Robust Pole Placement using Linear Quadratic Regulator Weight Selection Algorithm

The main advantage of pole placement technique is that it places all the poles at desired location using state feedback gain matrix. Using feedback, the poles of the system can be shifted so we can shape the closed loop characteristics of system to meet the design requirement. Even though pole placement method can give the desired characteristic but it does not guarantee a robust system. So controller design using pole placement may not be insensitive to system parameter variations and external disturbance. The linear quadratic regulator (LQR) is an optimal design technique that guarantees a robust system. The difficulty lies in choosing a weighting matrix for the LQR cost function that gives the desired poles. In this paper, an algorithm is developed that finds the location of poles which satisfy the desired goal and give a robust system also. The LQR method guarantees robustness, but not allows pole placement in a specific regions, and the pole placement gives the desired performance but not guarantees robustness. Therefore it may not be possible to use this method to achieve both robustness and exact pole placement. This paper has higher priority over pole placement and hence uses the LQR technique to choose the poles. This analysis is well supported by the simulation and experimental results done using MatLab and Simulink.