Moth Flame Optimization for Model Order Reduction of Complex High Order Linear Time-Invariant Systems

The moth flame optimization (MFO) method has been introduced as a means to approximate single–input–single–output (SISO) complex high-order linear time-invariant systems (CHOLTIS). Initially, the unknown parameters within the denominator and numerator of the reduced-order linear time-invariant system (ROLTIS) are determined through balanced truncation. This process establishes the initial values of the parameters for MFO. To confine the exploration space of MFO around the coefficients derived from the balanced truncated model, a strategic constant is employed. This constant defines the lower and upper bounds, effectively constraining the search area of MFO. Consequently, MFO can focus its optimization efforts within a targeted range, improving efficiency and efficacy. The optimization process with MFO is then applied to fine-tune the unknown parameters of the ROLTIS. Through iterative optimization, MFO adjusts these parameters to minimize the error between the step response of CHOLTIS and the desired ROLTIS. This iterative process ensures that the resulting reduced-order system closely approximates the original high-order system. Moreover, to enhance the accuracy of the approximation, a gain adjustment factor is introduced after the optimization process. This factor enables the ROLTIS to match the steady-state response with that of the CHOLTIS. By fine-tuning the gain, the methodology ensures that the reduced-order system maintains consistent behavior with the original system under steady-state conditions. The efficacy of the proposed methodology is validated by applying it to four distinct high-order systems sourced from the literature. These systems encompass various configurations, including those with only real poles, real and imaginary poles, and repeated poles. Through testing on variety of systems, the proposed methodology consistently produces optimal and stable reduced-order systems with the lowest error indices, demonstrating its versatility and reliability across different system types and complexities.