The four-tank control problem: Comparison of two disturbance rejection control solutions

Abstract

The paper aims to compare and prove a pair of disturbance/uncertainty rejection control laws for the well-known four tank control problems. Control requirements are expressed in terms of a set point sequence as it usual in the literature. Uncertainty class is defined as the union of four sub-classes: unknown disturbance, parametric uncertainty, measurement errors and neglected dynamics. Modelling and design allow insight of the dynamic properties of the problem. They are formulated by a pair of theorems which fix the range of application. Theorem are confirmed by the results simulated runs, and indicate the correct way to further broaden control design applicability. Disturbance rejection (better uncertainty) design is deployed using the Embedded Model Control methodology: only unknown disturbance and parametric uncertainty can be rejected, whereas neglected dynamics effects must be filtered. As a result, simple performance and stability inequality can be formulated in the frequency domain and lead to closed-loop pole placement. Inequalities are such to reveal whether pole placement is feasible and how feasibility can be recovered, an issue which at authors knowledge is rarely encountered in the literature. Simulated runs prove the design procedure.

Full and Reduced-Order Unknown Input Observer Design for Linear Time-Delay Systems with Multiple Delays

“…This system is composed of four coupled tanks, two pumps, and two valves [35]. Many research papers have been devoted to the problem of observer and controller design of this benchmark system without consideration of time delays [37][38][39][40][41][42][43] and to the best of our information, no researches have been investigated for unknown input observer design of time-delay quadruple-tank systems.…”

Disturbance Observer and L2-Gain-Based State Error Feedback Linearization Control for the Quadruple-Tank Liquid-Level System

“…This method can be used for state estimation and parameter estimation. The authors of [31] defined uncertainty as a combination of unknown interference, parameter uncertainty, measurement error, and ignoring dynamics. Modeling and designing gave us a deeper understanding of the dynamic nature of the problem.…”

Disturbance Observer-Based Integral Backstepping Control for a Two-Tank Liquid Level System Subject to External Disturbances

“…Gouta et al [30] proposed an adaptive control and a generalized predictive control method of the coupled two-tank system, which are to minimize the multilevel cost function defined on the prediction layer. Aiming at the problem of four-tank control [31], a set of disturbance uncertainty suppression control laws were compared and proved, whose control requirements were usually expressed in the literature in the form of a set value sequence. e uncertainty class was defined as the union of four subclasses:…”