AbstractThe 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 byoptimallyselecting 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 vibrato