Design and Development of an Optimal Control Model in System Dynamics through State-Space Representation

Abstract

Control engineering and state-space representation are valuable tools in the analysis and design of dynamic systems. In this research, a methodology is proposed that uses these approaches to transform a system-dynamics simulation model into a mathematical model. This is achieved by expressing input, output and state variables as input, output and state vectors, respectively, allowing the representation of the model in matrix form. The resulting model is linear and time-invariant, facilitating its analysis and design. Through the use of this methodology, the system transfer matrix is obtained, which allows the analysis and design of the optimal control of the simulation model. The Ackermann gain-control technique is used to determine the optimal control of the system, which results in a shorter settlement time. This research proposal seeks to mathematically strengthen simulation models and provide an analytical alternative through modern control engineering in SD simulation models. This would allow more informed and effective decisions in the implementation of dynamic systems.