Swing-free transport using variable structure model reference control

A variable structure model following control system design is proposed to reduce the vibrational motion of a suspended object transported by an overhead crane. The plant and the input matrices of the system are uncertain. The only information available about the uncertain parameters is the bounding sets in which they lie. A variable structure control law is developed to force the states of the uncertain system to track the states of a reference model. The control law also forces the system trajectories to hit a switching surface and slide along the surface where the system response is insensitive to parameter variations. The tracking error does not asymptotically decrease to zero; instead the error is bounded. This bound can be made arbitrarily small. The control law is developed for a general case and computer simulation results are provided to illustrate the application of the theory to a simple pendulum system.