Digital redesign of analog controllers based on minimizing integral of squared errors

Abstract

SUMMARYDigital redesign is to replace an existing well-designed analog feedback controller by a digital one along with a sampler and a hold. In this paper, we present a digital redesign technique which takes into account both closed-loop and intersample behaviour. More precisely, we give a numerical procedure to optimally discretize an analog controller such that the integral of the squared error between the closed-loop step responses of the analog and digital controlled systems is minimized. A parametric expression is derived for evaluating the integral performance index. With this expression, the optimal digital redesign problem becomes an optimal parameter selection problem which can be solved using existing optimal parameter search algorithms. Moreover, it allows one to obtain optimal reduced-order digital controllers for sampleddata control systems over a range of sampling periods.

Electromechanical Actuator Modeling and Its Application in Fault Diagnosis

“…With the continuous development of aircraft, the requirements of actuator in volume, weight, performance will be higher. Electromechanical actuator has the advantages of simple structure and easy maintenance [1], so we will continue to study it in depth. The electromechanical actuation system is in the severe high pressure, high temperature and continuous working environment for a long time, which will result in fatigue and wear failure [2] and will affect the normal flight of the aircraft.…”

Digital redesign via the generalised bilinear transformation

“…Keller and Anderson 1992;Markazi and Hori 1995;Rafee, Chen and Malik 1997;Shieh, Wang and Tsai 1998;Anderson, Chongsrid, Limebeer and Hara 1999;Rosenvasser, Polyakov and Lampe 1999;Rosenwasser, Polyakov and Lampe 1999;Rosenwasser and Lampe 2000;Hwang, Chang and Hwang 2003). In each of these approaches, given an analogue controller, an optimisation problem is solved to produce a digital controller which is optimal in a certain sense such as H 2 or H 1 .…”

“…Within each subset a two-dimensional optimisation problem (30) is to be solved. Since only two variables, and h, are involved, many standard optimisation methods (e.g., the differential evolution algorithms (Storn and Price 1997;Hwang et al 2003)) can be employed to find optimal and h. After finding all of them over all subsets, the global one can be obtained. In what follows, we formalise the procedure:…”

ℓp-equivalence of Discretizations of Analog Controllers

“…This transformation, we hereafter call hold equivalent transformation, maps an analog controller to a digital one. The third is optimization-based controller redesign studied in Keller and Anderson [1992], Rafee et al [1997], Hwang et al [2003], Shieh et al [1998, etc. In each of the approaches proposed in these papers, given an analog controller, an optimization problem is solved to produce a This research is partially supported by NSERC Discovery Grants to the second and third authors.…”