Robust Disturbance Reconstruction and Compensation for Nonlinear First-Order System

The article discusses the control of nonlinear processes with first-order dominant dynamics, focusing on implementation using modern hardware available in various programmable devices and embedded systems. The first two approaches rely on linearization with an ultra-local process model, considering small changes of the process input and output around a fixed operating point, which can be adjusted through gain scheduling with the setpoint variable. This model is used to configure either the historically established automatic reset controller (ARC) or a stabilizing proportional (P) controller enhanced by an inversion-based disturbance observer (DOB). This solution can be interpreted as an application of modern control theory (MCT), as DOB-based control (DOBC) or as advanced disturbance rejection control (ADRC). Alternatively, they can be viewed as a special case of automatic offset control (AOC) based on two types of linear process models. In the third design method, setpoint tracking by exact linearization (EL) is extended with a nonlinear DOB designed using the inverse of the nonlinear process dynamics (EEL). The fourth approach augments EL-based tracking with a DOB derived from the transfer functions of nonlinear processes (NTF). An illustrative example involving the control of a liquid reservoir with a variable cross-section clarifies motivation for the definition of (linear) local and ultra-local process models as well as their advantages in designing robust control that accounts for process uncertainties. Thus, the speed, homogeneity, and shape of transient responses, the ability to reconstruct disturbances, control signal saturation, and measurement noise attenuation are evaluated according to the assumptions specified in the controller design. The novelty of the paper lies in presenting a unifying perspective on several seemingly different control options under the impact of measurement noise. By explaining their essence, advantages, and disadvantages, it provides a foundation for controlling more complex time-delayed systems. The paper emphasizes that certain aspects of controller design, often overlooked in traditional linearization procedures, can significantly improve closed-loop properties.