Exponential Stabilization Of Control Systems Under Dual-rate Sampling

Sampled-data control system is a hybrid system which consists of a continuous-time physical plant and a discrete-time control law. In actual system, there may be large difference among change rates of various signals of a controlled plant, e.g., there is a difference of several orders of magnitude between change rates of an electrical signal and a temperature signal. Thus, using the same sampling period for all signals in the system is unrealistic. In general, the smaller sampling period is used for control systems, the better control performance can be obtained, but the smaller sampling period will greatly increase the cost of the control system. Therefore, a tradeoff way is to use a different sampling periods for different signals of a system, which results in a multi-rate control system. Lifting technique is often used to study the multi-rate control system in the existing literatures; however this method is not suitable for uncertain system, time-varying system and nonlinear system, etc. So this thesis studies stabilization problem of the control system with dual-rate sampling by input delay approach and switched system method.The main research contents of this paper are as follows:In chapter 1, both theory and application significance of this thesis are introduced. And the research situation is recalled at home and abroad.In chapter 2, the exponential stabilization problem of a class of dual-rate linear control system is studied by a switched system method. The system state variables are assumed to be measurable and are sampled by samplers which have two different sampling periods. The system state variables are divided into two groups, the state variables of each group have a same sampling period. Firstly, a periodically switched controller is designed. The dual-rate control system can be modeled as a switched system with two time-varying saw-tooth delays. Using Lyapunov functional method, the sufficient conditions of stability and stabilization are obtained. Finally, a simulation experiment is used to demonstrate the effectiveness of the proposed method.In chapter 3, absolute stabilization for a dual-rate control system with a sector bounded nonlinear term is studied by using a switched system method. It is assumed that the system state variables are measurable and are sampled by samplers which have two different sampling periods, and the system is with a sector bounded nonlinear term. By the input delay method, the nonlinear dual-rate control system is modeled as a switched system with time delay. The absolute stabilization problem of nonlinear dual-rate control system is equal to the robust stabilization problem of such a switched system. Then the stability criterion and controller design method of the dual-rate control system are given. Finally, a simulation example shows the effectiveness of the proposed method.In chapter 4, the main results of the thesis are concluded, and some future research works on dual-rate sampled-data control are proposed.