State Derivative Feedback by LQR for Linear Time-invariant Systems

Authors:	Abdelaziz Taha, Czech Technical University in Prague, Faculty of Mechanical Engineering, Czech Republic Valasek Michael, Czech Technical University in Prague, Faculty of Mechanical Engineering, Czech Republic
Topic:	2.4 Optimal Control
Session:	Optimal Control Theory and Design Methods
Keywords:	state derivative feedback, output derivative feedback, LQR control method, feedback stabilization

Abstract

In this paper, state-derivative and especially output-derivative feedbacks for linear time-invariant systems are derived using control approach similar to linear quadratic regulator (LQR). The optimal feedback gain matrices are derived for the desired performance. This problem is always solvable for any controllable system if the open-loop system matrix is nonsingular. Explicit expression of the state-derivative gain matrix is derived. Finally, simulation results are included to show the effectiveness of the proposed approach.