Robust Optimal Control Design for a Parallel Delta Robot

In this report we propose a Robust control scheme based on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> optimization. The closed-loop control system robustness is enhanced by minimizing a by minimizing a criterion based on mixed sensitivity and the control effort. The proposed resulting Robust optimal control <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> algorithm is applied to a Parallel DELTA Robot in order to test its capability, based on numerical simulation. The system model is a three-degree-of-freedom direct drive parallel manipulator. We show that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> robust optimal controller gives very good responses in term of reference tracking even in presence of disturbances and modeling uncertainties comparatively to the PD decentralized control scheme.