Order Reduction of Large-Scale Linear Dynamic Systems Using Balanced Truncation with Modified Cauer Continued Fraction

Abstract

This article discusses a new technique to reduce the order of high-dimensional, continuous, linear time-invariant dynamic systems. The proposed approach utilizes the merits of the balanced truncation method, and modified Cauer continued fraction expansion. The reduced model denominator was retrieved via the concept of Lyapunov balancing, and state truncation and numerator coefficients were obtained by using a modified Cauer continued fraction. The proposed technique circumvents the steady-state gain discrepancy and steady-state error mismatch of the conventional balanced truncation method, and the instability issue of continued fraction expansion. The proposed method assures steady-state gain approximation, few moments, Markov parameters, stability, and other essential control features of a high-order system. The efficacy and applicability of the proposed technique are demonstrated using some typical test systems adopted from the literature. This method gives improved performance indices like minimum H∞ norm, H2 norm, a minimum ISE (integral squared error), IAE (integral absolute error), and retains approximately the full IRE (impulse response energy) of the existing system in the reduced model. The simulation findings of the proposed technique are compared with other current model reduction methods in recent literature using MATLAB.