Optimal control of a single link flexible manipulator

Abstract

An exact state-space dynamic model for manipulator with flexible links is considered. The Bernoulli-Euler beam equations are used to derive a frequency domain matrix transfer function. This transfer function is then used to computer the Laplace transform of the state vector as a function of lateral position along a single link manipulator. The problem of optimal end-point control of the beam is addressed. A sixth-order state-space model is derived for the manipulator and the controller is based on this model. Several control laws are studied for this model. The manipulator is modeled as eighth-order, but the control law based on the sixth-order model is retained. The six states are estimated from the output of the eighth-order model. These states are fed back to the controller to derive the control torque used to drive the manipulator. A filter is introduced to compensate for spillover. The results are satisfactory, and are illustrated by simulated case studies.< >