Discrete-time filter proportional–integral–derivative controller design for linear time-invariant systems

This paper introduces a new discrete-time filter proportional–integral–derivative (FPID) controller framework for linear time-invariant (LTI) systems. The discrete-time FPID controller plays an important role in both determining the dynamic response of the system and further improving the performance of the controller in itself. However, the introduction of the filter parameter brings more challenge for the design of discrete-time FPID controllers than that of discrete-time PID controllers. A novel result on the co-design of such a controller via dominant eigenvalue assignment is first provided, which enables us to tune the controller directly in accordance with the desired system performance indexes. Then, a further result on the discrete-time FPID controller design to improve the dynamic response of the closed-loop system is derived by placing the non-dominant eigenvalues in some assigned region. Compared with the discrete-time PID controller, on the one hand, the discrete-time FPID controller plays a significant role in improving the output of the controller in addition to guaranteeing the desired dynamic performance of the closed-loop system. On the other hand, a discrete-time FPID controller makes it possible to expand the effective parameter region and give a set of parameters which makes the controller achieve the objective of dominant eigenvalue assignment for the closed-loop system when a traditional discrete-time PID controller cannot do. Numerical examples have illustrated the effectiveness of the proposed results.