Model Order Reduction using fractional order systems

In this work, a Model Order Reduction (MOR) technique is proposed to reduce the number of parameters required to describe a high dimensional integer system. Motivated by the fact a fractional order model is able to describe a large amount of system dynamics, the order reduction is achieved by expressing a given system as a product of fixed unknown fractional template and unknown minimum order integer subsystem to explain the uncaptured details by the fractional template. To determine the parameters of both subsystems, a fitness function is designed such that it depends on both subsystem parameters in addition to the integer part order as a penalty, contrary to that of the existing techniques where these issues remain a challenge. Fitness optimization is performed using a proposed Variable Dimension Particle Swarm Optimization (VDPSO) to modulate the full order system modes and estimate the relevant ones simultaneously with both unknown subsystems parameters in an efficient way. Moreover, the performance of the proposed technique has shown a significant performance increase in the mean square error sense in both frequency and time domain relative to that of the existing techniques.