Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear Transformation

This paper addresses a new method for order reduction of linear time invariant discrete-time controller. This method leads to a new algorithm for controller reduction when a discrete time controller is used to control a continuous time plant. In this algorithm, at first, a full order controller is designed in s-plane. Then, bilinear transformation is applied to map the closed loop system to z-plane. Next, new closed loop controllability and observability grammians are calculated in z-plane. Finally, balanced truncation idea is used to reduce the order of controller. The stability property of the reduced order controller is discussed. To verify the effectiveness of our method, a reduced controller is designed for four discs system.