Trajectory Control for Double-Linked Parallel Rotary Inverted Pendulum

Abstract

The rotary inverted pendulum (RIP) is a benchmark nonlinear underactuated system commonly used in control research, with various extensions such as multi-link and parallel configurations developed to increase complexity and evaluate advanced controllers. This paper presents a hybrid control strategy combining Linear Quadratic Regulator (LQR) and a Genetic Algorithm (GA) for stabilizing and tracking control of a rotary double-linked parallel inverted pendulum (RDPIP), a nonlinear under-actuated single input-multi output (SIMO) system. The LQR controller is designed based on a linearized state-space model at the TOP-TOP equilibrium point. To enhance performance, the weighting matrices Q and R are optimized using GA with a fitness function minimizing trajectory error. Simulation results demonstrate that the GA-optimized controller (LQR 2) achieves superior performance compared to the trial-based LQR (LQR 1), with a reduced settling time of 0.5 seconds, lower oscillation amplitudes, and improved tracking of reference signals under sinusoidal and pulse disturbances. Specifically, the pendulums reached steady state within 2–3 seconds, and the arm settled within 6 seconds. These findings confirm the effectiveness of a hybrid strategy and robustness of the proposed hybrid approach for RDPIP control, laying a foundation for future implementation in real-world applications.