Analysis and Synthesis of Disturbance Observer-Based Digital Robust Motion Control Systems in State Space

Despite its extensive applications in motion control, there remains a lack of systematic analysis and synthesis methods capable of ensuring high-stability and performance for disturbance observer (DOb)-based robust motion controllers. The development of such methods is essential for achieving precise disturbance rejection, enhanced robustness, and high-performance motion control. In response to this need, this article proposes a novel analysis and synthesis method for DOb-based digital robust motion controllers. By employing a unified state-space design framework, the proposed synthesis approach facilitates the implementation of both conventional zero-order (ZO) and high-order (HO) DObs, offering a systematic design method applicable to a wide range of motion control systems. Furthermore, this design method supports the development of advanced DObs [e.g., the proposed high-performance (HP) DOb in this article], enabling more accurate disturbance estimation and, consequently, enhancing the robust stability and performance of motion control systems. Lyapunov's direct method is employed in the discrete-time domain to analyze the stability of the proposed digital robust motion controllers. The analysis demonstrates that the proposed DObs are stable in the sense that the estimation error is uniformly ultimately bounded when subjected to bounded disturbances. Additionally, they are proven to be asymptotically stable under specific disturbance conditions, such as constant disturbances for the ZO and HP DObs. Stability constraints on the design parameters of the DObs are analytically derived, providing effective synthesis tools for the implementation of the digital robust motion controllers. The discrete-time analysis facilitates the derivation of more practical design constraints. The proposed analysis and synthesis methods have been rigorously validated through experimental evaluations, confirming their effectiveness.