The principles of underactuated rotary double inverted pendulum (RDIP) systems are extensively utilized in applications such as robotics and space explorations. Consequently, the design of an effective controller for such system is a multifarious task that demands expertise in system modeling, control systems, optimization, and real-time implementation. This study is a step towards developing intelligent control methods for RDIP systems having real-life implications, while emphasizing real-time applicability. A linearization technique for the RDIP system is presented, followed by the proposed design methodologies of the linear quadratic regulator with integrator (LQRI) controller using gravitational search algorithm (LQRI-GSA), particle swarm optimization (LQRI-PSO), and quantum PSO (LQRI-QPSO). The objective of the proposed controller architectures is to balance the RDIP system on an inverted position, while the rotary arm tracks a time-varying trajectory. Simulations and experiments corroborate that the proposed methods are successful in balancing the double pendulums on an inverted position while minimizing deviations of the pendulum angles and the rotary arm angle from the desired values. To further demonstrate the adaptability and applicability, the proposed methods are compared with controllers like H-infinity, sliding mode controller (SMC), fuzzy LQR (FLQR), and state feedback controller (SFC) across other two RDIP models and a cold gas thruster model which works on the principle of RDIP. The results show that the proposed methods outperform the other controllers in regulating dynamics, minimizing errors, and ensuring stability.
Ghosh et al. (2025) studied this question.