Optimal linear modeling and its applications on swing-up and stabilization control for Rotary Inverted Pendulum

Through the conventional Jacobian linearization, its operation has to be limited in the neighborhood of equilibrium. To address the control requirement in off-equilibrium region, optimal linearization is introduced to describe the exact dynamics at any operating point with minimal approximation error. In the illustrative example of Rotary Inverted Pendulum, a universal dynamic nonlinear model is firstly developed. Then its local linearized model is updated by every sampling period to match with the current operating point. Meanwhile, its controller is also updated to correspond with the updated local model. Thus, swing-up control and balance control can be both implemented through a unified Linear Quadratic Regulator controller, which can effectively avoid control law switching in the two stages.