Modelling and robust stabilisation of a closed-link 2-dof inverted pendulum with gain scheduled control

In this paper, modelling and stabilisation control of a closed-link driven 2-dof inverted pendulum system is discussed, which consists of two rotary robots and four closed linkages with holonomic constraint. A complete mathematical model derived by Lagrange's equations is partially linear approximated around the operating point. Then, the modelling error is regarded as a structured perturbation and the controlled object is described as a slight non-linear model with structured additive perturbation. In order to facilitate a controller design, model reduction is performed by removing redundant dynamics. Then, the reduced order simplified model is described as a linear parameter variable (LPV) system with structured additive perturbation. Stabilisation controller with L2-gain disturbance attenuation is designed to guarantee the stability of the controlled object robustly in the range of specified perturbation by applying gain scheduling control technique developed for the LPV system. Experimental works show the effectiveness of the proposed simplified model and the stabilisation controller.

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