Quasi PI-LOR Vibration Control and Its Controllability Analysis of Mechanical Systems

The controllability problem is a critical issue in the design and implementation of control systems for mechanical systems. The classical PI control always leads to that the state equation of a mechanical system may fail to satisfy the controllability condition in the Linear Quadratic Regulator (LQR) algorithm. This problem is particularly relevant in practical applications where vibration control is essential, such as in the robotics, aerospace, and automotive industries. To address this issue, we propose a quasi PI-LQR controller that involves modifying the system matrix of the mechanical system to ensure controllability, such that this approach could achieve that the control system is optimal and robust to disturbances. Mathematically, we analyze that the controllability of the modified mechanical system and the deviation from the classical PI control. Finally, a simulation example is given to verify the effectiveness of the proposed quasi PI-LQR control method.