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The design and analysis of active disturbance rejection control (ADRC) are considered for a globally Lipschitz nonlinear discrete-time system, which is nonaffine to control inputs. A local dynamic linearization is proposed to transfer the original nonaffined nonlinear system into a nonlinear system affine to control input such that the open problem of selecting a control gain in the feedback control law of ADRC is solved. Furthermore, both a parameter updating law and an adaptive extended state observer are designed to estimate control gains and total uncertainty, respectively. The stability of ADRC for nonlinear nonaffine discrete-time processes is analyzed rigorously for the first time with the aid of contraction mapping principle. The proposed adaptive feedback controller considers desired reference trajectory, parameter adaption, error feedback, and the compensation of total uncertainties caused by parameter estimation error and unknown nonlinearity simultaneously to achieve better control performance. The proposed method is nearly data driven since no other model information is needed except for the globally Lipschitz condition and the nonzero property of the partial derivative of the nonlinear system with respect to the control input. The theoretical result is verified by simulations. [ABSTRACT FROM AUTHOR]

Proportional-integral (PI) control/loop has been widely used in numerous industrial processes. This article focuses on integrating uncertainty estimator into PI controller for better robustness and transient performance against uncertain nonlinear coupling dynamics and time-varying disturbances. First, the descriptions for the sizes of three kinds of uncertainties in a class of multi-input–multi-output nonlinear systems are discussed. Then, the tuning laws of the typical uncertainty estimator, i.e., extended state observer (ESO), are quantitatively presented to ensure the stability of closed-loop systems. More importantly, it is shown that the desired transient performance of tracking error can be ensured by tuning the bandwidth of ESO. In addition, it is proven that much stronger disturbance rejection at low frequency can be achieved by integrating the uncertainty estimator module. The simulation results for calibration-free robotic eye-hand coordination system show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we study the output feedback exponential stabilization of a one-dimensional wave equation with control matched nonlinear disturbance. The well posedness of the open-loop system, which is essentially important for the designs of observer and controller, is verified. By designing an infinite-dimensional unknown input state observer in place of the conventional extended state observer, we estimate the total disturbance in real time. Moreover, we prove the convergence of the disturbance estimator. Based on the disturbance estimator, we design a state observer by compensating the total disturbance, and an estimated state feedback controller to exponentially stabilize the original system by means of the Riesz basis approach. Some numerical simulations are presented. [ABSTRACT FROM AUTHOR]

This paper investigates performance output tracking for a boundary controlled multidimensional heat equation. It is assumed that the so-called total disturbance (which is composed of internal possibly nonlinear uncertainty and external disturbance) the equation is subject to is on one part of the boundary, and that the control is applied on the rest of the boundary. Using only partial boundary measurement, we first propose an extended state observer to estimate both system state and the total disturbance. This allows us to design a servomechanism and then an output feedback controller. Under the condition that both the reference signal and the disturbance vanish or belong to spaces $H^1(0,\infty ;L^1(\Gamma _1))$ and $L^2(0,\infty ;L^2(\Gamma _0))$ , respectively. We show that the over-all control strategy achieves three objectives on the system performance: first, exponentially output tracking for arbitrary given reference signal; second, uniformly boundedness of all internal signals; and, third, the internal asymptotic stability of the closed-loop system. In addition, the control strategy turns out to be robust to the measurement noise. We provide numerical experiments to illustrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this technical note, the active disturbance rejection control (ADRC) is generalized to uncertain nonaffine-in-control nonlinear systems. The proposed controller incorporates both an extended state observer (ESO) as well as a dynamic inversion. The ESO is designed to estimate system state and total uncertainty, which includes the uncertain internal dynamics and the external disturbance, and is nonaffine-in-control. Based on the output of the ESO, the dynamic inversion is used to deal with the nonaffine-in-control problem. The proposed control has a multi-time-scale structure, in which the ESO is the fastest time scale; the dynamic inversion is the second; and the considered nonlinear system is the slowest. The practical convergence of the resulting closed-loop system is obtained. An example is presented to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]