Abstract
A robust computational technique for model order reduction (MOR) of multi-time-scale discrete systems (single input single output (SISO) and multi-input multioutput (MIMO)) is presented in this paper. This work is motivated by the singular perturbation of multi-time-scale systems where some specific dynamics may not have significant influence on the overall system behavior. The new approach is proposed using genetic algorithms (GA) with the advantage of obtaining a reduced order model, maintaining the exact dominant dynamics in the reduced order, and minimizing the steady state error. The reduction process is performed by obtaining an upper triangular transformed matrix of the system state matrix defined in state space representation along with the elements of B, C, and D matrices. The GA computational procedure is based on maximizing the fitness function corresponding to the response deviation between the full and reduced order models. The proposed computational intelligence MOR method is compared to recently published work on MOR techniques where simulation results show the potential and advantages of the new approach.
Highlights
Model order reduction (MOR) of multi-time-scale systems has been an important subject area in control engineering for many years [1, 2]
The reduction process is performed based on transforming the system state matrix while decoupling the multi-time-scale dynamics
The dominant dynamic preservation is performed by retaining the dominant poles of the original system as a subset in the reduced order model utilizing the transformed system state matrix
Summary
Model order reduction (MOR) of multi-time-scale systems has been an important subject area in control engineering for many years [1, 2]. Ponda et al [23] employed a particular swarm optimization technique to obtain a reduced order model of SISO large scale linear systems. Parmar et al [25] presented a technique for model order reduction using GA for SISO linear time systems They have focused on obtaining a reduced order model that maintains stability and retains the steady state value. As motivated by the singular perturbation method which has the characterization of multi-time-scale systems, the GA procedure is performed with the advantages of retaining the exact dominant dynamics in the designed model, obtaining a new robust model with a lower order, and maintaining a minimum steady state response error.
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