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Note for Control System Engineering - CSE By Divyansh Das

  • Control System Engineering - CSE
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CONTROL SYSTEM ENGINEERING

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Module ‐1.............................................................................................................................................. 4  Basic Concepts of Control Systems, Open loop and closed loop systems ........................................ 4  Open‐loop systems:....................................................................................................................... 4  Closed‐loop systems ...................................................................................................................... 4   Transfer Function........................................................................................................................... 6  Differential Equations of Physical Systems: Mechanical, Translational Systems ............................. 7  Rotational systems, Gear Trains, Electrical Systems....................................................................... 10  Derivation of Transfer functions, Block Diagram Algebra............................................................... 16  Signal flow Graphs, Mason’s Gain Formula. ................................................................................... 25  Feedback characteristics of Control Systems: Effect of negative feedback on sensitivity. ............ 27  Bandwidths, Disturbance, linearizing effect of feedback, Regenerative feedback ........................ 28  A.C. Tachometer, Synchro, Stepper Motors. .................................................................................. 31   Module ‐2............................................................................................................................................ 42  Time response Analysis: Standard Test Signals............................................................................... 42   Time response of first order systems to unit step and unit ramp inputs ....................................... 45  Time Response of Second order systems to unit step input .......................................................... 46  Time Response specifications, Steady State Errors. ....................................................................... 49  Static Error Constants of different types of systems. Generalized error series and generalized  error coefficients............................................................................................................................. 50  Stability and Algebraic Criteria, concept of stability, Necessary conditions of stability................. 51  Hurwitz stability criterion, Routh stability criterion, Application of the Routh stability. ............... 53  Root locus Technique: Root locus concepts, Rules of Construction of Root locus......................... 56  Systems with transportation lag, Phase‐Lead Compensation, phase‐Lag Compensation.............. 58  Phase‐Lag –Lead Compensation, Feedback Compensation............................................................ 61  Module ‐3............................................................................................................................................ 63  Frequency Response Analysis: Frequency domain specifications .................................................. 63  Procedure for drawing the bode plots. Determination of Gain Margin and Phase Margin from  Bode plot ......................................................................................................................................... 72 

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1. Introduction to Control Systems: Basic elements of control system • Open loop and closed loop systems • Tracking System, Regulators • Differential equation • Transfer function 2. Modeling of electric systems: Translational and rotational mechanical systems • Block diagram reduction techniques. • Signal flow graph, Mason’s Gain Formula. 3. Feedback  characteristics  of  Control  Systems:  Effect  of  negative  feedback  on sensitivity. • Bandwidth, Disturbance. • Linearizing effect of feedback, Regenerative feedback. 4. Control Components: D.C. Servomotors, A.C. Servomotors. • A.C. Tachometer. • Synchros, Stepper Motors. Module‐II 5. Time response Analysis: Standard Test Signals • Time  response  of  first  order  systems  to  unit  step  and  unit ramp inputs. • Time Response of Second order systems to unit step input. • Time Response specifications, Steady State Errors. • Generalised error series and Gensalised error coefficients. 6. Stability Theory: Stability and Algebraic Criteria • Concept of stability, Necessary conditions of stability. • Hurwitz stability criterion, Routh stability criterion. • Application  of  the  Routh  stability  criterion  to  linear feedback system. • Relative stability by shifting the origin in s‐plane. 7. Root locus Technique: Root locus concepts, Rules of Construction of Root locus • Determination of Roots from Root locus for a specified open loop gain. • Effect of adding open loop poles and zeros on Root locus. • Root contours. 8. Compensation Technique: Systems with transportation lag. • Lead compensation. • Lag compensation • Lead-Lag compensation Module‐III 9. Frequency Response Analysis: Frequency domain specifications • Correlation  between  Time  and  Frequency  Response  with

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10. Stability in frequency domain: Principle of argument, Nyquist stability criterion. • Application of  Nyquist  stability criterion  for  linear  feedback  system. • Constant Mcircles. • Constant N‐Circles. • Nichol’s chart. 11. Controllers: Concept of Proportional, Derivative and Integral Control actions. • P, PD, PI, PID controllers. • Zeigler‐Nichols method of tuning PID controllers.

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