Modeling and Control of Inertia Wheel Pendulum System with LQR and PID control

This study presents an analysis, control, and comparison of controllers used to stabilize the IWP with the help of the torque generated by a wheel driven by a DC motor. The dynamics of the IWP with the proportional integral derivative (PID) control and linear quadratic regulator (LQR) control are explored. The effect of actuator saturation on control performance is also studied. Controller performance is evaluated through simulation by using the nonlinear model developed in Simscape Multibody. The system can always return to equilibrium with any initial angle, but as the initial angle increases, a higher input voltage is required. In the saturated case, the system can only return to equilibrium with a maximum initial angle of 14.5 degrees. The LQR control has less overshoot but takes a longer time to return to the equilibrium point.