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.

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.

The article presents a modified Active Disturbance Rejection Control (ADRC) algorithm that uses the Kalman Filter (KF) for the estimation of extended state vector. The Kalman filter replaced the Extended State Observer (ESO) used in its basic form. The purpose of this modification was to improve the system robustness under conditions of stochastic measurement disturbances. The method of the control system synthesis and the Kalman filter gains selection, ensuring control efficiency, as well as their impact on the system operation, were presented. The experiments were carried out on a laboratory setup – the Ball Balancing Table (BBT). Control quality was assessed based on time plots of signals and integral performance indices for various algorithm gains configurations and different noise levels. As a result of the conducted research, the advantage of using the Kalman filter over the ESO in terms of sensitivity to measurement noises was demonstrated. Implementation of the Kalman filter as the ESO determined a positive impact on control quality and the ability to reject internal disturbance also in a deterministic system.

This paper addresses the problem of stabilizing an inverted pendulum actuated by a reaction wheel, a system relevant for robotic balancing platforms and aerospace applications. The study compares several state-space representations of the system and examines their implications for controller synthesis and parameter identification. A unified nonlinear model formulation is introduced, enabling a structural Lyapunov-based robustness analysis that reveals how variations in the gravitational gain affect closed-loop stability. Control strategies based on pole placement and Linear Quadratic Regulator (LQR) design are implemented and compared across the different representations. The analysis highlights a robustness–fidelity trade-off between model complexity and sensitivity to parameter uncertainty, providing insight that extends beyond the specific laboratory setup. Theoretical results are validated on a real laboratory platform. The controllers are evaluated in both upright and downward equilibrium configurations, and the influence of parameter shifts is assessed experimentally using global identification and performance indices. The work offers general modeling and robustness guidelines for reaction-wheel-based stabilization systems and related underactuated nonlinear mechanisms.

In this paper, the problem of backward compatibility of active disturbance rejection control (ADRC) is investigated. The goal is to contextualize ADRC to deliver its interpretations from the established field of linear control systems. For this study, a control algorithm, denoted here as integral disturbance rejection control (IDRC), is considered that combines classical state-feedback control with an integral compensator. At first, an interpretation of ADRC is involved in terms of existing state-space control approaches. Next, a transition to the frequency domain is performed, which is justified as a significant part of practical control engineering is conducted in that domain. For assumed specific plant structures, both ADRC and IDRC are then holistically compared in terms of transfer function representation and frequency characteristics, as well as steady-state convergence conditions. Such a juxtaposition helps to highlight the similarities and differences of both approaches, whereas the utilized bandwidth parameterization is shown to bring the control system to the same form, thus indicating some interesting practical aspects. Finally, the theoretical results concerning both considered control structures are validated in a set of numerical simulations and experiments conducted on a laboratory hardware testbed.

There are multiple ways to incorporate model information into active disturbance rejection control (ADRC) to facilitate a more reliable and efficient design. However, if this knowledge is misused, it can undermine the benefits of informed ADRC synthesis. In this paper, we provide design recommendations to guide ADRC users in selecting the control structure based on model availability, observer speed, and system characteristics. These guidelines stem from a comparative analysis of three linear ADRC variants, each utilizing a priori plant knowledge differently: the classical form, which relies only on basic plant information; the generalized version, which allows broader model incorporation; and a third approach, proposed by the authors, which modifies the generalized framework. While the latter two share the same assumed model, they differ in how it is integrated into the control architecture: the former embeds the linear drift directly into the state matrix, altering both observer and controller gains, whereas the proposed approach introduces it via a regression-based formulation that preserves the original gain structure of classical ADRC. A transfer function-based analysis shows that, even with identical models, the integration method yields distinct closed-loop properties. In particular, the proposed approach outperforms the generalized ADRC variant in cases where observer bandwidth is limited relative to plant dynamics. In this work, we focus on benchmark second-order systems, which strike a balance between generality and tractability in control design. The theoretical insights are supported by simulations and validated experimentally.