A 2-DEGREE-OF-FREEDOM LQR DESIGN OF CONTROL-SYSTEMS

This paper presents practical considerations regarding the design of linear quadratic optimal regulators. With the help of a new classical interpretation of the full-state feedback system, two degrees of freedom are built for the famous LQR procedure. As a result, the feedback loop of a system can be designed to satisfy engineering requirements, while the overall system performance is optimal with respect to a certain linear quadratic performance index. Moreover, the LQR procedure is guaranteed to work with non-minimum-phase and/or unstable plant without right half-plane pole-zero cancellation. An analytical method is given to derive the optimal Luenberger estimator when state-space realization is wanted. For the purpose of clarity, only single-variable systems are considered. Numerical examples are given to illustrate the LQR design.