Gain-Scheduling Control for Crane via Parameter Dependent Lyapunov Function Considering All Varying Parameters in Dynamics
نویسندگان
چکیده
In this paper, Gain-Scheduling (GS) control via parameter dependent Lyapunov function for crane is synthesized. A purpose of cranes system is to lift and carry a load to assigned positions. Cranes are required to transport the load fast, accurately and to reduce oscillations. In previous research, a method to robust control of cranes to suppress effects by variation of the rope length have been reported[1]. For improvement of cranes efficiency, cranes should be operated in movement of the load horizontal and vertical directions simultaneously. It has been reported that decentralized control is effective for cranes[2]. We have reported a method to synthesis GS control via parameter dependent Lyapunov function in concept of treating complete dynamics[3]. The crane model not to ignore velocity and acceleration of the rope length in the dynamics has been derived. However, a mass of the load is not constant and included in the dynamics. Variation of the mass of the load is not considered. By using parameter dependent Lyapunov function, a controller becomes less conservative synthesis in comparison with adopting parameter independent Lyapunov function[4]. However, there is Lyapunov matrix derivative. For this problem, a estimation method of Lyapunov matrix derivative has been reported[5]. In this paper, a GS controller via parameter dependent Lyapunov function which guarantees variation of the rope length, its velocity, acceleration and the mass of the load is synthesized. All varying parameters in the dynamics which is related to operating the crane are taken into account. The rope length, its velocity and acceleration are treated as time-varying parameters. The mass of the load is different in every operation, it is treated as uncertain but time-invariant parameter. Time-varying parameters are assumed to measurable, they are treated as scheduling parameters. Linear Parameter Varying (LPV) system for scheduling parameters is obtained. Robust stability with vertexes of varying parameters is guaranteed. By using parameter dependent Lyapunov function, there are product of scheduling parameters and derivative of Lyapunov matrix. For these problem, descriptor representation, Linear Fractional Transformation (LFT) and a estimation method of Lyapunov matrix derivative are adopted. The former problem of parameter dependent Lyapunov function can be solved by adopting descriptor representation. We show that adopting descriptor representation and LFT, the controller performance is improved from a viewpoint of evaluated function. By several simulations, it is shown that the controller is effective.
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