Linear Matrix Inequalities Based H∞ Control of Gantry Crane using Tensor Product Transformation

This paper describes a H∞ controller design procedure for tensor product based model of gantry crane augumented with friction model in order to minimize friction effects. The Tensor Product (TP) model transformation is a recently proposed technique for transforming given Linear Parameter Varying (LPV) state-space models into polytopic model form, namely, to parameter varying convex combination of Linear Time Invariant (LTI) systems. H∞ controller guarantee stability and L2 norm bound constraint on disturbance attenuation. H∞ controller is found using relaxed LMIs which have proof of asymptotic convergence to the global optimal controller under quadratic stability. Control algorithm is experimentally tested on single pendulum gantry (SPG).

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