Modeling and Direct Adaptive Robust Control of Flexible Cable-Actuated Systems
Abstract
Cable-actuated systems provide an effective method for precise motion transmission over various distances in many robotic systems. In general, the use of cables has many potential advantages such as high-speed manipulation, larger payloads, larger range of motion, access to remote locations and applications in hazardous environments. However, cable flexibility inevitably causes vibrations and poses a concern in high-bandwidth, high-precision applications. Cable vibrations typically occur in both the longitudinal and mutually perpendicular transverse directions and are coupled. The coupling between longitudinal and transverse modes is usually assumed to be minimal since longitudinal resonances are usually at much higher frequencies compared to transverse frequencies. In a cable-pulley system, the coupling between the cable and high-inertia components such as pulleys can lead to a drastic reduction in the fundamental longitudinal mode. This coupling becomes more prominent under conditions of autoparametric or internal resonance in the system. When these conditions are met, transverse cable vibrations and pulley rotations exchange significant energy leading to higher amplitudes of oscillations not predicted by classical linear analyses. The design parameters needed to facilitate autoparametric resonance are further examined through a parametric analysis of the system. The coupled cable-pulley dynamics are derived and the flexible modes of the overall system are calculated analytically and verified experimentally. In the system examined, the dominant resonance mode is caused by cable elasticity and cannot be ignored in high-bandwidth high-precision applications. This is in contrast to most robot manipulators where the resonant modes are assumed to be dominated either by joint or link flexibility. Experimental observations of the system's frequency response are used to model the cables as axial springs and a trajectory tracking problem is formulated using a lumped parameter model of the system with matched uncertainty in the drive motor dynamics as well as unmatched uncertainty in the load pulley 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 in the system. The proposed controller guarantees prescribed output-tracking transient performance as well as final tracking accuracy in the presence of both parametric uncertainties and other uncertain nonlinearities. Experimental results are presented to demonstrate its effectiveness.
Degree
Ph.D.
Advisors
Yao, Purdue University.
Subject Area
Mechanical engineering
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