On the Equivalence of IMP and RODOB-Based Controllers: Application to BLDC Motor Position Control

While the Internal Model Principle (IMP) and Disturbance Observer (DOB) are fundamental to robust control, their systematic equivalence within a unified framework has received limited attention. IMP-based control achieves robustness through the structural inclusion of signal generators, whereas DOB-based methods rely on extended state representations for disturbance estimation. This paper bridges this gap by designing a state-space Reduced-Order Disturbance Observer (RODOB)-based controller that achieves systematic equivalence with an IMP-based transfer function controller. As a design example, an IMP-based controller is synthesized using a Linear Quadratic Regulator (LQR) for an augmented system in error space, with reference inputs directly integrated into the RODOB structure to eliminate the need for additional filters. Simulations and hardware experiments on a Brushless DC (BLDC) motor verify that both structures exhibit consistent control input and output characteristics, significantly outperforming conventional cascade and PID strategies. Numerical stability during digital implementation is ensured via partial fraction expansion. Furthermore, a method for estimating equivalent disturbances—encompassing both external loads and model uncertainties—is proposed by leveraging RODOB states. These findings suggest significant potential for future applications in fault diagnosis and real-time condition monitoring.