Riazollah Firoozian - Servo Motors and Industrial Control Theory

Servo Motors and Industrial Control Theory — read online for free the complete book (whole text) full work

Below is the text of the book, divided by pages. System saving the place of the last page read, allows you to conveniently read the book "Servo Motors and Industrial Control Theory" online for free, without having to search again every time where you left off. Put a bookmark, and you can go to the page where you finished reading at any time.

Light

Font size:

↓

↑

Georgia Tahoma Arial Verdana

Reset

Interval:

↓

↑

Bookmark:

Make

1234567...63

Riazollah Firoozian Mechanical Engineering Series Servo Motors and Industrial Control Theory 10.1007/978-0-387-85460-1_1 Springer Science+Business Media, LLC 2009

1. Feedback Control Theory

Riazollah Firoozian 1

(1)

Firoozian Electronics and Electro-Technique Co, Tehran, Iran

Riazollah Firoozian

Email:

In any system, if there exists a linear relationship between two variables, then it is said that it is a linear system.

Linear System

In any system, if there exists a linear relationship between two variables, then it is said that it is a linear system.

For example, the equation

(1.1)

represents a linear system. It means that if K is constant then the relationship (1.1) represents a linear relationship between two variables y and x. In general, any governing differential equations between two variables x and y in the form of

(1.2)

is linear, where n and m represent the order of differential equations, and a n , b m are constants. For real system n>m, any other form of equations that is not similar to equation () is called nonlinear system.

There are extensive theories that deal with linear systems, but the theories on nonlinear systems are very complex and little.

Example 1

The circuit diagram of equivalent DC servo motors is shown in Fig..

Fig. 1.1

Equivalent circuit diagram of a DC servo motor

The governing differential equation may be written as

(1.2)

where V i , I , m are the input voltage, current, and angular speed. R and L are the resistance and inductance, respectively. This represents a linear system, where m is the output variable and V i represents the input voltage.

For DC servo motor, we can write

(1.3)

(1.4)

where K i , J are the torque constant and rotor moment of inertia.

Eliminating T , from equations () yields

(1.5)

Equation (), we ignore the external torque acting on the motor. If we consider the external torque, the governing differential equation would have two input variables and one output variable.

For linear systems, the principle of superposition holds. It means that if input x1 causes output y1 and input x2 causes output y2, then input x1+x2 causes output y1+y2. This is a powerful principle, and we will use it throughout this book.

Nonlinear Systems

There are different kinds of nonlinearities. For example, onoff control systems are inherently nonlinear. Transport lag, saturation, and transport lag are other kinds of nonlinearities. These kinds of nonlinearities cannot be solved with linear control theory. This is shown in Fig..

Fig. 1.2

Some discontinuous nonlinearities

For linearized equation, it is better to use Laplace Transform. In this way, the differential equations become algebraic equation in s . Throughout this book, the lower case s represents Laplace Transform.

Some nonlinearity is continuous, and they can be solved by the linearization technique. One example of this kind of nonlinearity is

(1.6)

This is shown in Fig.

Fig. 1.3

A continuous nonlinearity

Linearization Technique

If there is a continuous nonlinearity in the form of

(1.7)

Assuming small perturbation from the equilibrium point, equation () can be linearized as

(1.8)

or it can be written as

(1.9)

In equations () can be written as

(1.10)

where

(1.11)

K is constant at an operating point. Throughout this book, the lower case variable represents small perturbation from equilibrium point. This is shown in Fig..

Equation () represents one variable system. For a multivariable system, similar linearized equation can be obtained.

The solution of the governing equation simplifies if Laplace Transform is used.

Laplace Transform

By the definition, the Laplace Transform is defined as

(1.12)

By taking the Laplace Transform, the variable t is eliminated and the result is only function of s .

Equation () appears to be very complicated, and indeed for complicated transformation, the integral becomes very complex. Fortunately, for control systems only a few functions are needed.

Example 2

Constant A.

(1.13)

This is a simple integration, and the integral becomes

(1.14)

Next page

1234567...63

Light

Font size:

↓

↑

Georgia Tahoma Arial Verdana

Reset

Interval:

↓

↑

Bookmark:

Make

Similar books «Servo Motors and Industrial Control Theory»

Look at similar books to Servo Motors and Industrial Control Theory. We have selected literature similar in name and meaning in the hope of providing readers with more options to find new, interesting, not yet read works.

F. E. Powell

Windmills and Wind Motors: How to Build and Run Them

Danny Staple

Learn Robotics Programming: Build and Control Autonomous Robots Using Raspberry Pi 3 and Python

Mohammed Fazlur Rahman

Modeling, Simulation and Control of Electrical Drives

K Ambika Parameswari

Arduino IR Remote Control, LED Scroll Bar, Digital Clock with Alarm, ATmega328 Chip, Servo Motor Control etc,...

Austin Hughes

Electric Motors and Drives: Fundamentals, Types and Applications

Farrokh Sassani

Industrial Engineering Foundations: Bridging the Gap Between Engineering and Management

Alfred P. Sloan Jr.

My years with General Motors

Christopher Rush

Programming the Intel Galileo: Getting Started with the Arduino -Compatible Development Board

Fouad Giri

AC Electric Motors Control. Advanced Design Techniques and Applications

Mark A. Yoder

BeagleBone Cookbook: Software and Hardware Problems and Solutions

Eric D. Knapp

Industrial Network Security: Securing Critical Infrastructure Networks for Smart Grid, SCADA, and Other Industrial Control Systems

Don Wilcher

Learn Electronics with Arduino

Discussion, reviews of the book Servo Motors and Industrial Control Theory and just readers' own opinions. Leave your comments, write what you think about the work, its meaning or the main characters. Specify what exactly you liked and what you didn't like, and why you think so.