Partial gain scheduling control of crane via parameter dependent Lyapunov function

This paper proposes a method to design partial gain scheduling (GS) controller for a jib crane via parameter dependent Lyapunov function. The state feedback partial GS controller has scheduled gains and fixed gains. From pendulum property, angular velocity of the load depends on rope length. However, trolley position does not depend strongly on the rope length. Thus the scheduled gains are applied for the swing angle and the angular velocity of the load. The fixed gains are for the other states. To obtain a linear parameter varying (LPV) system for designing the partial GS controller, we adopt linear fractional transformation (LFT) and redundant descriptor representation for state space representation of jib crane, where the time-varying parameters are the rope length, its velocity and acceleration. The designed controller guarantees the robust stability for time-varying parameters. The problem of the controller design can be formulated as solving a finite set of linear matrix inequalities (LMIs). The effectiveness of the proposed method is illustrated by simulations.