Fine Torsion Torque Control for Geared Motors by a State-Reference-Dependent Variable-Order Friction Observer

Controlling torsion torque in geared motors is essential for precise control of load-side dynamics. An I-P torsion torque controller (TTC) structure combined with a friction observer based on the disturbance observer has been previously proposed for this means. However, in motors with strong nonlinear friction, this method is not able to quickly compensate nonlinear friction when rotation direction changes, severely affecting the torsion torque control performance. This paper proposes a variable-order friction observer with a switching law based on the motor-side velocity (state) and torque command (reference) that is able to compensate for the effects of friction in the torsion torque response, while also preventing limit cycles due to the friction compensation itself. First, a review of the conventional I-P TTC with zero-order friction observer method is given. Followed by this we explain the decomposition process of a high-order friction observer into a variable-order form. Next, a stability analysis of the variable-order friction observer is done. Then, appropriate switching functions are designed to effectively compensate friction and prevent limit cycles. Finally, the effectiveness of the proposed method is proven by numerical simulation results and experimental results with a 1 DOF robotic arm.