Design of reduced-order controllers using a set of measurements: Application to a DC servomotor

This paper presents a new control design approach for unknown SISO systems by using measurements. In control approaches existing in the literature, controllers are usually designed on the basis of mathematical models obtained by either using physical laws or via identification system using a set of measured data. However, due to the complex dynamics of real systems, such parametric models are only an approximation obtained after some simplifying assumptions. Therefore, the design of controllers based on a simplified model leads to a degradation in the expected performance for the closed-loop system. Our proposed approach is based on measurements to directly design controllers without going through the use of mathematical models. The principle of the proposed control methodology is to design fixed-structure controllers for which the error modulus between the closed-loop frequency response and a desired frequency response is bounded by given quantity. This problem is formulated as a nonlinear programming problem based on inequality constraints. The main advantage of our proposed approach is that the controller design is based only on a set of measurements, which allows to avoid errors associated with the identification process. Moreover, with such a proposed control method, it is guaranteed that the error between the computed and desired closed-loop frequency responses is less than a small quantity. Another feature of the proposed technique is that the structure of the controller can be selected a priori, which allows to design low-order controllers. A simulation application to measurement-based controller design for DC servomotors is presented to validate and illustrate the efficacy of the proposed approach.