Theoretical Analysis on Observer and Operator Based Nonlinear Tracking Control of a Flexible Arm Using Shape Memory Alloys Actuators

Abstract

To achieve high-speed operation and reduce energy consumption in manufacturing, lightweight industrial robot arms are highly desirable. However, reducing their weight decreases structural stiffness and induces undesired vibrations. To realize high-speed and high-precision motion, this study proposes an observer and operator based nonlinear reference tracking control method for flexible arms using shape memory alloy (SMA) actuators, along with its comprehensive theoretical analysis. The primary challenges in this implementation stem from the SMA's strong nonlinear hysteresis and thermal dynamics, which can severely degrade tracking performance. To overcome these issues, a dual-loop control scheme is designed, where an inner loop utilizes an error-based Extended State Observer (eESO) to compensate for uncertainties and hysteresis, and an external loop based on operator theory to ensure robust stability and tracking accuracy. Finally, simulation validation is conducted to verify the effectiveness of the proposed method.