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LINEAR CONTROL SYSTEM
Chapter-1 basics of control systems
Background
Definitions
Classification of control systems
Open loop system
Advantages
Disadvantages
Real time applications of an open loop system
Sprinkler used to water a lawn
Stepper motor positioning system
Automatic toaster system
Traffic light controller
Automatic door opening and closing system
Closed loop system
Advantages
Disadvantages
Real time applications of closed loop system
Human being
Home heating system
Ship stabilization system
Manual speed control system
D.C motor speed control
Temperature control system
Missile launching system
Voltage stabilizer
Comparison of open loop and closed loop control system
Digital and sampled data control systems
Advantages of digital control
Limitations of digital control
Applications
Sampled data systems
Servomechanisms
Regulating systems
Feedback and feed forward system
Real time application of feed forward system
Requirements of an ideal control system
Review questions
Chapter-2 Basics of Laplace transform
Background
Definition of Laplace transform
Properties of Laplace transform
Linearity
Scaling theorem
Real differentiation
Real integration
Differentiation by s
Complex translation
Real translation
Initial value theorem
Final value theorem
Inverse Laplace transform
Simple and real roots
Multiple roots
Complex conjugate roots
Use of laplace transform in control system
Special case of inverse laplace transform
University examples with solutions
Review questions
Chapter-3 transfer function and impulse response
Background
Concept of transfer function
Transfer function
Definition
Advantages and features of transfer function
Disadvantages
Procedure to determine the transfer function of a control system
Impulse response and transfer function
Some important terminologies related to the T.F
Poles of a transfer function
Characteristics equation of a transfer function
Zeros of a transfer function
Pole-zero plot
Order of a transfer function
Laplace transform of electrical network
Examples with solutions
Review questions
Chapter-4 Mathematical modeling of control systems
What is mathematical model
Analysis of mechanical systems
Translational motion
Mass
Linear spring
Friction
Rotational motion
Equivalent mechanical system
Remarks on nodal method
Gear trains
Gear train with inertia and friction
Belt or chain drives
Leavers
Electrical systems
Analogous systems
Mechanical system
Force voltage analogy
Force current analogy
Steps to solve problems on analogous systems
Models of thermal systems
Heat transfer system
Thermometer
Actuators
Hydraulic actuator
Pneumatic actuator
Comparison between pneumatic and hydraulic systems
Liquid levels systems
Resistance and capacitance
Transfer function of simple liquid level system
Transfer function of liquid level system with interaction
Analog in various systems
Concept of state variable modeling
Concept of state
Definitions
State model
Examples with solutions
University examples with solutions
Review questions
Chapter-5 Block diagram representation
Background
Elements of block diagram
Illustrating concept of block diagram representation
Advantages of block diagram
Simple or canonical form of closed loop system
Derivation of T.F. of simple closed loop system
Rules for block diagram reduction
Critical rules
Converting nonunity feedback to unity feedback
Procedure to solve block diagram reduction problems
Examples with solutions
Analysis of multiple input multiple output systems
Review questions
Chapter-6 Signal flow graph representation
Background
Properties of signal flow graph
Terminology used in signal flow graph
Methods to obtain signal flow graph
From the system equations
From the given block diagram
Mason’s gain formula
Comparison of block diagram and signal flow graph methods
Application of mason’s gain formula to electrical network
Obtaining block diagram from signal flow graph
Examples with solutions
University examples with solutions
Review questions
Chapter-7 Time domain analysis of control systems
Background
Definition and classification of time response
Standard test inputs
Steady state analysis
Derivation of steady state error
Effect of input on steady state error
Effect of change in G h on steady state error
Analysis of TYPE 0,1 AND 2 systems
Disadvantages of static error coefficient method
Generalized error coefficient method
Transient response analysis
Method to determine total output
Analysis of first order system
Unit step response of first order system
Closed loop poles of first order system
Analysis of second order system
Effect of on second order system performance
Derivation of unit step response of a second order system
Transient response specifications
Derivations of time domain specifications
Derivation of peak time T p
Derivation of Mp
Derivation of T,
Derivation of Ts
Examples with solutions
University examples with solutions
Review questions
Chapter-8 Concepts of stability
Background
Concept of stability
Stability of control systems
Zero input and asymptotic stability
Remarks about asymptotic stability
Relative stability
Routh-hurwitz criterion
Necessary conditions
Hurwitz ‘s criterion
Disadvantages of Hurwitz’s method
Routh’s stability criterion
Routh’s criterion
Special cases of routh’s criterion
Special case 1
Special case 2
Procedure to eliminate this difficulty
