Regulation and Tracking Control of Omnidirectional Rotation for Spherical Motors
Kun Bai, Yaowu Ding, Zixin Que, Han Yan, Xiang Chen, Shengxiong Wen, Kok-Meng Lee
Abstract
Spherical motors capable of omnidirectional rotations in a ball joint provide a highly dexterous actuator system yet also present great challenges in developing a high-performance regulation and tracking controller due to the complex rotor dynamics. This article presents a complementary <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-H<sub>∞</sub></i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-H<sub>∞</sub></i> ) control method for precisely controlling the multidegree of freedom (DOF) orientation of spherical motors in presence of external disturbances as well as model uncertainties and inaccuracies. In order to deal with the tradeoff between the robustness and control performance resulted from conventional control methods, the proposed controller featured with a 2-DOF structure presents an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> controller for a nominal plant and then complements it with an additional regulator designed in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H<sub>∞</sub></i> sense to assure robustness. Unlike traditional <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H<sub>∞</sub></i> or mixed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H<sub>∞</sub></i> controller, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H<sub>∞</sub></i> regulation is conducted online in accordance with the monitored modeling mismatch in a way that does not adversely degrade the performance delivered by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> control, hence, improving the conservativeness of the total control performance and leading to significant improvements of tracking accuracy and response time at same time. Both numerical simulations and experiments on a spherical motor testbed are conducted to validate the superior performance of the proposed controller versus conventional control methods.