# MODELAGEM DE PROTÓTIPOS PARA SISTEMAS REAIS

## Palavras-chave:

modeling, state space, coupled tanks## Resumo

Models represent physical phenomena mathematically. Through it, it’s possible to obtain

mathematical expressions that describe the behaviour of the real system, allowing, for example, to simu-

late its evolution in time as a response to some input stimulus without actually operating the real system.

They also allow the creation of control laws that are mathematically correct and adequate to the system,

allowing the development of formally correct and performant controllers. In this study, a system of cou-

pled tanks, present in CEFET Campus V’s Signals and System Analysis laboratory, was modelled in 6

different configurations. The system is composed of 4 water tanks, two on the top shelf and two on the

bottom, with valves that allow the water to flow to its sibling or the one directly below it. The valves

allow the user to chose how the water will flow through them. We developed a model for each configura-

tion using physical laws of water flow in cylindrical recipients and estimated the values of the constants

through tests. The models are represented using state-space, as it allows to identify the dynamics of

the system internal energy, as well as the use of modern control techniques. Each model was validated

against the real system to measure its correctness. The models obtained are available for students of the

laboratory, both undergraduate and postgraduate, to streamline the study of system analysis and control

theory.