Robust control of two-link flexible manipulators using the μ-synthesis technique

Two-link robot manipulators are commonly used in industrial sectors such as manufacturing. Some manipulators are often bulky and their power consumption is relatively high. Others, such as the arm on the space shuttle, are driven slowly to prevent the onset of flexible oscillations. The efficiency of these manipulators can be improved by reducing the weight of some of these arms and/or increasing the speed of others. These modifications complicate the dynamic behavior of the system due to the possible onset of low frequency oscillations. This article addresses the issue of modeling and end-point robust control of two-link flexible manipulators using the μ-synthesis technique. The Timoshenko beam theory along with the assumed modes method are used to derive reference equations of motion for the flexible manipulator. Discrepancies between the control design model and the actual dynamics of the manipulator are attributed to neglected nonlinearities such as cross-coupling, which should be included in the controller design. A linear estimation of these errors will be identified and used in the control design to compensate for the unmodeled dynamics of the flexible arm and parameter uncertainties. The μ-synthesis control design techniques are then employed to synthesize controllers for the two-link flexible robot manipulator.