Stabilization System of Convey-Crane Position Via Sigmoidal Function

Abstract

In this paper, we consider the convey-crane system, which can transport loads for industrial purposes. The mathematical model, describing the motion of convey-crane, is presented by a Lagrangian mechanical system of nonlinear equations with two degrees of freedom and one control action. It is supposed that the rope has no mass, its stiffness is not taken into account, and there is no friction in the joints. The stabilization problem of the desired convey-crane position is posed underuncertain mass inertia characteristics, an action of non-smooth bounded disturbances and incomplete measurements. Based on the passivity property, the control law with linear and sigmoidal parts is constructed for the solution of the problem. The only measurement of the convey-crane position is available without a noise in the measurements. We use the low order observer with sigmoidal corrective action to obtain the needed velocity estimates for the control law. It is shown that the using of sigmoidal function as a prelimit realization of sign-function provides disturbances invariance with the given accuracy. With respect to the smoothness and boundness, sigmoidal function helps to avoid overshoot in the transient responses and excessive consumption of control resources. Moreover, unlike the sign-function, a sigmoidal function is realized in the electromechanical systems with actuator dynamics, in which the physical restrictions on the forces and general moments are posed. The constructed control law with linear and sigmoidal parts is simulated for the convey-crane system in MATLAB- Simulink. The classical PD-controller is simulated too for the purpos e of comparison. The results of modeling are proved the effectiveness of the proposed approach.