A Synthetic LQR Control for The Planar Inverted Pendulum

As a kind of inverted pendulum, the planar inverted pendulum (PIP) is a well known nonlinear system to research the control strategy. The trajectory tracking control of PIP has been researched for many years, however, the tracking ability for large angular frequency is relatively limited, when the controller is designed by linear theory. In this study, a synthetic controller named PLQR, which is composed by the pole placement and linear quadratic regulator (LQR) is designed to realize the trajectory tracking control. Firstly, the nonlinear model of PIP is linearized at the upside equilibrium point. Then, the expanded system composed by tracking error and linearized PIP model is constructed. The control gain got by pole placement will ensure the tracking error convgenerge to zero, while the LQR controller can ensure the system stable. Finally, the simulation results show that the PLQR can ensure the PIP tracking trajectory with lager angular frequency than LQR does.