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

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