High-Order State-Filtering System Design and Its Application to Feedback Control of a Three-Phase BLDC Motor

Existing state estimation methods use a combination of measurement error and fixed gains to update high-order states. However, if these fixed gains are not finetuned, it will inevitably lead to significant phase distortion and violation of calculus relationship among updated states. To handle these issues, this article proposes a high-order state-filtering system that directly uses measurement data, thereby providing precise high-order differential states for potential applications. The estimated highest order derivative is produced by an online planned polynomial that satisfies all state-error constraints. To fulfill calculus relationship among updated states, each low-order state is uniquely determined by the integration of this highest order derivative. To validate the effectiveness of the proposed state-filtering system, it is applied to closed-loop position control of a brushless direct current (BLDC) motor. In this application, its rotor angle is measured by a high-resolution encoder. Compared to a differentiator, a high-gain observer, and a Kalman filter, the proposed method outperforms them by eliminating the need for parameter optimization, being insensitive to the sampling time step, effectively mitigating phase distortion, and strictly satisfying calculus relationship among updated states. Experimental results have verified the superiority and robustness of the proposed method.