A measurement-based approach for designing reduced-order controllers with guaranteed bounded error

The objective of this paper is to present a measurement-based control-design approach for single-input single-output linear systems with guaranteed bounded error. A wide range of control-design approaches available in the literature are based on parametric models. These models can be obtained analytically using physical laws or via system identification using a set of measured data. However, due to the complex properties of real systems, an identified model is only an approximation of the plant based on simplifying assumptions. Thus, the controller designed based on a simplified model can seriously degrade the closed-loop performance of the system. In this paper, an alternative approach is proposed to develop fixed-order controllers based on measured data without the need for model identification. The proposed control technique is based on computing a suitable set of fixed-order controller parameters for which the closed-loop frequency response fits a desired frequency response that meets the desired closed-loop performance specifications. The control-design problem is formulated as a nonlinear programming problem using the concept of bounded error. The main advantages of our proposed approach are: (1) it guarantees that the error between the computed and the desired frequency responses is less than a small value; (2) the difficulty of finding the globally optimal solution in the error minimisation problem is avoided; (3) the controller can be designed without the use of any analytical model to avoid errors associated with the identification process; and (4) low-order controllers can be designed by selecting a fixed low-order controller structure. To experimentally validate and illustrate the efficacy of the proposed approach, proportional-integral measurement-based controllers are designed for a DC (direct current) servomotor.