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This paper presents a novel tuning method for the extended state observer (ESO), which is applied in the active disturbance rejection control (ADRC) algorithm operating in a stochastic environment. Instead of the traditional pole placement (PP) method, the selection of ESO gains based on the noise variances of the Kalman filter (KF) is proposed. Also, a simple parametrization of ESO gains for the particular control process based on the observer bandwidth is introduced. A root locus and frequency analysis is conducted for the KF-based observer and presented with regard to the proposed tuning method. The presented results come from experiments carried out on the ball balancing table (BBT) real plant for various measurement noise levels. The possibilities of rejecting measurement noise by the estimation algorithm were investigated to ensure effective control and minimize the control signal energy. Based on the conducted experiments, one can conclude that the presented tuning method provides better results than the traditional PP algorithm in the stochastic environment in terms of control quality and reduction in measurement noise. [ABSTRACT FROM AUTHOR]

This paper presents a new adaptive modification of active disturbance rejection control (ADRC) with parameter estimation based on a recursive least-squares (RLS) method. The common ADRC used in many applications relies on the simple approach, which assumes the simplification of the object into an integral chain form. However, this model-free ADRC does not guarantee the stability of a closed-loop system in the presence of noticeable modeling uncertainties, so it is compared in this paper to another approach, in which the linear part of the system is included in the ADRC framework (generalized ADRC). This incorporation of the model is examined in the paper for a wide range of model and controller parameters, considering also the presence of external disturbances as well as parameter uncertainties, pointing out the limitations of fixed-gain algorithms. Then, the adaptive modification of the model-based ADRC is proposed, which is equipped with a real-time estimation of model parameters by means of the RLS method in continuous time. The stability conditions of the proposed modification of the algorithm in the closed control loop are also analyzed. It can be concluded that, under appropriate conditions, the inclusion of information about known plant parameters into the ADRC can noticeably improve the conditions of the control system. The proposed adaptive model-based approach enables quality improvement during the control process even with initially unknown parameters, for time-varying parameters, and in the presence of parametric uncertainties and external disturbances. The tests were performed on a real plant—the task of controlling the angular velocity of the direct current (DC) motor was considered. [ABSTRACT FROM AUTHOR]