## 1 Introduction
The absence of a mechanism to influence one's values and achieve the goals set by the organization, as well as the projection of new goals, is a limitation that must be taken into account. In addition, it is important to mention that this approach does not allow the finding of the optimal value of the system, as is achieved in the state-space technique with the use of Ackermann. The integration of these techniques allows a more precise and effective optimization of the system parameters to achieve the desired objectives. As seen in previous research, recently eigenvectors and eigenvalues have been important concepts in SD, as they are used to analyze and understand the behavior of dynamic systems. In SD, a dynamic system can be represented by a matrix equation [25]. Eigenvalues are matrix values that satisfy Equation (1). \[Av=\lambda v \tag{1}\]  
where \(A\) is the system matrix, \(\lambda\) is the eigenvalue and \(v\) is the corresponding eigenvector. Eigenvalues are used to determine the long-term stability and behavior of the system. If all eigenvalues are negative, the system is stable and tends to converge to a stationary state. If one or more eigenvalues are positive, the system is unstable and may have oscillatory or chaotic behaviors [26]. However, eigenvectors represent the directions in which the system matrix does not change significantly when multiplied by the eigenvector. These vectors are used to analyze the behavior and interactions of different system variables. In short, eigenvectors and eigenvalues are important concepts in system dynamics, as they are used to analyze and understand the behavior of systems dynamics [27; 28]. The approach presented in [29] makes an integration between simulation models and dynamical-system theory, where differential equations are reduced in a time-invariant differential linearized model. By analyzing the stability of the equilibrium points of the simulation model and using [PERSON]'s dynamic-systems technique, the authors analyze different regions of the simulation model and offer a new alternative to sensitivity analysis. This approach represents an interesting alternative to traditional sensitivity analysis or the test-and-error method. On the other hand, the proposed approach has a similar objective, as it will provide a different alternative to conventional sensitivity analysis, in order to perform through optimal control another alternative for simulation models. The research carried out by the authors of [30] proposes a methodology based on control engineering to transform the simulation model of system dynamics into a mathematical model expressed as a system transfer function. Instead of using the differential equations present in the Forrester diagram in the time domain, the Laplace transform is used to represent the system in the frequency domain. Using the conventional approach of control engineering, the block diagram is used to present and reduce the dynamic system, which allows determination of its structure. Each state variable is represented by a transfer function that describes its behavior in response to different system inputs. This methodology represents a breakthrough in the search for accurate mathematical models for simulation models. In this research, we seek to obtain mathematical models using the state space and control technique of Ackermann. With the proposed methodology, we will obtain a desired behavior of the system when determining the optimal values of the parameters. System dynamics and control engineering are two interconnected disciplines used to analyze and model complex systems in different areas of engineering and science. System dynamics focuses on the study of complex and dynamic systems, and how these systems evolve and behave over time. SD through software represents and simulates systems, and is used in areas such as business management, economics, ecology and engineering. On the other hand, control engineering focuses on the design and implementation of control systems to regulate the behavior of dynamic systems.