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A lot of problems are generated by present-day technology and societal and environmental processes which are highly complex and large in dimension and stochastic by nature. Scientists and engineers have faced the analysis, design, and synthesis of real-time problems. The first step in such studies is the development of a ‘mathematical model’ which can be replaced for the real-time problem. Every physical system can be translated into a mathematical model. The mathematical procedure of system modeling often leads to a comprehensive description of a process in the form of high order differential equations which are difficult to use either for analysis or controller design. It is therefore useful, and sometimes necessary to find the possibility of finding some equations of the same type but of lower order that may be considered to adequately reflect the dominant properties of the high order systems (HOSs). The process of finding the reduced models (RMs) from the original HOSs is known as model order reduction (MOR). MOR is a branch of system and control theory, which reduces the complexity of large-scale dynamic systems while retaining their input-output behaviors. Hence the RMs can be efficiently used for analysis, design automation, and optimization.
The model order reduction techniques (MORTs) for dynamic HOSs have boomed in the field of control system engineering. The mathematical modeling of any physical system may consist of many mathematical equations, including differential equations. The relation between input and output in the frequency domain in the form of the transfer function can be found out by taking Laplace- transform assuming zero initial conditions. Similarly, the state model can also be found in the time domain using state variables. It is worthwhile to note that these models may be very complicated in the term of ‘order’ of the system, which will pose difficulties in understanding the behavior of the system and also not suitable for the controller design. Many classical MORTs (Tiwari & Kaur, 2017)(Choudhary & Nagar, 2019)(Singh et al., 2015)(Vishwakarma & Prasad, 2014)(Kumari & Vishwakarma, 2019b)(Kumari & Vishwakarma, 2019a)(Kumari & Vishwakarma, 2021c)(Kumari & Vishwakarma, 2021b)(Kumari & Vishwakarma, 2021a)(Tiwari & Kaur, 2020)(Arun et al., 2020)(Prajapati & Prasad, 2019c)(Prajapati & Prasad, 2019b)(Prajapati & Prasad, 2019a) are suggested in the last few decades. Still, most of the algorithms are not equally efficient for all types of systems. Although the MORTs guarantee the stability of the RM, sometimes the RM may turn out to be a non-minimum phase. Therefore it is a requirement to use optimization techniques to generate better RM. Many optimized reduction techniques (Hund & Saak, 2018)(Therapos, 1983)(Rozsa & Sinha, 1974) Cuckoo Search (Narwal & Prasad, 2016)(Sikander & Prasad, 2015) BAT Algorithm (Alsmadi & Abo-Hammour, 2015) Genetic algorithm (Kumar et al., 2016) (Soloklo et al., 2014) TLBO algorithm (Singh et al., 2019) Harmony Search (Soloklo & Farsangi, 2013) BCO (Bansal et al., 2011) have been suggested in the frequency domain, but there is slackness in the time domain.
In the present paper, a new algorithm is proposed to solve the problem of reduction and optimization of HOSs in the time domain. The RM is obtained by minimizing the error between the step responses of the original HOSs and RM by the proposed GA optimization technique.
Advantages of the proposed GAs are: