A MULTIINPUT MULTIOUTPUT OPTIMAL PI CONTROLLER FOR REDUNDANT ROBOTS IN THE PRESENCE OF FLEXIBLE DISTURBANCES

The two-stage synthesis of a multi-input/multi-output optimal proportional-integral (PI) controller is described for linear, time-invariant systems. In the first stage the PI controller is designed by solving a steady state algebraic Riccati equation. As a result, the optimal cost is expressed in terms of the system's constant output set-points. In the second stage the cost is further reduced by optimally selecting the output set-points to minimize a static quadratic performance index subject to linear algebraic constraints. The design framework is applied to a planar redundant robotic manipulator equipped with four joints and mounted at the tip of a long flexible arm. We then address the problem of self-motion control in the presence of vibratory disturbances.