Research On Parameter Tuning And Application Of Fractional Order Controller Based On Extremum Seeking

As an extension of the regular PID controller,the theory of fractional order PI~?D~?controller is gradually becoming a research hotspot in the field of control due to its proven performance advantages.In fractional order PI~?D~?controller,the regular integer calculus is replaced by the fractional calculus with an adjustable order,which allows the fractional order controller to have a more flexible structure and a larger adjusting range,while the parameter tuning difficulty is increased.Extremum seeking algorithm,which is a kind of adaptive optimization algorithm based on gradient estimation,studies show that this tuning method can achieve excellent control effect.Based on the extremum seeking algorithm,this paper will study the parameter tuning for the fractional order PI~?controllers.The research content mainly includes:(1)The classical tuning approach for the fractional order PI~?controller based on the performance specifications in frequency domain is analyzed and improved,and the improved setting process will no longer need accurate mathematical model of the controlled process,and the necessary frequency domain characteristics of the controlled process can be achieved by the open-loop experiments.The fractional order controller obtained by classical tuning method has strong robustness due to the consideration of the iso-damping property.(2)The extremum seeking algorithm is applied to the parameter tuning for the fractional order PI~?controller,and the whole tuning is based on the experimental data,therefore the accurate model of the controlled process is also not required.The simulation results show that the algorithm can effectively reduce the cost function and improve the control performance of the closed loop system.However,the tuning result is not constrained by iso-damping property,and it leads to some closed loop systems with poor robustness.(3)Combining the classical tuning method which considers iso-damping property with the extremum seeking algorithm,a novel parameter tuning method for the fractional order PI~?controller is proposed.Simulation results show that because of the constraint of iso-damping property,the fractional order controller tuned by the proposed method could achieve an excellent balance between the control performance and robustness,although its closed loop control performance is not as good as the controller directly tuned by extremum seeking tuning method.(4)Tuning the parameter of the fractional order PI~?controller at the typical real-life process which includes the electro-hydraulic position servo system and the DC torque motor platform.The experimental results are consistent with the simulation results,and prove the feasibility and effectiveness of the proposed parameter tuning method for the fractional order controller in practical application.