QFT Control of a Two-Link Rigid-Flexible Manipulator

This paper evaluates a new and simple controller design method based on QFT (quantitative feedback theory) for a two-link manipulator whose first link is rigid and the second is flexible. A piezoelectric patch is attached to the surface of the flexible link for vibration suppression of it. This system is modeled as a nonlinear multi-input multi-output (MIMO) control systems whose inputs are two motor torques which are applied on the joints and a voltage which is applied on the piezoelectric patch. To control the manipulator’s end point position, motion of the manipulator is divided to two rigid and flexible parts. To control both parts, nonlinear equations of the motion is replaced by a family of uncertain linear time-invariant equivalent systems using Rafeeyan-Sobhani’s method(RS method) which results in three decoupled transfer functions established in the Laplace domain. Then the QFT method is used to design a diagonal matrix as the prefilter of the system an another diagonal matrix as the system controller. Results demonstrate the remarkable performance of the proposed controllers in reduction of residual vibration of elastic link and tracking a circular trajectory by the manipulator end point.