LQR based tuning of PID controller for magnetic levitation system and its performance comparison with conventional method

Abstract: This paper proposes a Linear Quadratic Regulator (LQR) based tuning of PID controller and is implemented for controlling the ball position of magnetic levitation system. Since the system is highly nonlinear in nature, nonlinear differential equations are used to model the system. For the controller design, this nonlinear model is linearized around the operating point using Taylor series expansion method. Performance of the proposed method is compared with that of PID controller which is tuned using conventional Ziegler Nichol‟s method. From the simulation studies it is clear that even though both the schemes are capable to control the ball position of magnetic levitation system the proposed method yields better result. Quantitative performance comparison is also made based on the time domain specifications such as settling time, maximum overshoot and steady state error. The result shows that LQR based PID controller outperforms its counterpart as the settling time and maximum overshoot are reduced considerably.

Keywords: Proportional-integral-derivative (PID), Linear Quadratic Regulator (LQR), Magnetic Levitation System, Zeigler Nichol‟s Method (ZN).