TP transformation based control of rotary pendulum

The Tensor Product (TP) model transformation is a recently proposed technique for transformation of a given Linear Parameter Varying (LPV) state-space model into polytopic model form, namely, to parameter varying convex combination of Linear Time Invariant (LTI) systems. The main advantage of the TP model transformation is that it is executable in a relatively short time and the Linear Matrix Inequality (LMI)-based control design frameworks can immediately be applied to the resulting polytopic models. In this paper, such control approach of nonlinear systems is applied to the control of rotary pendulum gantry. Pendulum in hanging position represents simplified model of the real industry crane application. On the other hand, inverted pendulum is a classic problem in dynamics and control theory and widely used as a benchmark for testing control algorithms. In order to reach upright position, self erecting technique is employed. LMI control algorithm obtained for both positions is merged using self erecting control algorithm and tested in real experimental setup.