Design Of The Optimal Control System With Pure Time Delay Using The Improved High Order Butterworth Optimal Transfer Function

In modern control theory, Lag phenomenon was very common, and was a objectwhich was more difficult to control. Currently, ITAE, Butterworth optimal transferfunction was widely applied in the pure time delay optimal control system. Whenusing model devided by time and Pade approximation to approximate the puretime-delay factor, the high order optimal transfer function would be used in the puretime-delay optimal control system, but the overshoot and regulation time of the highorder ITAE and Butterworth optimal transfer function would become more biggerand more longer. Therefore,we would improve the high order Butterworth optimaltransfer function, and apply them to the pure time delay optimal control system. Sodesigning of the optimal control system with time delay which used the improvedhigh order Butterworth optimal transfer function had important theory significanceand actual application value.This paper has the main working point and innovation points as follows:Firstly, Based on the traditional Butterworth optimal transfer function, we putforward an improved high order Butterworth optimal transfer function. According toanalyse the main characteristics of the improved high order Butterworth optimaltransfer function, reasearched the inverse problem of the improved Butterworthoptimal control firstly.Secondly, when we designed the pure time-delay state feedback optimal controlsystem using model devided by time to approach the pure time delay factor.In thepaper,we designed the pure time delay state feedback optimal control system withobserver using the improved high order Butterworth optimal transfer function as theclosed-loop transfer function of the system,optimization and coordination between thestate feedback gain matrix and state observer. The system had strong robustness andthe anti-interference characteristics.But the system has steady-state error because ofits single degree of freedom.So we will add an integrator to constitute the puretime-delay cascade state feedback optimal control system.Through the simulation experiments showed that the control system can eliminate the steady-state error andhave strong robustness and the anti-interference characteristics.It is a two degree offreedom control system.Thirdly, when we designed the pure time delay optimal control system usingsymmetrical Pade approximation to approach the pure time delay factor. we tookmeasures mainly as follows:kept the pure time delay factor of the molecularunchanged and approached the pure time delay factor of the denominator bysymmetrical Pade approximation,then used the improved high order Butterworthoptimal transfer function as the closed-loop transfer function of the system to designthe controller.When we designed the pure time-delay optimal control system byasymmetric Pade approximation to approach the pure time delay factor,also used theimproved high order Butterworth optimal transfer function as the closed-loop transferfunction of the system and optimize the state feedback gain matrix and state observerto design the control system.According to reaserching,the control system designed bythe two methods had good stability and strong robustness.