Ability Analysis of a Linear Quadratic Regulator for Optimal Control of a Dynamical System

The optimal control of a dynamical system is one of the key ways of control and it is applicable in most of the systems due to its control capability under minimum use of energy. Although a system can be controlled in a classical Proportional-Integral (PI) controller but the optimal control approach drives the system from one state to another state with the minimum time and energy. This is due to its control law based on the minimization of the energy function, popularly known as ‘cost functional’. This paper concentrates on the optimal control of a dynamical system and improvement of its performance in terms of mitigation of the oscillations, overshoot, steady state error and its stability through Linear Quadratic Regulator (LQR). The state-space model of a second-order classical dynamical system has been investigated under optimal control through LQR to improve the system responses and then compared with the PI controller. The efficacy of the proposed LQR control of the system under different disturbances was examined and found its ability to improve the performance of the studied system.