Design Of H_∞PID Contollers For Time-Delay Systems

It is well known that the majority of controllers in the industral community are proportional integral derivative(PID) controllers, witch have good performances and simple structure, provided that their parameters are properly tuned.At the same time,time-delay is a common phenomenon in many processes.The existence of time-delay in a control loop is a source of the instability and performance deterioration.On the other hand,the uncertainty existing in the analysis and design of the practical system is another difficult problem. Solving this kind of uncertainty problem belongs to robust control. Among this, one of the representative control theory to solve the robust problem is the H, control theory, which minimizes the H∞-norm of a prescribed system transfer function. The aim of this paper is to combine PID control with H∞, control, and develop a computationally efficient procedure for carrying out a stabilizing parameter sets,in which the H∞-norm constraint curves of the sensitivity function of the closed-loop is considered.This paper considers the problem of designing H∞. proportional-integral-derivative(PID) controllers for which the time-delay system (First-Order plus Delay Systems and Second-Order plus Delay Systems) is internally stable and the H∞-norm of a related transfer is less than a prescribed level. Firstly a proportional gain of the PID controller is fixed. Secondly the stable region in(ki, kd) —plane is drawn.And then within the stability region, the H∞, performance indicators are made to meet the proposed requirements by choosing appropriate weighting function. In this paper weight function is studied for constant and function constant. Selecting the set values which are connected into a line within the stability region by algebra of trail and error method, when drawing the boundary curve of H∞-norm condition. Finally First-Order plus Delay Systems and Second-Order plus Delay Systems are studied respectively. Illustrating examples are followed in each calculation and MATLAB simulation to show if the boundary curve is in accordance with the requirements for H∞-norm condition and the stability of the step response.By using a graphical stability criterion to set the parameters of H∞PID controller, this paper enjoys the characteristics of vivacity and flexibility. Besides this, it can not only select the parameters conveniently and accurately according to the design requirements, but also can realize other performance requirements under the H∞ constraits condition, i.e, the multi-objective is realized.By using the graphical stability criterion and adopting theoretical derivation and simulation experiment, it can be seen that the parameter setting method based on the H∞-norm of the sensitivity function in this paper is feasible and that the.simulation shows good effects, in this way, theoretical results are verified.