Position control of a single-link flexible manipulator using H∞-based PID control

Abstract

The application of the H∞ proportional-integral-derivative (PID) control synthesis method to tip position control of a flexible-link manipulator is investigated. For this system, it is first shown that the classical PID tuning formula may yield poor closed-loop performance. This underlines the need for a rigorous PID control synthesis methodology for this infinite-dimensional and non-minimum-phase system. To achieve high performance in PID control, this particular control design problem is cast into the H∞ framework. On the basis of a recently proposed H∞ PID control synthesis method, a set of admissible controllers is then obtained to be robust against uncertainty introduced by neglecting the higher-order modes of the link and to achieve the desired time-response specifications. The most important feature of the H∞ PID control synthesis method is its ability to provide the knowledge of the entire admissible PID controller gain space, which can facilitate controller fine tuning. Finally, experimental results are given to demonstrate the effectiveness of the H∞ PID control.