The Stability Analysis Of Multiple Time-Delay System Based On Spectral Discrietization Method

There are many time delay phenomena in the field of industrial process. Time delay is one of the main reasons causing the performance deterioration even instability of the control system. Moreover, the system has a lot of control points and different time delays because of the different distances between the control points and the exit of the product in the long process. The characteristics of multiple time-delay may lead to long time instability of conditions, large fluctuations of production indexes in closed control or adjustment of work points. It can seriously affect the normal production, the output and quality of product and energy consumption. The multiple time-delay increases the difficulty of stability analysis and the control of the system. So there are a lot of theoretical significances and practical values to study the stability of multiple time-delay control system.The spectral discretization method is an efficient method to compute all the characteristic roots in the given right half plane or in a given region. In this paper, the basic principle of spectral discretization method is discussed, and then this method is introduced to the field of stability analysis of multiple time-delay control system. The following are the main research works and creativity results:(1) Study on the PID stability algorithm of multiple time delays based on the spectral discretization method. First, all possible stability boundaries are obtained in the frequency domain. Then, the system is transformed from transfer function to state space. In the end, the real stability regions are determined by using the spectral discretization method. The algorithms are simple in computation and the results have high accuracy.(2) The stability algorithm of the smith predictive control system is proposed when the predictive model is mismatch. The algorithm transforms the smith system into multiple time-delay system, and the new multiple time-delay system is reconstructed based on the fact that the stability is related to system poles instead of zeros. The reconstructed system has the same stability regions with the smith predictive system. The stability regions of the constructed system are acquired based on the spectral discretization method, and these regions also reflect the relations between the degree of model mismatch and the stability of smith predictive control system. This algorithm solves the hard problem about the stability of smith predictive control system.(3) Based on the required PID stability regions of multiple time-delay system, the PID design method of this system is proposed by using the spectral discretization method. The PID parameters are designed by spectral discretization method to limit the distribution of closed-loop characteristic roots. The proposed method can improve the design efficiency of PID controller without model reduction. This method has superiority in response speed and load disturbance rejection performance compared with other methods. Figures(36), tables(5), references(66).