Optimal design of time-varying parameter fractional order controller using ameliorated gazelle optimization algorithm

The model parameter uncertainty and controller gain disturbance of the factory servo system are challenges that affect the robustness and control performance of the system. In this paper, a class of factory servo systems with non-integer order is studied. The stable boundary trajectory method of the fractional order system is used to determine the parameter stability domain that makes the control system stable. An optimal gain trade-off design method for time-varying parameter fractional order PID controller (TPPI lambda D mu$$ \mathrm{TP}{PI}<^>{\lambda }{D}<^>{\mu } $$) is proposed. The time function is introduced as the adjustment formula to realize the adaptive adjustment of the controller gain. The Lyapunov theorem analyzes the stability of the method. At the same time, an ameliorated gazelle optimization algorithm (AGOA) is proposed to optimize the parameters of the TPPI lambda D mu$$ \mathrm{TP}{PI}<^>{\lambda }{D}<^>{\mu } $$ controller, and the weight relationship is changed to set the objective function to obtain the optimal performance combination after optimization. The benchmark function optimization test is completed. Statistical analysis shows that AGOA can enhance the global search ability, prevent the acquisition of local optimum, and have faster convergence speed. The final simulation results show that the proposed scheme is a promising alternative to improve the system control performance.