4 1. EXTRACTION OF UNCERTAIN MODEL OF DC-DC CONVERTERS
1.3 ROBUST CONTROL
Robust control is a design methodology that explicitly deals with uncertainty. Robust control
designs a controller such that:
• some level of performance of the controlled system is guaranteed; and
• irrespective of the changes in the plant dynamics/process dynamics within a predefined
class the stability is guaranteed.
Some of the well-known robust control design techniques are studied briefly below.
1.3.1 KHARITONOV’S THEOREM
Kharitonov’s theorem is used to assess the stability of a dynamical system when the physical pa-
rameters of the system are uncertain. It can be considered as a generalization of Routh–Hurwitz
stability test. Routh–Hurwitz is concerned with an ordinary polynomial, i.e., a polynomial with
fixed coefficients, while Kharitonov’s theorem can study the stability of polynomials with un-
certain (varying) coefficients.
Kharitonov’s theorem is an analysis tool more than a synthesis tool. Kharitonov’s the-
orem can be used to tune simple controllers such as Proportional-Integral-Derivative (PID).
Designing high-order controllers using Kharitonov’s theorem is not so common.
Barmish [1993] and Bhattacharyya et al. [1995] are good references for control engi-
neering applications of Kharitonov’s thorem. Plenty of tools and related theorems are gathered
there.
Kharitonov’s theorem used to design robust controller for DC-DC converters. For in-
stance, Bevrani et al. [2010] used Kharitonov’s theorem to tune the PI controller of a quadratic
buck converter. Chang [1995] designed a robust lead-lag controller for a buck converter.
1.3.2 H
1
CONTROL
H
1
techniques formulates the required design specifications (control goles) as an optimal con-
trol problem in the frequency domain. In order to do this, some fictitious weighting functions
are added to the system model. Weighting functions are selected with respect to the required
design specifications. Selection of weights is not a trivial task and requires some trial and error
to obtain the desired specifications. In fact, the most crucial and dificult task in robust controller
design is a choice of the weighting functions. Lundstron [1991], Skogesttad and Postlethwaite
[2000], and Beaven [1996] give very general guidelines for selection of the weights. Donha and
Katebi [2007] and Alfaro-Cid et al. [2008] used intelligent optimization methods (i.e., Genetic
Algorithm) to find the best weighting functions.
e H
1
design does not always ensure robust stability and robust performance of the
closed-loop system. is is the main disadvantage of H
1
design techniques.
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