A measurement-based technique for designing fixed-order RST controllers and application to a coupled water tank system

This paper addresses the control design problem for unknown linear single-input single-output systems using a set of measurements. In standard control methods, controllers are designed on the basis of a mathematical model. Such a mathematical model, which describes the behavior of the system, can be developed using either physical laws or measured data. However, due to the complex dynamics of many physical systems, some prior assumptions are usually made to build simplified models. The efficacy of such model-based control techniques depends greatly on the quality of models used. Hence, data-based control design methods appeared as an alternative to model-based methods. Such data-based techniques are powerful in the sense that no mathematical model is needed for controller design. In this paper, we propose an approach that uses frequency response data to directly design controllers without going through any modeling stage. The main idea of our proposed method is to design polynomial RST controllers, for which the closed-loop frequency response fits a desired frequency response that describes some desired performance specifications. This problem is formulated as an error minimization problem, which can be solved using efficient optimization algorithms. The main feature of our proposed control approach is that it enables the designer to pre-select the controller structure, which allows the design of low-order controllers. Moreover, this control design approach does not depend on the increasing order and complexity of the system. An application to water level control of a coupled tank system is presented to validate and illustrate the efficacy of the proposed approach.