A Measurement‐Based Approach for Designing Fixed‐Order Controllers for Unknown Closed‐Loop Architecture

Abstract

This paper presents a new technique to design fixed‐structure controllers for linear unknown systems using a set of measurements. In model‐based approaches, the measured data are used to identify a model of the plant for which a suitable controller can be designed. Due to the fact that real processes cannot be described perfectly by mathematical models, designing controllers using such models to guarantee some desired closed‐loop performance is a challenging task. Hence, a possible alternative to model‐based methods is to directly utilize the measured data in the design process. We propose an approach to designing structured controllers using a set of closed‐loop frequency‐domain data. The principle of such an approach is based on computing the parameters of a fixed‐order controller for which the closed‐loop frequency response fits a desired frequency response that describes some desired performance indices. This problem is formulated as an error minimization problem, which can be solved to find suitable values of the controller parameters. The main feature of the proposed control methodology is that it can be applied to stable and unstable plants. Additionally, the design process depends on a pre‐selected controller structure, which allows for the selection of low‐order controllers. An application of the proposed method to a DC servomotor system is presented to experimentally validate and demonstrate its efficacy.

Stability analysis of dynamic interval type‐2 fuzzy control systems in frequency domain

“…Recently, to learn or adjust the parameters of T2F systems, researchers have presented different methods [36][37][38][39][40][41][42][43][44] which have been classified into derivative-based optimization approaches (i.e. gradient descent, extended Kalman filter) and non-derivative-based optimization methods (i.e.…”

Robust data‐driven fixed‐order controller synthesis: Model matching approach

“…The effectiveness of the obtained controller largely depends on the selection of this constraint line. A non-linear optimisation based solution approach for tuning fixed-order controllers is presented in [22,23]. This approach is based on frequency domain data that is obtained from closed-loop tests.…”

Fixed-order data-driven H∞ controller synthesis for flexible mechanical systems: Two-stage approach

“…DDC methods also differ according to the way input/output data is obtained. In Khadraoui et al (2016), a DDC method is introduced for both stable and unstable systems, by using input/output data obtained from the closed-loop system identification tests performed with three different initial controllers. In Karimi and Galdos (2010), open-loop system identification input/output data is used to optimize parameters of linearly parametrized controller under convex H ∞ constraints.…”