Research On The Preview Control Theory For Multirate Systems

Based on the plentiful research achievements of the preview control theory and the multirate systems theory,the preview control theory and the multirate systems are further combined to study the optimal preview control problem for several different types of mulirate systems.The main contributions of this paper are as follows:(1)Design of an optimal preview controller for linear time-varying discrete-time systems in a multirate input setting.By using the discrete lifting technique,the multirate time-varying discrete-time system is converted to a formal single-rate system.Then by introducing the first-order forward difference operator and combining the property of difference operator,the augmented error system is obtained.The optimal control input for the original system is derived by using the result of the optimal control theory on time-varying system,and the high-order Riccati equation is transformed into a lower-order one based on matrix partition.(2)The problem of robust preview control for multirate-input uncertain discrete-time systems with input delay is studied.First,by using the discrete lifting technique,the input delay and the characteristic of multirate system are eliminated in form.Second,according to the basic method of preview control,an augmented error system for the uncertain system is constructed and an optimal preview controller for the corresponding nominal system is designed.Finally,by using the Lyapunov stability theory and the properties of matrix norm,some robust stability criterions of the closed-loop system are obtained.(3)The disturbance preview optimal control problem for discrete-time systems with multirate output sampling is studied.The difference between the state of system and the steady state is used to construct the augmented error system instead of the previous differential operator.Meanwhile,introducing a discrete integrator to eliminate the static error,a controller with preview action for the original system is given.(4)A design strategy of optimal output regulators for dual-rate discrete-time systems,whose output sampling period is an integer multiple of the input updating period,is investigated.By using the discrete lifting technique,the original system is converted to a single-rate augmented system.The performance index function is modified according to the optimal regulator theory and the contract transformation matrix,and then the optimal output regulator of the original system is derived.On the basis of this method,an optimal preview control problem for the general dual-rate linear discrete-time systems is studied.And the lifted state-space model for the general dual-rate discrete-time system is derived.Then,combining preview control theory,an optimal preview controller with preview compensation for the original system is obtianed.The rigorous mathematical proofs for the condition of the theorems have been given in all of the case,and simulation results show the effectiveness of the studied methods.