Direct adaptive robust control of a cable-pulley system

Cable-actuated systems provide an effective method for precise motion control over various distances. Traditionally, their control has focused on eliminating transverse resonances and disturbances. Longitudinal cable resonances are usually neglected since they are assumed to be at much higher frequencies and much lower amplitudes compared to transverse resonances. However, in high-speed high-precision applications, all longitudinal modes cannot be ignored in the presence of high-inertia components. In this paper, we consider the trajectory tracking problem of a cable-pulley system using a reduced-order model of the dynamics. The controller is constructed using a Lyapunov-type direct adaptive robust control (DARC) framework with necessary design modifications to accommodate uncertain and non-smooth nonlinearities of the the system. The proposed controller guarantees prescribed output-tracking transient performance, as well as final tracking accuracy. Parameter estimates are obtained using a modified gradient law with the sole purpose of reducing tracking error. Experimental results are presented using a prototypical cable-pulley system to demonstrate its effectiveness.