i SYLLABUS osmania university UNIT - I CHAPTER - 1 : CONTROL SYSTEMS CLASSIFICATION Open Loop and Closed Loop Systems, Mathematical Models and Transfer Functions from Governing Equations of Mechanical, Electrical, Hydraulic, Pneumatic, Thermal Systems, AC, DC Servomotors and Electromechanical Servo Systems. UNIT - II CHAPTER - 2 : BLOCK DIAGRAMS AND SIGNAL FLOW GRAPHS Block Diagrams, Block Diagram Reduction, Signal Flow Graphs, Mason s Gain Formula. CHAPTER - 3 : TIME DOMAIN ANALYSIS Transient Response, Time Domain Specifications of 1 st and 2 nd Order Systems, Steady State Error, Error Coefficients, Sensitivity, Performance Indices. UNIT - III CHAPTER - 4 : STABILITY ANALYSIS AND ROOT LOCUS TECHNIQUE Routh Criteria, Root Locus Method. CHAPTER - 5 : FREQUENCY DOMAIN ANALYSIS Bode, Polar Plots, Correlation Between Transient and Frequency Response, Bandwidth, Experimental Determination of Transfer Functions. UNIT - IV CHAPTER - 6 : NYQUIST CRITERIA Nyquist Criteria, Gain and Phase Margins, Lead-Lag and Lead Lag Compensator Design, PID Controller, Linearization of Non-Linear Systems.
ii UNIT - V CHAPTER - 7 : STATE TE SPACE REPRESENTATION TION OF CONTROL SYSTEMS State-Space Representation of Linear Control Systems, State Transition Matrix, Solution of State Equations, Zero Input Response and Zero State Response, Concept of Controllability and Observability.
control systems theory FOR b.e. (o.u) Iii year Ii semester (MECHANICAL ENGINEERING) CONTENTS iii UNIT - I [CH. H. - 1] ] [CONTROL SYSTEMS CLASSIFICATION]... 1.1-1.108 1.1 INTRODUCTION... 1.2 1.2 DEFINITIONS... 1.2 1.3 BASIC COMPONENTS OF AUTOMA OMATIC CONTROL SYSTEM... 1.2 1.4 CLASSIFICATION OF CONTROL SYSTEMS... 1.4 1.5 OPEN AND CLOSED LOOP SYSTEMS... 1.6 1.5.1 Open Loop Systems... 1.6 1.5.1.1 Advantages and Disadvantages of the Loop Systems... 1.6 1.5.2 Closed Loop Systems... 1.7 1.5.2.1 Advantages and Disadvantages of Closed Loop Systems... 1.7 1.5.3 Comparison Between Open Loop and Closed Loop Systems... 1.8 1.6 EXAMPLES OF CONTROL SYSTEMS... 1.9 1.6.1 Temperature Control System... 1.9 1.6.2 Liquid Level Control System... 1.10 1.6.3 Numerical Control System... 1.10
iv 1.7 MATHEMA THEMATICAL TICAL MODELS AND TRANSFER FUNCTIONS OF CONTROL SYSTEM... 1.12 1.7.1 Steps to Determine the Transfer Function unction... 1.13 1.7.2 Characteristic Equation... 1.13 1.7.3 Poles and Zeros of a Transfer Function unction... 1.14 1.8 MATHEMA THEMATICAL TICAL MODEL OF MECHANICAL SYSTEMS... 1.15 1.8.1 Mechanical Translational Systems... 1.15 1.8.2 Mechanical Rotational Systems... 1.23 1.9 MATHEMA THEMATICAL TICAL MODEL OF ELECTRICAL SYSTEMS... 1.31 1.9.1 Transfer Function of Series RLC Circuit... 1.31 1.9.2 Transfer Function of Parallel RLC Circuit... 1.32 1.10 ELECTRICAL ANALOGOUS OF MECHANICAL TRANSLATIONAL TIONAL SYSTEMS... 1.33 1.10.1 Force orce-voltage oltage Analogy... 1.33 1.10.2 Force-Current Analogy... 1.35 1.10.3 Solved Problems... 1.36 1.11 ELECTRICAL ANALOGOUS OF MECHANICAL ROTATIONAL TIONAL SYSTEMS... 1.42 1.11.1 Torque orque-voltage oltage Analogy... 1.42 1.11.2 Torque orque-current Analogy... 1.44 1.11.3 Solved Problems... 1.46 1.12 MATHEMA THEMATICAL TICAL MODEL OF HYDRAULIC SYSTEMS... 1.48 1.12.1 Liquid Level System... 1.48 1.12.2 Hydraulic Devices... 1.53 1.12.3 Advantages and Disadvantages of Hydraulic Devices... 1.57 1.13 MATHEMA THEMATICAL TICAL MODEL OF PNEUMATIC SYSTEMS... 1.58 1.13.1 Differences Between Hydraulic and Pneumatic Systems... 1.61 1.14 MATHEMA THEMATICAL TICAL MODEL OF THERMAL SYSTEMS... 1.61