Importance of an auxiliary equation
Change in criterion of stability in special case 2
Applications of routh’s criterion
Relative stability analysis
Determining range of values of K
Advantages of routh’s criterion
Limitations of routh’s criterion
Marginal k and frequency of sustained oscillations
Examples with solutions
Review questions
Chapter-9 Root locus
Background
Basic concept of root locus
Angle and magnitude condition
Angle condition
Use of angle condition
Magnitude condition
Use of magnitude condition
Graphical method of determining ‘k’
Construction of root locus
Rules for construction of root locus
Graphical determination of ‘k’ for specified damping ratio
General steps to solve the problem on root locus
Effect of addition of open loop poles and zero
Addition of pole
Addition of zeros
Advantages of root locus method
Obtaining G H from characteristics equation
University examples with solutions
Review questions
Chapter -10 Basic of frequency domain analysis
Background
Advantages of frequency domain approach
Limitation of frequency response methods
Conceptual approach to frequency response
Steady state response sinusoidal input
Frequency domain methods
Co-relation between time domain and frequency domain for second
Order system
Derivations of M,and
Comments on co-relations between time domain and frequency domain
B.W
Examples with solutions
Review questions
Chapter-11 Stability analysis using bode plots
Introduction to bode plot
Magnitude plot
The phase angle plot
Logarithmic scales
Standard form of open loop T.F
Bode plots of standard factors of G
Factor 1 system gain ‘k’
Factor 2 poles or zeros at the origin
Factor 3 simple poles or zeros
Factor-4 quadratic factors
Steps to sketch the bode plot
Frequency response specifications
Calculation of G.M. and P.M.from bode plot
What should be values of G.M.and.P.M of a good system
How to improve the G.M.and.P.M
Determination of wgc and P.M.for standard second order system
Calculation of transfer function from magnitude plot
Advantages of bode plots
Examples with solutions
University examples with solutions
Review questions
Chapter -12 Polar and nyquist plots
Background
Polar plot
Wgc and wpc in polar plot
Determination of G.M and P.M. from polar plot
Determining wpc mathematically
Stability determination from polar plot
Nyquist plot analysis
Pole-zero configuration
Encirclement
Counting number of encirclements
Analytic function and singularities
Mapping theorem or principles of argument
Nyquist stability criterion
Generalized nyquist path and its mapping
Steps to solve problems by nyquist criterion
Behavior of right half pole
Advantages of nyquist plot
Magnitude-phase plots
Stability analysis using magnitude-phase plot
Closed loop frequency response
Circles (constant magnitude loci)
Circles (constant phase loci)
Use of M circles
Use of N circles
Nichol ‘s chart
Frequency specifications from the nichol’s chart
Examples with solutions
University examples with solutions
Review questions
Chapter-13 Compensation techniques
Introduction
Types of compensation
Series compensation
Parallel compensation
Series-parallel compensation
Compensating networks
Lead compensator
Maximum lead angle m and
Polar plot of lead compensator
Bode plot of lead compensator
Steps to design lead compensator
Effects of lead compensation
Limitations of lead compensation
Lag compensator
Maximum lag angle and b
Polar plot of lag compensator
Bode plot of lag compensator
Steps to design lag compensator
Effects and limitations of lag compensator
Lag –lead compensator
Polar plot of lag-lead compensator
Effects of lag-lead compensator
Effects of lag-lead compensator
Compensation using root locus
Designing lead compensator using root locus
Designing lag compensator using root locus
Designing lag-lead compensator using root locus
Examples with solutions
Review questions
Chapter-14 control system components
Potentiometer
Potentiometer as an error detector
Types of potentiometers
Characteristics of precision potentiometer
Loading in potentiometers
Synchros
Synchro transmitter
Synchro control transformer
Synchros as an error detector
Tachogenerators
D.C tachometer
Advantages
A.C.tachometer
Advantages
Servomotors
Requirements of good servomotor
Types of servomotors
D.C. servomotor
Field controlled D.C servomotor
Features of field controlled D.C servomotor
Armature controlled D.C servomotor
Features of armature controlled D.C servomotor
Characteristics of D.C servomotors
Applications of D.C servomotor
Transfer function of field controlled D.C motor
Transfer function of armature controlled D.C motor
A.C servomotor
Construction
Rotor
Torque-speed characteristics
Features of A.C servomotor
Applications
Transfer function of A.C servomotor
Comparison of servomotors
Comparison between A.C D.C servomotors
Comparison between armature controlled and field controlled D.C servomotors
Magnetic amplifier
Various control systems used in industry
Generators
Generator driving motor
Position control system
Position control with field controlled motor
Speed control system
Speed control using generator driving motor
Typical position control system used in industry
Examples with solutions
Review with solutions
Review questions
Appendix A controllers
Introduction to P-I-D controllers
PD type of controller
PI type of controller
PID type of controller
Rate feedback compensation