A Design Method of Three-Dimensional Fuzzy Controller

Abstract

The present invention discloses a design method for a three-dimensional fuzzy controller, which combines fuzzy control with optimal PID control. For a typical first-order lag integral delay control object, an analytical form and parameter tuning method of the three-dimensional fuzzy controller are proposed. The advantages of the present invention are that the controller principle is simple, the algorithm is easy to implement, and the rule explosion and static error problems of the fuzzy controller can be avoided.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent control, and in particular relates to a design method of an analytical three-dimensional fuzzy controller. Background Art

[0002] Intelligent control theory is a new generation of control theory, developed in response to the lack of precise models of controlled objects in both classical and modern control theories. It is a form of computer digital control that combines artificial intelligence and feedback control theory. Fuzzy control, as an important and effective form of intelligent control, has rapidly developed. In the design of fuzzy control systems, the number of fuzzy rules increases exponentially with the number of controlled variables and their domains. Excessive numbers of rules complicate the implementation of fuzzy control algorithms and make it difficult to meet the requirements of real-time control.

[0003] One way to solve this problem is to use an analytical fuzzy controller, which approximates the fuzzy control rules through analytical descriptions and has the characteristics of fast operation and strong adaptability. Currently, there are few published patents, scientific papers, and graduation theses related to three-dimensional fuzzy control. Summary of the Invention

[0004] The present invention aims to provide a design method for an analytical three-dimensional fuzzy controller for a typical first-order lag and integrator plus delay (FOLIPD) control object, so as to guide the design of an analytical fuzzy control system.

[0005] The related technical problems of the present invention are mainly solved by the following technical solutions: A design method of a three-dimensional fuzzy controller is used for a typical first-order lag integral delay control object, the general form of the transfer function of the control object is Let the parameter tuning formula be:

[0006]

[0007] The analytical expression is G F (s) = K F (α+βs+γs 2 ) three-dimensional fuzzy controller, where K is the magnification of the model, T is the integral time constant, τ is the delay time, e is the natural constant, K Fis the proportional factor of the three-dimensional fuzzy controller, a1, a2, a3, b1, b2, b3 are constants, and their values vary according to the calculation method of the controller performance index. α, β, γ are adjustment factors, and their values are α∈[0,1], β∈[0,1], γ∈[0,1], and α+β+γ=1, which represents the weighting of error, error change and error change rate.

[0008] In the design method of a three-dimensional fuzzy controller, the coefficients of the controller parameter tuning formula are as follows:

[0009]

[0010] In the parameter setting coefficient table, IAE, ISE, and ITAE represent three different error integral performance indicators, and the formula is: IAE = ∫|e(t)|dt, ISE = ∫e 2 (t)dt, ITAE=∫t|e(t)|dt, where e(t) is the error function.

[0011] The present invention has the following advantages: The design method for a three-dimensional fuzzy controller proposed in this patent has two innovations compared to the prior art: first, it proposes an analytical three-dimensional fuzzy controller parameter tuning formula; second, it proposes a coefficient table for the analytical three-dimensional fuzzy controller parameter tuning formula. When the controlled object model is known, the control method proposed in this patent achieves better control results than classic PID control; and when the controlled object model is inaccurate, the control method proposed in this patent has greater adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 This is the basic structure diagram of the three-dimensional fuzzy control system of the present invention;

[0013] Figure 2 This is a comparison chart of simulation results with the best IAE index of the controller of the present invention;

[0014] Figure 3 This is a comparison chart of simulation results with the best ISE index of the controller of the present invention;

[0015] Figure 4 This is a comparison chart of simulation results with the best ITAE index of the controller of the present invention. DETAILED DESCRIPTION

[0016] The technical solution of the present invention is further described in detail below through examples and in conjunction with the accompanying drawings.

[0017] The present invention discloses a design method for a three-dimensional fuzzy controller. For a typical first-order lag integral delay control object, a first-order lag integral delay controlled object model is taken. Let the parameter tuning formula be

[0018]

[0019] The analytical expression is G F (s) = K F (α+βs+γs 2 )'s three-dimensional fuzzy controller.

[0020] Where K is the magnification of the model, T is the integration time constant, τ is the delay time, e is the natural constant, K F is the proportional factor of the three-dimensional fuzzy controller, α, β, γ are adjustment factors, and the values are α∈[0,1], β∈[0,1], γ∈[0,1], and α+β+γ=1, which represents the weighting of error, error change and error change rate.

[0021] The coefficients of the controller parameter tuning formula are as follows:

[0022]

[0023] In the parameter setting coefficient table, IAE, ISE, and ITAE represent the error integral performance index, and the formula is as follows:

[0024] IAE=∫|e(t)|dt

[0025] ISE=∫e 2 (t)dt

[0026] ITAE=∫t|e(t)|dt

[0027] Where e(t) is the error function.

[0028] According to the formula and coefficient table proposed in this patent, the parameters of the three-dimensional fuzzy controller are calculated. The calculation results are shown in the table below (controller parameters for G1 object), which also lists the parameters of the optimal PID control.

[0029]

[0030] The simulation comparison results are as follows Figures 2 to 4 From the simulation results, it can be seen that the control effect of the three-dimensional fuzzy controller using the design method proposed in this patent is better than that of the optimal PID controller in terms of integral indicators such as IAE, ISE, and ITAE, and control indicators such as overshoot and response time.

[0031] The design method for a three-dimensional fuzzy controller proposed in this patent has two innovations compared to existing technologies: first, it proposes an analytical three-dimensional fuzzy controller parameter tuning formula; second, it proposes a coefficient table for this analytical three-dimensional fuzzy controller parameter tuning formula. When the controlled object model is known, the control method proposed in this patent achieves better control results than classic PID control; and when the controlled object model is imprecise, the control method proposed in this patent has greater adaptability.

[0032] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described specific embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

Claims

1. A design method for a three-dimensional fuzzy controller for a first-order lag integral delay control object Its characteristics are: Let the parameter tuning formula be The analytical expression is G F (s) = K F (α+βs+γs 2 ) three-dimensional fuzzy controller, where K is the magnification of the model, T is the integral time constant, τ is the delay time, e is the natural constant, K F is the proportional factor of the three-dimensional fuzzy controller, a1, a2, a3, b1, b2, b3 are constants, α, β, γ are adjustment factors, and the values are α∈[0,1], β∈[0,1], γ∈[0,1], and α+β+γ=1, which represents the weighting of error, error change and error change rate.

2. The design method of a three-dimensional fuzzy controller according to claim 1, characterized in that: The coefficients of the parameter tuning formula are as follows: In the parameter setting coefficient table, IAE, ISE, and ITAE represent the error integral performance index, and the formula is: IAE=∫|e(t)|dt ISE=∫e 2 (t)dt ITAE=∫t|e(t)|dt Where e(t) is the error function.

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