Dominant-Dynamics-Based Reduced Order Modeling Using Genetic Algorithm ADNAN M. AL-SMADI 1 , OTHMAN M. AL-SMADI 2 , AND MAIS W. MARJI 1 Yarmouk University 1 , Hijjawi Faculty for Engineering Technology, Irbid, Jordan University of Jordan 2 , Department of Electrical Engineering, Amman, Jordan Smadi98@yahoo.com Abstract: - Model Order Reduction (MOR) plays a very essential role in reducing the complexity of the models, such as communication systems, transmission lines and most physical systems that impose major difficulties in analysis, simulation and control designs. MOR was developed in control theory areas that study the performance of dynamical systems in order to reduce their complexity. The objective of this paper is to obtain reduced model that is approximated to the original complex high order model with optimal solution and less complexity and with maintaining the same behavior of the original model. This is done using Genetic Algorithm (GA). MATLAB software will be utilized for simulations and testing the achieved results. Key-Words: - Model Order Reduction; Genetic Algorithm; Eigenvalues; Transfer Function. 1 Introduction Modeling of linear dynamical systems is encountered in many fields including financial markets, environmental sciences, control engineering, and many other fields. Mathematically modeling for a real system in the area of Engineering, a high order model of the system under consideration is obtained from theoretical concepts. The primary goal of modeling of physical and real- life problems is for the purpose either controlling the process or performing future forecasts. The modeling process can be achieved depending on the complete understanding of the physical process that leads to the derivation of the governing differential equations describing the process. In this case, the model might be fully known in terms of the order and the parameters or might be partially known where some or all of the parameters are unknown [1]. In 1966, Model Order Reduction (MOR) started when Davison [8][9] presented “The Model Analysis” approach using state space techniques. Then several modifications had offered to Davison’s approach by Chidambara [10][12]. Later on, Chen and Shieh [13] started to add their imprints using frequency domain expansions. Gibilaro and Lees [14] matched the moments of the impulse response. Then, Hutton and Friedland [15] used the Routh approach for high frequency approximation that was modified by Langholz and Feinmesser [16]. Later on, Pinguet [17] showed that all those methods have state space reformulations. The classical approach to model order reduction dealt only with eigenvalues[17]. However, Moore [18] presented a revolutionary way of looking at model reduction by showing that the ideal platform to work from is that when all states are as controllable as they are observable. This gave birth to “Balanced Model Reduction”, that the concept of dominance is no longer associated with eigenvalues, but rather with the degree of observability and controllability of a given state. El-Attar and Vidyasagar [19] presented new procedures for model order reduction based on interpreting the system impulse response (transfer function) as an input-output map. Hakvoort [20] noted that in L1 robust control design and model uncertainty can be handled if an upper-bound on the L1 Norm of the model error is known. Hakvoort presented a new L1 Norm optimal reduction approach resulting in a nominal model with minimal upper-bound on the L1 Norm of the error [20]. MOR has been an active research area in design automation over the past two decades. In recent years, MOR has come to be viewed as a method for generating compact models from all sorts of physical systems modeling tools [2][5]. For example, in integrated Circuits (ICs), where increasing package density forces developers to include side effects. Knowing that these devices are often modeled by very large RLC circuits, this would be too demanding computationally and practically due to the detailed modeling of the original system [8]. In control system, in order to obtain an acceptable model of the physical system, a designer does not usually consider all the dynamics of the system [6–10]. The MOR problem has been A. M. Al-Smadi et al. International Journal of Control Systems and Robotics http://www.iaras.org/iaras/journals/ijcsr ISSN: 2367-8917 96 Volume 1, 2016