Stability Analysis And Controller Design Of Sampled-data Control Systems With Non-uniform Sampling

With the rapid development of computer technology and microelectronic technology,digital control systems are applied to all walks of life.And sampled-data theory as the fundamental theory of digital control system has been widely investigated.Traditionally,the sampling interval has been assumed to be constant in a periodic sampled-data system.Such an assumption is,however,not always true in practical engineering.For example,in embedded control systems,it is often the case that the sampling intervals are uncertain and/or vary with time due largely to unpredictable network-induced phenomena,calculation overload in a processor and some unknown reasons of system itself.When a sampling period is variable,the classic control theory method is inapplicable.It is important in both theory and practice to investigate the stability,and controller design procedure for non-uniformly sampled-data systems.This thesis mainly focuses on modeling,stability analysis and controller design of the nonuniformly sampled-data systems.The main results of this thesis are as follows:Firstly,the stability condition of the non-uniformly sampled-data control system is proposed.Different from other methods,we model the non-uniformly sampled-data control systems as a system with uncertainties,and the uncertainties of are dealt with ploytopic inclusions.What's more,robust control methods are employed to ensure the stability of the control system in corresponding with variable sampling intervals.To reduce conservatism introduced by modeling time varying parts as a single uncertainty,the time-varying parts are modeled as M uncertainties.With larger M,a less conservative stability condition is derived at sacrifice of more computation.Secondly,based on the characteristics of time-varying sampling period of the sampleddata control system,a method is proposed to design a state feedback controller and output feedback controller,respectively.When the sampling period is variable in a given interval,the stability of the sampled-data system can be guaranteed according to controller gain.Finally,we obtain the actual mathematical model of control system by the time domain system identification method,which is used to design a controller to show the effectiveness of proposed methods based on a brush direct current motor.