Design of Robust Fractional-Order PID Controller for DC Motor Using the Adjustable Performance Weights in the Weighted-Mixed Sensitivity Problem

Abstract

This paper deals with the robust series and parallel fractional-order <em>PID</em> synthesis controllers with the automatic selection of the adjustable performance weights, which are given in the weighted-mixed sensitivity problem. The significant contribution of the paper is to achieve the good trade-off between nominal performances and robust stability for DC motor regardless its nonlinear dynamic behavior, the unstructured model uncertainties and the effect of the sensor noises on the feedback control system. The main goal is formulated as the weighted-mixed sensitivity problem with unknown adjustable performance weight. This problem is then solved using an adequate optimization algorithm and its optimal solution leads to determine simultaneously the robust fractional <em>PID</em> controller, which is proposed by the series and the parallel fractional structures, As well as, the obtained optimal solution determines the corresponding adjustable performance weight.<strong><em> </em></strong>The proposed control technique is applied on DC motor where its dynamic behavior is modeled by unstructured multiplicative model uncertainty. The obtained performances are compared in frequency- and time-domains with those given by both integer controllers such classical <em>PID</em> and <em>H<sub>∞</sub> </em>controllers.

Robust control of a UPFC system with H~ control technique

“…and modeling errors (reduced order model, idealization actuators, parametric uncertainties, etc.) as shown in Figure 5 [7].…”

“…It is Kimura [4] who, in 1984, formulated the first robust control problem in terms of H∞. Although his position of the problem is hardly different from that proposed by Doyle and Stein [6,7] (novelty residing in the explicit use of the H∞ framework that allowed Kimura to solve the synthesis problem). Thanks to the important concept of the standard problem that the work of Francis Doyle and [8] were unified.…”

“…b) Assumptions (II), (IV) and (V) ensure that the problem is well posed, in other words, the compensator is appropriate. c) Assumptions (IV) and (V) indicate that P 12 (s) and P 21 (s) have no zeroes on the imaginary axis, they can be avoided [7]. d) Assumption (III) simplifies the solution.…”

Resolving of optimal fractional PID controller for DC motor drive based on anti-windup by invasive weed optimization technique

“…Fractional Order PID (P ) Controller PI λ D μ controller is derived from a conventional PID controller established upon fractional order differentiation and integration. The PI λ D μ controller has five control parameters (K p , Ki, K d , λ, and μ) that requirement tuning to get a robust controller with extra freedom and provide better control of dynamic systems [9,12,13]. The P I λ D μ controller can be describing as:…”

“…To optimize the parameters of PID and FOPID controller, there are several methods utilized. Some of these methods are intelligent such as Genetic Algorithm (GE) [5], Particle Swarm Optimization (PSO) [3][4], Ant and Bee colony [8][9], etc. Invasive Weed Optimization (IWO) technique is utilized for tuning PID controller parameters in drives other than DC drive such as in brushless DC motor drive [10].…”