Optimal robust fractional order pi for time-delay systems λ Optimization method of d controller

Abstract

The invention belongs to the technical field of automatic control, and discloses an optimal robust fractional order PI for a time-delay system λ Optimization methods for D controllers. The method comprises the following steps: (a) constructing the closed-loop transfer function of the control system to be optimized; (b) obtaining the closed-loop transfer function with respect to the PI λ The characteristic equation of the unknown parameter in the D controller; (c) construct the constraint condition that the first-order inertia delay control system to be optimized needs to satisfy, utilize described characteristic equation to determine described PI λ The value range of the unknown parameter in the D controller is solved according to the constraints and the value range and the PI is obtained λ The values ​​of the unknown parameters in the D controller are used to determine the PI λ D controller, which realizes the optimization process. Through the present invention, the realization of PI λ The optimization of the D controller makes the control system have strong robustness and optimal dynamic performance.

Description

technical field [0001] The invention belongs to the technical field of automatic control, and more specifically, relates to an optimal robust fractional order PI for a time-delay system λ Optimization methods for D controllers. Background technique [0002] The time-delay system is the most common type of system in industrial systems. The design of fractional-order controllers for this system is extremely important. Fractional-order PI λ The transfer function of the D controller: [0003] [0004] Among them, K p 、K i and K d They are proportional, differential and integral gains respectively, and λ is the integral order, and its range is: 0<λ<2. Compared with the classic PID controller, there is one more adjustable parameter, which can achieve better control performance, but Due to the large number of adjustable parameters, parameter tuning has certain difficulties. [0005] At present, the tuning of fractional order controllers is mainly divided into frequen...

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Problems solved by technology

[0004] Among them, K p 、K i and K d They are proportional, differential and integral gains respectively, and λ is the integral order, and its range is: 0<λ<2. Compared with the classic PID controller, there is one more adjustable parameter, which can achieve better control performance, but Due to more adjustable parameters, parameter tuning is difficult

[0005] At present, the tuning of fractional order controllers is mainly divided into frequency domain tuning method and time domain tuning method. The tuning method is to meet the minimum performance index (integral square error, time multiplied by error absolute value integral, etc.) through the optimization algorithm, but it cannot meet the frequency domain index desired by the user, and the robustness is poor

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