Abstract
Balancing control of a rotary double inverted pendulum system is a challenging research topic for researchers in dynamics control field because of its nonlinear, high degree-of-freedom, under actuated and unstable characteristics. The system always works under uncertainties and disturbances. Many control algorithms fail or ineffectively control the rotary double inverted pendulum system. In this article, mixed sensitivity H∞ control is proposed to balance the rotary double inverted pendulum system. The controller is proposed to ensure the robust stability and enhance the time domain performance of the system under uncertainties and disturbances. Structure of the system, dynamics model and controller synthesis are presented. For performance evaluation, the proposed mixed sensitivity H∞ controller is compared with linear quadratic regulator from both simulation and experiment on the rotary double inverted pendulum system. The results show high performance of the proposed controller on the rotary double inverted pendulum system with model uncertainties and external disturbances.
Highlights
Inverted pendulum system is a nonlinear, under actuated and unstable system
The results show that peak value of the inner and the outer pendulums of the mixed sensitivity H1 controller are only 23% and 27.5% of linear quadratic regulator (LQR) when the inner pendulum is perturbed and only 9.7% and 11% when the outer pendulum is perturbed
In order to verify the robustness of the proposed controller, several experiments are conducted on the developed rotary double inverted pendulum (RDIP) system
Summary
Inverted pendulum system is a nonlinear, under actuated and unstable system. It has been used in control field to evaluate control performance and efficiency of several controllers. Cheang and Chen[3] successfully controlled a single inverted pendulum on moving cart system by using the H1 loop shaping They proved that dynamic system under uncertainty was effectively controlled by loop shaping controller. Static H1 loop shaping controller was applied to a double inverted pendulum on moving cart system by Liu and Zhou.[5] Their loop shaping weighting functions were optimized by genetic algorithm. Alfaya et al.[24] and Bejarano et al.[25] applied S/KS/T-based multivariable H1 controller for one-stage refrigeration cycle Their results showed better tracking performance and robustness against disturbance over PID and model predictive controller.
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