Research On Two Sampling Control Problems Of Networked Systems

Nowadays,with the wide application of computers,many controllers in control systems are composed of computers,which use some discrete sampling signals to make the system meet some control requirements.The sampling method is gener-ally periodic sampling method and the holder is generally zero order holder.Such a system is called the sampled-data system.If the controlled system and the con-troller are connected through the network communication channel,it constitutes a networked control system.Networked control systems have the advantages of information sharing,easy expansion and enhancing system reliability and so on.However,due to the introduction of computer technology and communication technology,some new problems have emerged,such as packet losses and noises in communication.The addition of network makes the demand for communica-tion resources surge.In order to save communication resources,one solution is to reduce the frequency of communication.Two sampling control problems are proposed because of two ideas.The first idea is to use as large a sampling interval as possible.The second idea is to adopt event based sampling method instead of periodic sampling method.The first sampling control problem deals with the maximum sampling interval in which the sampled-data system with communication packet losses maintains the mean square stability.The size of the control signal is zero when the packet is lost.According to the definition of mean square stability,the critical sampling intervals are obtained for sampled-data systems with no packet loss and indepen-dent and identically distribution(i.i.d.)process packet loss.For the sampled-data system with Markov chain packet loss,the sampled-data system is understood as a stochastic sampled-data system,and the condition that the critical sam-pling interval satisfies is obtained when the system is mean square stable.The mean square stability condition of the sampled-data system is obtained by using the equivalence of the mean square stability of the sampled-data system and its corresponding discrete time systems.The second sampling control problem deals with the performance comparison of periodic sampling and event based sampling impulse control for first order stochastic systems with multiplicative noise.Event based sampling refers to sampling when the system state leaves a symmetric open interval containing the origin.Firstly,for the periodic sampling impulse control,the control performance index the average state mean square value is obtained.Then,according to the solution of Poisson problem in the boundary value problems,the mathematical expectation of the first exit time and the cumulative mean square value of the state are obtained for the event based sampling impulse control,and the control performance index is obtained.Finally,the control performance index of the two cases is compared at the same sampling frequency.It is found that the event based sampling impulse control has a smaller average state mean square value than the periodic sampling impulse control for the first order stochastic systems with multiplicative noise.