Control Engineering

Fundamentals

Jing Sun

• Publisher: De Gruyter
• Year: 2018
• ISBN:
  9783110573367
• Edition: 1
• Topic: Sciences physiques
• Subtopic: Mécanique

The book introduces the fundamentals (principle, structure, characteristics, classification etc.) of control systems. The dynamic behavior are also illustrated in detail. The authors also present the time/ frequency/stability/error response analyses of control system. This book is an essential reference for graduate students, scientists and practitioner in the research fields of mechanical and electrical engineering.

1Introduction

Fundamentals of control engineering is a part of cybernetics. Cybernetics is a branch of science that focuses on the control relationships and regulation rules among different organisms, machines, and systems. Cybernetics is not only an important branch of science, but also a remarkable methodology.

Engineering cybernetics is accompanied by the combination of cybernetics and practical engineering problems. The basis of engineering cybernetics was introduced in the book, Engineering Cybernetics, by Xuesen Qian in 1954. In this outstanding work, the concept of engineering cybernetics was put forward for the first time and cybernetics was generalized in the field of engineering.

In fundamentals of control engineering, also known as fundamentals of control theory, we are concerned with some fundamental theories of automatically controlled technology. In fact, fundamentals of control engineering is a part of engineering cybernetics and belongs to the field of classical control theory.

So, in general, this book focuses on introducing the principles and methods in the field of classical control theory. In particular, the emphasis is on dynamics and controls of mechanical engineering systems. In addition, the importance of understanding and being able to determine the dynamic response of physics systems is the main purpose of the book.

1.1System and System Analysis

Because the most frequently used keyword in this book is “system”, we should define it at the onset. A system is a collection of interacting elements for which there are cause-and-effect relationships among the variables. This definition is certainly general, because it must encompass a broad range of systems. The most important feature of the definition is that interactions among the variables, rather than individual elements, should be taken into account in system modeling and analysis. So, a system is a combination of components or elements and is constructed to achieve an objective or multiple objectives.

Our study concentrates on dynamic systems, where the variables are time dependent. In most of our examples, not only will the excitations and responses vary with time, but also at any instant the derivatives of one or more variables will depend on the values of the system variables at that instant. The system’s response will normally depend on initial conditions, such as stored energy, in addition to any external excitations.

In the process of analyzing a system, two tasks must be performed: modeling the system and solving for the model’s response. The combination of these two steps is referred to as system analysis.

1.2Modeling the System

A mathematical model, or model for short, is a description of a system in terms of equations. The physical laws are the basis for constructing a model of a system (such as the conservation of energy and Newton’s laws), which the system elements and their interconnections need to obey.

The type of model sought depends on both the objective of the engineer and the tools for analysis. If a pencil-and-paper analysis with parameters expressed in literal rather than numerical form is to be performed, a relatively simple model will be needed. To achieve this simplicity, the engineer should neglect elements that do not play a dominant role in the system.

On the other hand, if a computer is available for carrying out simulations of specific cases with parameters expressed in numerical form, a comprehensive mathematical model that includes descriptions of both primary and secondary effects might be appropriate. In short, a number of mathematical models are possible for a system, and the engineer must decide which form and complexity are most consistent with the objectives and the available resources.

The most common example of a dynamic system is the automobile. To limit the complexity of any model, some of the system’s features must be omitted. In fact, many of the parameters may be relatively unimportant for the objective of a particular study. Among many possible concerns are the ease of handling on the straightaway or while turning around a corner, comfort of the driver, fuel efficiency, stopping ability, crash resistance, the effects of wind gusts, potholes, and other obstacles.

Suppose that we limit our concern to focus on the driver when the vehicle is traveling on a rough road. Some of the key characteristics of the system are represented in Fig. 1.1(a) by masses, springs, and shock absorbers. The chassis has by far the largest mass, but other masses that may be significant are the front axles, rear axles, wheels, and driver. Suspension systems between the chassis and the axles are designed to minimize the vertical motion of the chassis when the tires undergo a sudden change in motion because of the road surface. The tires themselves have some elasticity, which is represented in Fig. 1.1(a) by additional springs between the wheels and the road. The driver is slightly cushioned from the chassis motion due to the characteristics of the seat, and there is also some friction between the driver and the seat-back.

Fig. 1.1 is adapted from a drawing in Chapter 42 of The Shock and Vibration Handbook, third edition (1988), edited by Cyril M. Harris. It is used with the permission of the publisher, McGraw-Hill, Inc. Fig. 1.1a also appears in the fourth edition (1996) of that book.

Let us assume that the vehicle is traveling at a constant speed and that the horizontal motion of the chassis does not concern us. We must certainly allow for the vertical motion caused by the uneven road surface. We may also consider the pitching effect when the front tires hit a bump or depression, causing the front of the chassis to move up or down before the rear. This would require us to consider not only the vertical motion of the chassis but also rotation about its center of mass.

Fig. 1.1: The representation for automobile: (a) a representation of an automobile and (b) a simplified representation.

The complexity of a system model is sometimes measured by the number of independent energy-storing elements. As in Fig. 1.1(a), energy can be stored in four different masses and in five different springs. If the pitching effect is ignored, the analysis might be simplified by combining the front and rear axles into a single mass, as shown in Fig. 1.1(b), which has only three masses and three springs.

In the initial phase of the analysis, other simplifying assumptions might be made. Perhaps some of the elements remaining in Fig. 1.1(b) could be omitted. Possibly a mathematical description of the individual elements that is simpler than that required for the final analysis would be used.

On the other hand, for a more thorough study of the effect of a bumpy road on the driver, it might be necessary to add other characteristics to those represented in Fig. 1.1(a).When one of the two wheels on the front axle encounters a bump or depression, the displacement and forces on it are different from those on its mate. Thus, we might want to consider each of the four wheels as a separate mass and to allow for side-to-side rotation of the chassis, in addition to the vertical and pitching motions.

When devising models at various stages in the design process, engineers usually give considerable thought to how detailed the representation of the system’s characteristics should be. Many of the remarks we have made about the automobile can be extended to airplanes, boats, rockets, motorcycles, and other vehicles. In the following chapters, we shall show how to describe important characteristics by sets of equations.

1.3Solving the Model

The process of using a mathematical model to determine certain features of the system’s cause-and-effect relationships is referred to as solving the model. For example, the responses to specific excitations may be desired for a...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• Contents
• 1 Introduction
• 2 Laplace Transform Solution
• 3 Formulation and Dynamic Behavior of Translational Mechanical Systems
• 4 Formulation and Dynamic Behavior of Electrical Systems
• 5 Fundamentals of Control Systems
• 6 Time Response Analysis of Control Systems
• 7 Frequency Response Analysis of Control Systems
• 8 Stability Analysis of Control Systems
• 9 Error Analysis and Calculation of Control Systems
• References
• Index