Genetic algorithm approach with frequency selectivity for model order reduction of MIMO systems

Abstract

A novel genetic algorithm (GA) approach with frequency selectivity advantage for model order reduction (MOR) of multi-input-multi-output (MIMO) systems is presented in this article. Motivated by singular perturbation and other reduction techniques, the new MOR method is formulated using GAs, which can be applied to single-input-single-output (SISO)-or MIMO-type systems. The GA procedure is based on maximizing the fitness function corresponding to the response deviation between the full-order model and the reduced-order model with the option of substructure preservation. The proposed GA-MOR method is compared to the well-known reduction techniques, such as the Schur decomposition balanced truncation, proper orthogonal decomposition (POD) and state elimination through balancing-related frequency-weighted realization in addition to other recent methods. Simulation results validate the superiority and robustness of the new MOR technique as it can search the solution space for almost optimal solutions.

Order Reduction based on Coulomb’s and Franklin’s laws Algorithm

“…by proposed CFLA method and recent published article given in [1,20,21,21]. It is evident from the Table 3 that ISE value obtained using the proposed CFLA method is 5.4196 × 10 −4 which is very much lower than the reduced order system obtained by MCS algorithm [1].…”

Firefly artificial intelligence technique for model order reduction with substructure preservation

“…For the purpose of analysis and design, physical systems are mathematically modeled. The main objective of such analysis and design is for controlling the process and or enhancing its performance (Alsmadi et al, 2011a, 2011b, 2016; Antoulas et al, 2001; Yadav et el., 2012). For some practical systems, mathematical modeling using higher order differential equations yields complex large order multi-time scale systems.…”

A Robust Computational Technique for Model Order Reduction of Two-Time-Scale Discrete Systems via Genetic Algorithms

“…The objective of simplification is to obtain a low order model of the existing high order model such that both are equivalent in terms of system response and being close to each other in some physical representation means. Model reduction problems have attracted much attention in recent years; for example, the model reduction problem has been investigated using artificial neural networks [ 3 ], genetic algorithms [ 4 ], and invasive weed optimization [ 5 ]. It was also used in nonlinear systems [ 6 ], gain scheduling [ 7 ], linear time-varying systems [ 8 , 9 ], and linear parameter-varying systems [ 10 ].…”

“…To obtain a model of lower order, a significant number of methods have been proposed in recent and earlier years, some for continuous time systems [ 3 – 5 ] and some for discrete-time systems [ 1 , 11 – 15 ]. Some methods, such as model order reduction by matching Markov parameters [ 16 ], were introduced to ensure stability of the reduced order model.…”

“…A popular technique for obtaining reduced order models is the Krylov subspace [ 17 ]; however, stability of the reduced model is not guaranteed. Another important group of reduction algorithm is the eigenvalue preservation technique [ 3 – 5 , 11 ] where important eigenvalues of the system are retained to find suitable lower order models.…”