Independence work Theme : Modeling of control systems Plan: Introduction Main Part

Independence work

Theme : Modeling of control systems

Plan:

Introduction

Main Part

1 Modeling Concepts

2 Control Systems

3 Modeling of the Idle Speed System

Conclusion

References

Introduction

In studying control systems the reader must be able to model dynamical systems in mathe‐ matical terms and analyze their dynamic characteristics. This section provides an introduction to basic concepts and methodologies on modeling control systems. It also introduces some fundamentals to solve realistic models used basically in mechanical, electrical, thermal, economic, biological, and so on. A mathematical model is composed by a set of equations that describe a real system accurately, or at least fairly well. However a mathematical model is not unique for a given system, and the system under study can be represented in many different ways, in the same way a mathematical model can be used to represent different systems. Algorithms used to solve the set of equations that represent a control system require a great amount of programming instructions. Matlab is a tool that simplifies and accelerates such algorithms allowing to modeling a great variety of control systems in a very elegant way [1]. There are special Matlab toolbox useful to solve different control systems, in particular Control System Toolbox (included in MATLAB Version 7.8.0.347 (R2009a)): Creating linear models, data extraction, time-domain analysis, frequency-domain analysis, state space models, etc. Some of these are used throughout the chapter to facilitate algorithm development. A physical system is a system in which physical objects are connected to perform an objective. We cannot represent any physical system in its real form. Therefore, we have to make assumptions for analysis and synthesis of systems. An idealized physical system is called a physical model. A physical system can be modeled in different ways depending upon the problem and required accuracy with which we have to deal. A model is a precise representation of a system’s dynamics used to answer questions via analysis and simulation. The model we choose depends on the questions that we wish to answer, and so there may be multiple models for a single physical system, with different levels of fidelity depending on the phenomena of interest. In this chapter we provide an introduction to the concept of modeling, and provide some basic material on two specific methods that are commonly used in feedback and control systems: differential equations and difference equations. The ideas of dynamics and state have had a profound influence on philosophy where they inspired the idea of predestination. If the state of a natural system is known at some time, its future development is completely. As the development of dynamics continued in the 20th century, it was discovered that there are simple dynamical systems that are extremely sensitive to initial conditions, small perturbations may lead to drastic changes in the behavior of the system. The behavior of the system could also be extremely complicated. The emergence of chaos also resolved the problem of determinism: even if the solution is uniquely determined by the initial conditions, in practice it can be impossible to make predictions because of the sensitivity of these initial conditions.