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.

In this paper, a new object in the form of a theoretical network is presented, which is useful as a benchmark for particle filtering algorithms designed for multivariable nonlinear systems (potentially linear, nonlinear, and even semi-Markovian jump system). The main goal of the paper is to propose an object that potentially can have similar to the power system grid properties, but with the number of state variables reduced twice (only one state variable for each node, while there are two in the case of power systems). Transition and measurement functions are proposed in the paper, and two types of transition functions are considered: dependent on one or many state variables. In addition, 10 types of measurements are proposed both for branch and nodal cases. The experiments are performed for 14 different, four-dimensional systems. Plants are both linear and highly nonlinear. The results include information about the state estimation quality (based on the mean squared error indicator) and the values of the effective sample size. It is observed how the higher effective sample size resulted in the better estimation quality in subsequent cases. It is also concluded that the very low number of significant particles is the main problem in particle filtering of multivariable systems, and this should be countered. A few potential solutions for the latter are also presented.

This paper presents the robust Active Disturbance Rejection Control method in an aerodynamical object with two degrees of freedom. Full derivation of control algorithm equations and the settings values depending on the desired properties of the system, based on the dynamics of the second order oscillating object, have been shown. The equations of the control algorithm were discretized and its discrete implementation was proposed. The tests were carried out on the Inteco aerodynamical laboratory kit, whose mathematical model is strongly non-linear, has two degrees of freedom and crosscoupling. The quality of operation was assessed on the basis of time graphs as well as integral quality indices. The conducted research shows the advantage of the applied algorithm over PID control for the tested system. The presented control algorithm is also more portable – the settings are selected only on the basis of the object order and once selected are correct regardless of the mathematical model. The proposed discrete equations can be implemented using any programming language theoretically for any object, taking into account the order of its dynamics.

The paper discusses the possibilities of using particle filter estimation algorithms in embedded systems. For this purpose, the dedicated testing platform was built, which allowed for the determination of the estimation quality of a particle filter on a real system, and the microcontroller performance in that scenario. Tests were performed using the obsolete and not very efficient, although energy-saving, STM32F4 Discovery board—it has allowed for an in-depth analysis, and the results can be easily improved by switching to a modern platform. The quality of operations in open- and closed-loop systems was investigated based on the analysis of time simulations conducted for various mathematical models. These analyses made it possible to establish a correlation between the number of particles and the required calculation power. They have shown that it is possible to successfully implement and run a particle filter algorithm on an older and computationally limited device, as well as in real-time scenarios.

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.