Design of fractional — Order PID controller based on genetic algorithm

Wang, Lingxin; Wang, Chunyang; Yu, Liting; Liu, Yonghua; Sun, Jingxue

doi:10.1109/ccdc.2017.7978631

Cited by 5 publications

(1 citation statement)

References 7 publications

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“…In each iteration, a group of candidate solutions is reserved, and the better individuals are selected from the solution group according to a certain index, and these individuals are combined by genetic operators (selection, crossover, and mutation) to produce a new generation of candidate solution group. Repeat the process until a convergence index is satisfied 28 . The basic steps of the genetic algorithm are as follows: Initialize the population (decode/encode); Detection and evaluation of individual fitness; Selection algorithm; Crossing and variation. During the parameter adjustment process, the fitness function is selected as

f ((), a, b, ω_{c}, ω_{x}, k_{d}) = (||, f_{1}) + (||, f_{2}) + (||, f_{3}) + (||, f_{4}) + (||, f_{5}) .

The problem of calculating five nonlinear multiparameter equations is transformed into the following optimization problem:

\min f ((), a, b, ω_{c}, ω_{x}, k_{d}) .

With

f_{1} = (||, L ((), j ω_{c})) - 1,

f_{2} = ∠ L ((), j ω_{c}) - italicpm + π,

f_{3} = ∠ L ((), j ω_{x}) + π,

f_{4} = (||, L ((), j ω_{x})) - 0.5,

f_{5} = \frac{\partial ∠ L (italicjω)}{\partial ω}|

…”

Section: Parameters Tuning Based On Frequency Domain Analysismentioning

confidence: 99%

Tuning of fractional complex‐order direct current motor controller using frequency domain analysis

Zheng

Zhang

Huang

2020

Math Methods in App Sciences

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For the speed control of direct current motor, a fractional complex‐order controller (FCOC) is proposed in this paper. The FCOC is an extension of the fractional‐order controller. It is known that fractional‐order controllers exhibit strong robustness to open‐loop gain variations. However, in actual situations, due to external interference, the phase angle and gain of the system may change at the same time. The FCOC proposed in this paper adds an additional parameter, which makes the system show strong robustness when the phase angle and gain change simultaneously. Existing methods for parameter tuning of FCOCs only consider the preset gain crossover frequency and the expected phase margin. This may not allow the system to exhibit good dynamic and stable performance. In this paper, based on the frequency domain analysis, the parameters of the FCOC are tuned by integrating the gain crossover frequency, cutoff frequency, phase margin, and amplitude margin. The optimal solution satisfying a set of constraint equations is obtained by optimization algorithm. Finally, the simulation results are compared with those of the fractional‐order controller and the integer‐order controller. At the same time, the robustness of the system under disturbance is analyzed. The results show that the complex fractional‐order control presented in this paper has better dynamic performance and robustness.

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