DESIGN AND EVALUATION OF ENERGY-BASED SWING-UP AND LQR CONTROL STRATEGIES FOR AN INVERTED PENDULUM ON A CART
Abstract
The cart-inverted pendulum is a fundamental underactuated nonlinear system, extensively utilized as a benchmark for validating control algorithms. This paper proposes a comprehensive hybrid control architecture addressing both the swing-up and upright stabilization problems. The dynamic model is derived using the Euler-Lagrange formulation and locally linearized via the Jacobian matrix. Initially, a Lyapunov-based controller pumps energy into the system, driving the total mechanical energy to the upright equilibrium. Upon entering the linear basin of attraction, the system seamlessly transitions to a fixed-gain Linear Quadratic Regulator (LQR) using a normalized angle (θwrap) logic to maintain balance. Simulations validate the hybrid algorithm and demonstrate the LQR’s enhanced performance in eliminating transient overshoot and rejecting aggressive dynamic disturbances (up to ± 3 N impulses under ± 25 N actuator saturation constraints). Quantitative evaluation further confirms that the system maintains a low angular Root Mean Square Error (RMSE) of 0.48o under persistent white noise and remains stable under parametric uncertainties of up to ±10%.
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