Engineering

## Control Systems

This textbook is designed for an undergraduate course in control system for the engineering students in the Indian universities. It is very suitable for self-study. It will also help the practical engineers to enhance their knowledge on this subject. The authors have made sincere attempts to explain the basic principle of control system, and provide detailed explanation including stepwise methods to make it easy for students to understand and cope with the complicated derivations. Most of the examples are given to clearly understand the theoretical topic. Step wise methods are incorporated to sketch the complicated graphs, plots and diagrams.
• Publisher: Laxmi Publications
• Language: English
• ISBN : 978-93-86035-55-4
Total Price: 0
• Chapter 1

• Chapter 2

### Preface

This document contains preface.

• Chapter 3

### Chapter 1 - Concept of Control System Price 0.11  |  0.11 Rewards Points

To understand the meaning of the word control system, one has to define, first the word ‘system’. The system comprises of a number of functional elements or different physical components which are combined in a sequence to perform a specific function. Whenever the output quantity is controlled by varying the input quantity then the system is called control system.

• Chapter 4

### Chapter 2 - Mathematical Models Price 0.11  |  0.11 Rewards Points

Mathematical modeling infact, belongs to or interacts with the real world. Mathematical models are developed to describe relationship between different quantities of different engineering systems. The term modeling refers to the derivation of appropriate equations that are solved for a set or system of process variables and parameters. Process model extracts information from the system. True representation of a physical system is called model and in mathematical modeling system is defined by a set of equations.

• Chapter 5

### Chapter 3 - Control System and Components Price 0.11  |  0.11 Rewards Points

As explained earlier, a control system is an interconnection of physical elements arranged in a planned manner. A closed loop control system can be represented by the block diagram. It consists of error detector, controller, plant and feedback path element.

• Chapter 6

### Chapter 4 - Block Diagram Representation Price 0.11  |  0.11 Rewards Points

Block diagram is a pictorial representation of the given system. It is very simple way of representing the given complicated practical system. To draw the block diagram of a particular system, each element of practical system is represented by a block. The block is called functional block. It means, block explains mathematical operation on the input by the element to produce the corresponding output. The actual mathematical function is indicated by inserting corresponding transfer function of the element inside the block. The connection between the blocks is shown by lines called branches of the block diagram. The signal can travel along the direction of an arrow only. It cannot pass against the direction of an arrow. Hence block diagram is an unilateral property of the system.

• Chapter 7

### Chapter 5 - Time Response Analysis Design Specification Price 0.11  |  0.11 Rewards Points

Most of the control systems, use time as an independent variable, it is usually of interest to evaluate the state and output responses with respect to time or simply the time response. It is denoted by c(t). The time response can be obtained by solving the differential equation governing the system. Alternatively, the response c(t) can be obtained from the transfer function of the system and the input to the system. As the input to a control system cannot be assessed before hand, therefore, an input test signal is specified for ascertaining comparative time performance of a control system.

• Chapter 8

### Chapter 6 - Stability Analysis in S Domain Price 0.11  |  0.11 Rewards Points

Stability in a system implies that small changes in the system input, in initial condition or in system parameters, do not result in large changes in system output. Stability is a very important characteristics of the transient performance of a system. Almost every working system is designed to be stable. Within the boundaries of parameter variations permitted by stability considrations, we can then seek to improve the system performance.

• Chapter 9

### Chapter 7 - Root Locus Technique Price 0.11  |  0.11 Rewards Points

In the previous chapter we have seen that the stability of any closed loop system depends on the locations of the roots of the characteristics equation. Root locus analysis is a graphical method for examining how the roots of a system change with variation of a certain system parameter, commonly a gain within a feedback system. This is the technique used in the field of control system developed by Walter R. Evans in 1948, which can determine stability of the system. The root locus plots the poles of the closed loop transfer function as a function of gain parameter, which is to be varied from zero to infinity.

• Chapter 10

### Chapter 8 - Applying Frequency Response Price 0.11  |  0.11 Rewards Points

The frequency response is the steady state response (output) of a system when the input to the system is a sinusoidal signal. At the steady-state, one should except to see that the output is also sinusoidal in nature.

• Chapter 11

### Chapter 9 - Stability Analysis in Frequency Domain Price 0.11  |  0.11 Rewards Points

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction. The fixed point (analogous to the origin of a Cartesian system) is called the pole, and the ray from the pole in the fixed direction is the polar axis. The distance from the pole is called the radial coordinate or radius, and the angle is the angular coordinate, polar angle or azimuth.

• Chapter 12

### Chapter 10 - Classical Control Design Technique Price 0.11  |  0.11 Rewards Points

The design of automatic control systems is perhaps the most important function that the control engineer carries out. All the control systems are designed to achieve specific application have to meet certain performance specifications. A good control system has less error, good accuracy, good speed of response, small peak overshoot, less settling time, sufficient gain margin, sufficient phase margin, least steady– state error, good relative stability, etc. For satisfactory performance of the system gain is adjusted first. It may be possible to meet the given specifications on performance of simple control systems.

• Chapter 13

### Chapter 11 - State Space Analysis Price 0.11  |  0.11 Rewards Points

Analysis and design of feedback control systems are usually carried out by either of two approaches. The first approach is the frequency domain technique (or classical approach) in which the differential equation representing the mathematical model of the system is converted to transfer function. The algebraic equation in terms of s simplifies modelling interconnected subsystems. The transfer function model provides us with simple and powerful analysis and design techniques. This technique yields stability and transient response information. However it suffers from the major disadvantage that it is applied only to linear time invariant systems which are again restricted to single input single output (SISO) system. It may be noted that other classical design methods such as root locus method are essentially trial and error procedures which are difficult is visualize even in moderately complex systems.

• Chapter 14

### Chapter 12 - Non - Linear Systems Price 0.11  |  0.11 Rewards Points

We have, so far discussed and analysed linear time invariant systems we have seen that many control systems when subjected to linear control theory have yielded good results. In practice, systems are found to be non-linear in nature. In fact, many practical systems are sufficiently non-linear and analysis and design of these systems through linear techniques may obscure the important features of their performances. Hence such systems call for the applications of special analytical, graphical and numerical techniques.

• Chapter 15

### Appendix 1

This document contains appendix.

• Chapter 16

### Appendix 2

This document contains appendix.

• Chapter 17

### Bibliography

This document contains bibliography.

• Chapter 18

### Index

This document contains index.