Optimal Control Of Multi-sampling Rate Networked Control System

Because of its advantages of low cost,less connection,remote control and high flexibility,networked control system has been widely used in industrial control and automation.However,due to the limitations of network technology and hardware at present,there are inevitable problems such as delay,packet loss and sampling cycle fluctuation in the transmission of control data.Meanwhile,a control system is no longer limited to a single sampling rate,and the research on multi-sampling rate networked control system has been widely concerned.This paper first studies theH_?optimal control of networked control systems with uncertain short time delay and packet loss.On this basis,the uncertainty of sampling period is further considered,and the design of h?optimal controller for a generalized multi-sampling rate networked control system is studied.The details are as follows:(1)A design method of the optimalH_?state feedback control law is presented for a networked control system with uncertain short time delay and packet loss.Suppose that the output sampling period is an integer multiple of the input sampling period.The system is discretized according to the output sampling period.Bernoulli random sequence is used to describe packet loss and the probability of packet loss is assumed to be known.By using lyapunov stability theory and linear matrix inequality to analyze the stability of the system,a sufficient condition for the existence of the optimalH_?state feedback control law is obtained.Finally,taking permanent magnet synchronous motor as an example,MATLAB simulation is used to illustrate the effectiveness of the method.(2)A design method of the optimalH_?dynamic output feedback control law for networked control system with uncertain short delay and packet loss is presented.If the state of the system is not measurable,a dynamic output feedback controller with time delay compensation is selected.At this point,the input sampling period is an integer multiple of the output sampling period.Bernoulli random sequence is used to describe packet loss and the probability of packet loss is assumed to be known.The uncertainty of delay is transformed into the uncertainty of matrix parameters.In the same way,lyapunov stability theory and linear matrix inequality are used to analyze the stability of the system,and sufficient conditions for the existence of the optimalH_?dynamic output feedback control law of the system are obtained.Finally,taking permanent magnet synchronous motor as an example,MATLAB simulation is used to illustrate the effectiveness of the method.(3)A design method of the optimalH_?dynamic output feedback control law is presented for a generalized multi-sampling rate networked control system with uncertain sampling period,uncertain short time delay and packet loss.In the case of generalized multi-sampling rate,the system is considered to be composed of multiple subsystems with different sampling periods.The uncertainty of sampling period and time delay is transformed into the uncertainty of matrix parameters by the interval matrix principle.Lyapunov stability theory and linear matrix inequality are used to analyze the stability of the system,and sufficient conditions for the existence of the optimalH_?dynamic output feedback control law of the system are obtained.Finally,taking permanent magnet synchronous motor as an example,MATLAB simulation is used to illustrate the effectiveness of the method.