Optimal Preview Controller for Linear Discrete-Time Systems: A Virtual System Method

In this paper, a new method for the design of the preview controller for a class of discrete-time systems is proposed based on the virtual system. Firstly, by taking the known future reference signal as the output, the virtual system with similar structures to the controlled system is constructed. Then, the augmented error system is received by translating the controlled system to it and by integrating the error equation. Thus, the tracking problem of the controlled system is transformed into the regulation problem of the augmented error system. Secondly, in view of the minimum principle, the optimal controller of the augmented error system is acquired, and the preview controller of the controlled system is also gained. Further, by discussing the stabilizability and detectability of the augmented error system, the conditions for the existence of the unique positive semidefinite solution to an algebraic Riccati equation are obtained. By using the method in this paper, making difference and dimension expansion for the state equation in designing the augmented error system is avoided and the output can track the reference signals better. Finally, the numerical simulation shows the effectiveness of the proposed controller.