Modeling and Control of Reaction Wheel Pendulum with Feedback Linearization and LQR Control

The chapter delves into the intricate dynamics of the reaction wheel pendulum (RWP), a nonlinear mechanical system known for its underactuated nature and multiple equilibrium points. It addresses two primary control challenges: the swing-up problem and the stabilizing problem. The proposed approach leverages feedback linearization to transform the nonlinear dynamics of the RWP into a linear form, making it amenable to Linear Quadratic Regulator (LQR) control. This combination allows for the determination of optimal control gains that stabilize the pendulum while minimizing control effort. The effectiveness of this combined approach is demonstrated through simulations using a multibody dynamics model, highlighting the advantages of feedback linearization in handling nonlinear dynamics and the optimality of LQR control. The chapter also explores the impact of weighting matrices in the LQR design, providing insights into the trade-offs between faster responses and control effort. The simulations compare the proposed method with standard LQR control, showcasing the superior performance of the combined feedback linearization and LQR approach in stabilizing the reaction wheel pendulum.