A Dead-beat Internal Model System With Optimal Performance Index

In this paper, two design methods of dead-beat controller with various optimal performance index are proposed based on the two-degree-of-freedom internal model control (IMC) structure. Based on the proposed minimal-energy dead-beat IMC system, we use the same feedback part of the controller structure to achieve the robustness with respect to plant perturbations or output disturbances while the feedforward part of the controller is designed to minimize the tracking errors or minimize the quadratic performance index respectively for a given deadbeat number. A formula is derived for the optimal control that minimizes the tracking errors and also another formula is derived for the optimal control that minimizes the weighted quadratic performance index for the specified setting time. As a result, the final design of the feedforward controller is represented in the form of a matrix which makes the design procedure easy. It offers further prospect of engineering application Furthermore, this paper compares the minimal-energy dead-beat control, the dead-beat control with minimal tracking error and the dead-beat optimal control with weighted quadratic performance index. In the end, we discuss the meaning and the selection of the weighting matrix in the performance index. Simulation results show that the strategy is effective.