LQR/PID controller design of PLC-based inverted pendulum

This paper presents an LQR based PID controller to control the inverted pendulum system. The control design employs a control zoning approach whereby the entire pendulum system is divided into two regions: a normal pendulum region and the inverted pendulum region where the system is approximately linear close to the upright position. The LQR architecture is used to obtain optimal gains for the PID controller. An algebraic approach is also presented for selection of Q and R matrices. Experimental implementations with a PLC based system show that the computed gains yield the most stable controlled responses compared to the gains chosen through trial and errors.