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A procedure to specify the weighting matrices for an optimal load-frequency controller

Mariano, S.J.P.S. ; Pombo, J. ; Calado, M.R.A. ; Ferreira, L.A.F.M.

Turkish Journal of Electrical Engineering and Computer Sciences Vol. 20, Nº 3, pp. 367 - 379, March, 2012.

ISSN (print): 1300-0632
ISSN (online): 1303-6203

Scimago Journal Ranking: 0,25 (in 2012)

Digital Object Identifier: 10.3906/elk-1003-413

The linear quadratic optimal regulator is one of the most powerful techniques for designing multivariable
control systems. The performance of the system is specified in terms of a cost, which is the integral of a
weighted quadratic function of the system state and control inputs, that is to be minimized by the optimal
controller. The components of the state cost weighting matrix, Q, and the control cost weighting matrix,
R, are ours to choose in mathematically specifying the way we wish the system to perform. Changing these
matrices, we can modify the transient behavior of the closed-loop system. This paper addresses the stabilization
and performance of the load-frequency controller by using the theory of the optimal control. A new technique,
based on pole placement using optimal regulators, to overcome the difficulties of specifying weighting matrices
Q and R is proposed. The design method employs successive shifting of either a real pole or a pair of complex
conjugate poles at a time. The proposed technique builds Q and R in such a way that the system response
also obeys conventional criteria for the system pole location. The effectiveness of the proposed method is
illustrated by numerical examples.