a motor system with state constraints, to estimate and compensate for unknown disturbances in motor operation, and to design a fuzzy adaptive controller with predetermined performance at a fixed time.

[0086] The stability proof module is used to construct the Lyapunov function and apply Lyapunov stability theory to prove that the controller makes the motor system stable within a preset fixed time, thus obtaining a stable result.

Claims

1. A high-performance motor control method based on fixed-time adaptive fuzzy control, characterized in that, Includes the following steps: S1. Construct a dynamic model of the motor system including state constraints; S2. Combine the preset time performance function with the obstacle Lyapunov function to generate the desired tracking trajectory within a preset fixed time. S3. Introduce a composite disturbance observer into the dynamic model of the motor system containing state constraints to estimate and compensate for unknown disturbances in the operation of the motor, and design a fuzzy adaptive controller with a fixed time and predetermined performance. S4. Construct the Lyapunov function and apply the Lyapunov stability theory to prove that the controller makes the motor system stable within a preset fixed time, and obtain a stable result.

2. The high-performance motor control method according to claim 1, characterized in that, The dynamic model formula for the motor system with state constraints described in S1 is as follows: Where x1 represents the position of the motor rotor, and x2 represents the speed of the motor. Let J represent the rotational acceleration of the motor, B represent the moment of inertia of the system load referred to the motor, u represent the viscous damping coefficient of the system referred to the motor, f(x1,x2) represent the nonlinear friction function, d(t) represent the unknown disturbance, and k represent the rotational acceleration of the motor. x1 k x2 Represents the state constraint boundary.

3. The high-performance motor control method according to claim 1, characterized in that, The formula combining the preset time performance function and the obstacle Lyapunov function described in S2 is as follows: Where φ1=z1-δ1, z1=x1-y d To track error variables, δ1 and δ2 are compensation signals. The estimated value of the fuzzy parameter θ. Let y be the observation error value of the composite disturbance. d This is the desired tracking signal.

4. The high-performance motor control method according to claim 1, characterized in that, The fuzzy adaptive controller described in S3 is as follows: Where α1 is the input of the first-order filter, i.e., the virtual control variable to be designed. The derivative of the desired tracking signal, For the adaptive law, φ1=z1-δ d τ1=φ1 / (λ1) 2 -φ1 2 ), τ2=φ2 / (λ2) 2 -φ2 2 ), m1, m2, σ1, σ2, b 11 b 12 b 21 b 22 , where a is a positive parameter For fuzzy parameter estimation, ξ is the radial basis function vector, 0 <k d <2, k1>0, k2>0, 1 / 2 <M<1,N> 1.

5. A high-performance motor control system based on fixed-time adaptive fuzzy control, characterized in that, include: The modeling module is used to construct a dynamic model of an electric motor system that includes state constraints. The performance constraint module is used to combine a preset time performance function and a barrier Lyapunov function to output the expected tracking trajectory within a preset fixed time. The disturbance observation module is used to introduce a composite disturbance observer into the dynamic model of a motor system with state constraints, to estimate and compensate for unknown disturbances in motor operation, and to design a fuzzy adaptive controller with predetermined performance at a fixed time. The stability proof module is used to construct the Lyapunov function and apply Lyapunov stability theory to prove that the controller makes the motor system stable within a preset fixed time, thus obtaining a stable result.

6. The high-performance motor control system according to claim 5, characterized in that, The disturbance observation module includes an introduction of a fuzzy logic system to approximate the unknown nonlinear friction function and eliminate the influence of the nonlinear friction function.

7. The high-performance motor control system according to claim 6, characterized in that, The fuzzy logic system, combined with the adaptive control method, dynamically updates the adaptive rate to approximate the changes in nonlinear friction in real time.

8. The high-performance motor control system according to claim 5, characterized in that, The disturbance observation module includes a command filter to avoid calculating higher-order derivatives and reduce complexity.

9. A computer device, characterized in that, It includes one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs, when executed by the processors, implement the steps of the high-performance motor control method as described in claims 1-4.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the high-performance motor control method as described in claims 1-4.

Images