LMI-Based Control of a Double Pendulum Crane

This paper presents the design of a Linear Matrix Inequality (LMI) based state feedback controller for position tracking, hook and payload oscillations of a double pendulum crane. In this work, a linearised model of the crane was firstly obtained. The idea of formulating the stability condition in the form of LMIs using the linearised model was proposed. Using this approach, the stabilisation conditions constraints the closed-loop poles of the system to be in an LMI region to guarantee the system stability and gives satisfied transient performance. Based on the stabilization conditions formulated, an LMI based state feedback tracking controller for trolley position tracking and swing angles control of the double pendulum crane is proposed.  Mostly, two or more controllers were used for the control of double pendulum crane to control the trolley, hook and payload. However, in this work a single LMI based controller is used to achieve similar performance. This reduces the number of controllers which minimises cost, complexity and size of the control system. The performance of the proposed controller is investigated via simulations. The simulation result shows the proposed controller is able to track the trolley position relatively fast with minimum hook and payload swing angles hence, reduce the main problem of a double pendulum crane. From the performance comparison of the results, the proposed method has improved in terms of reducing the trolley position percentage overshoot, hook oscillation and payload oscillation with 72%, 52% and 65% respectively.

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