Dr. Yuhong Zhang, May 3rd
Modeling and Control of Flexible Cable Systems
Flexible cable systems are widely used in many industrial applications,
such as high-rise elevators, tethered satellite systems/submarines,
cable suspended robots, and construction cranes. Under external
disturbances, flexible cables tend to vibrate, thus degrading the
performances of the overall system. Modeling and vibration control of
such cable systems are the topic of this talk. The governing equations of
motion for a cable system are developed using both Newton’s law and Hamilton’s principle.
Calculus of variations is applied when using Hamilton’s principle. The theory of differential flatness and
H∞ robust control theory are applied to modulate the residual vibration when the cable
lengths are constant. The H∞ robust controller can compensate the bounded external disturbances.
Subspace system identification theory is utilized to obtain an approximate state-space model from the
experimental frequency response data for controller design. The minimax Linear Quadratic Gaussian (LQG)
method is used to minimize the cost functional for multiplicative nonparametric bounded uncertainties.
The controller design involves solutions of two simultaneous Riccati equations. The experimental results show
that there are about 9 dB peak resonance reductions when implementing the proposed controller on a real time
dSPACE CP1103 system. Modeling and control of cable systems with varying lengths is still an open question.
In this work, we assume that the axial velocity of the cable system is unspecified, which
has been usually assumed to be constant or prescribed in existing literature. The derived
general motion equations complement the existing literature. Lyapunov-based controllers are proposed,
which suppress the vibrations effectively, and assure the attainment of the slider goal, simultaneously.
Closed-loop stability is guaranteed by the Lyapunov stability theory. An approximate numerical solution of the
system is provided using a modified Galerkin’s method. Simulation results have
verified the effectiveness of the proposed Lyapunov controller.
