An LQR Based MIMO PID Controller Synthesis Method for Unconstrained Lagrangian Mechanical Systems

This paper presents an LQR based procedure for the synthesis of MIMO PID controllers that is primarily intended to be applied to unconstrained Lagrangian mechanical systems. The procedure is based on an appropriate interpretation of the plant-PID-controller interconnection that leads to a static state feedback problem that can be tackled using standard methods. If, in addition, a decentralized MIMO PID controller is to be designed, then the problem turns to be a sparse-constrained static state feedback problem. To solve this problem, a simple gradient-like search method is proposed and an example is considered to illustrate the proposed methodology