Open-Loop Observer Structure for Disturbance Compensation using Adaptive Robust Design

High accuracy and stability are generally indispensable in industrial control applications of servomechanism. Many unavoidable factors negatively influence the control performance in real-word applications, such as the modeling uncertainties and the external disturbance. Therefore, a disturbance compensation scheme is stipulated need to reduce ad-verse effects resulting from modeling uncertainty and external disturbance.

The disturbance observer (DOB) is a popular control scheme for disturbance estimation and attenuation in actual applications [1-8]. The conventional DOB design requires an in-verse nominal model and a low pass filter, and the disturbance can be accurately estimated within the bandwidth of the low pass filter [1, 2]. Furthermore, the Luenberger observer can be considered as a closed-loop observer structure, whose gain can be adopted to estimate the disturbance [3-5]. Additionally, the extended state observer regards the lumped disturbance as an augmented state and utilizes the Luenberger observer structure to estimate the lumped disturbance [6-8].

Even if a DOB-based controller provides excellent disturbance attenuation, the disturbance rejection performance of the DOB is constrained by the bandwidth of the low pass filter. Moreover, since Luenberger observer would feed the estimated disturbance back to the nominal plant, this method may reduce the accuracy of disturbance estimation. Significantly, the open loop disturbance observer avoids this problem, but has another inherent drawback, its performance depends strongly on the accuracy of system modeling. To solve this problem, this investigation develops an adaptive algorithm to improve the performance affected by the modeling uncertainty, the adaptive control is a popular approach for the modeling uncertainties in control application [9-11]. The proposed algorithm aims to ensure that the output of the actual plant asymptotically con-verges to the output of the nominal plant by using the adaptive gain adjustment, and the gain is bounded through the projection type adaptive law. Additionally, the backstepping algorithm is adopted to enhance robustness in the disturbance compensation. The study makes three contributions: (1) adaptive gain adjustment of the disturbance compensation is proposed to solve the modeling inaccuracy, and the stability and convergence have proved by Lyapunov theorem, and (2) the proposed adaptive open loop observer can effectively suppress the external disturbance in the absence of modeling uncertainties; (3) the backstepping algorithm is adopted to enhance the performance of the proposed approach.