Robustifying adaptive model predictive control for a one-link flexible manipulator using super-twisting integral sliding mode control

Abstract

Vibration depreciates positioning accuracy and productivity of flexible manipulators and make their modeling and/or controlling a very demanding task. In this paper, an Adaptive Model Predictive Control (AMPC) algorithm is detailed to actively damp a nonlinear one-link flexible manipulator while tracking its rigid body position. The derived controller involves in-loop linearization of the plant, around the actual state and control signal, to adapt the required model over the prediction horizon. The robustness of the proposed control strategy is improved using Super-Twisting Integral Sliding Mode Control (STISMC). The proposed controller compensates for the assumed matched uncertainties and external disturbances affecting the nominal plant, so the robustness is guaranteed. The effectiveness of the active vibration control is appraised via numerical simulation carried out using Matlab/Simulink.

Appendix: Numerical Values of Model Matrices Used for Simulation

The Mass Matrix:

$$M\left(q\right)=\left[\begin{array}{ll}0.13 +0.2783{q}^{2}& 0.1163\\ 0.1162& 0.2783\end{array}\right]$$

The vector of nonlinear centrifugal and Coriolis terms:

$$ h\left( {q,\dot{q}} \right) = \left[ {\begin{array}{*{20}c} {0.5566\;q\dot{q}\dot{\theta }} \\ { - 0.2783\;q\dot{\theta }^{2} } \\ \end{array} } \right] $$

The stiffness matrix

$$K\left(q\right)=\left[\begin{array}{cc}0& 0\\ 0& 22.94\end{array}\right]$$