v 1.15 AC AND DC SERVOMO OMOTORS ORS... 1.66 1.16 DC SERVOMO OMOTORS ORS... 1.66 1.16.1 Permanent Magnet Motors... 1.67 1.16.2 Electromagnetic Field Motors... 1.68 1.16.2.1 Classification of Electro Magnetic Field Motors... 1.68 1.16.2.2 Advantages and Disadvantages of Electromagnetic Field Motors... 1.69 1.16.2.3 Comparison Between Armature Controlled and Field Controlled DC Servomotors... 1.70 1.16.3 Advantages and Applications of DC Servomotors... 1.70 1.17 AC SERVOMO OMOTORS ORS... 1.71 1.17.1 Transfer Function of AC C Servomotor... 1.73 1.17.2 Advantages and Disadvantages of AC Servomotor... 1.74 1.17.3 Applications of AC Servomotor... 1.74 1.18 COMPARISON BETWEEN DC AND AC C SERVOMO OMOTORS ORS... 1.74 1.19 ELECTROMECHANICAL SERVO SYSTEMS... 1.75 1.19.1 Transfer Function of Armature Controlled DC Motor... 1.75 1.19.2 Transfer Function of Field Controlled DC Motor... 1.78 1.20 SOLVED PROBLEMS... 1.81 Short Questions and Answers... 1.99-1.103 Expected University Questions with Solutions... 1.104-1.106 UNIT - II [CH. - 2] ] [BLOCK DIAGRAMS AND SIGNAL FLOW GRAPHS]... 2.1-2.52 2.1 INTRODUCTION... 2.2 2.2 BLOCK DIAGRAMS... 2.2 2.2.1 Elements of Block Diagram... 2.2 2.2.2 Basic Connections for Blocks... 2.3 2.3 BLOCK DIAGRAM REDUCTION... 2.6 2.3.1 Solved Problems on Block Diagram Reduction... 2.8 2.3.2 Advantages and Disadvantages of Block Diagram Reduction... 2.17
vi 2.4 SIGNAL FLOW GRAPHS... 2.18 2.4.1 Basic Terminology Related to Signal Flow Graph... 2.18 2.4.2 Properties of Signal Flow Graph... 2.19 2.4.3 Signal Flow Graph Algebra... 2.20 2.5 MASON S GAIN FORMULA... 2.21 2.6 COMPARISON OF BLOCK DIAGRAM AND SIGNAL FLOW GRAPH... 2.28 2.7 CONVERSION OF BLOCK DIAGRAM TO SIGNAL FLOW GRAPH... 2.28 2.8 CONVERSION OF SIGNAL FLOW GRAPH TO BLOCK DIAGRAM GRAM... 2.30 2.9 SOLVED PROBLEMS... 2.33 Short Questions and Answers... 2.44-2.47 Expected University Questions with Solutions... 2.48-2.52 UNIT - II [CH.. - 3] ] [TIME DOMAIN ANALYSIS YSIS]... 2.53-2.124 3.1 TIME RESPONSE OF A SYSTEM... 2.54 3.2 STAND ANDARD ARD TEST-SIGNALS SIGNALS... 2.55 3.2.1 Step Signal... 2.55 3.2.2 Ramp Signal... 2.56 3.2.3 Parabolic Signal... 2.56 3.2.4 Impulse Signal... 2.57 3.2.5 Summary of Test est Signals... 2.58 3.3 ORDER OF A SYSTEM... 2.60 3.4 TYPE NUMBER OF A SYSTEM... 2.61 3.5 RESPONSE OF FIRST ORDER SYSTEM... 2.61 3.5.1 Response of First Order System for Unit Step Input... 2.62 3.5.2 Response of First Order System for Unit Ramp Input... 2.64 3.5.3 Response of First Order System for Unit Impulse Input... 2.65
vii 3.6 RESPONSE OF SECOND ORDER SYSTEM... 2.66 3.6.1 Response of Second Order System for Unit Step Input... 2.67 3.6.2 Response of Second Order System for Unit Impulse Input... 2.74 3.7 TIME DOMAIN SPECIFICATIONS... 2.78 3.7.1 Definitions of Time Domain Specifications... 2.79 3.7.2 Expressions for Time Domain Specifications... 2.80 3.8 STEADY STATE TE ERRORS... 2.91 3.8.1 Static Error Co-efficients... 2.92 3.8.2 Steady State Error When Input is Unit Step Signal... 2.93 3.8.3 Steady State Error When Input is Unit Ramp Signal... 2.94 3.8.4 Steady State Error When Input is Unit Parabolic Signal... 2.95 3.8.5 Solved Problems... 2.97 3.8.5 Limitations of Static Error Co-efficients... 2.100 3.9 DYNAMIC OR GENERALIZED ERROR CO-EFFICIENTS... 2.100 3.9.1 Evaluation of Dynamic Error Co-efficients... 2.102 3.9.2 Alternate Method to Determine Dynamic (or) Generalized Error Coefficients... 2.104 3.9.3 Correlation Between Static and Dynamic Error Coefficients... 2.104 3.9.4 Solved Problems... 2.105 3.10 SENSITIVITY... 2.108 3.10.1 Sensitivity of Closed Loop Transfer Function unction... 2.108 3.10.1.1 Sensitivity With Respect to Forward Path ath Elements (G) in Feedback Loop... 2.109 3.10.1.2 Sensitivity With Respect to Feedback Elements (H)... 2.110 3.10.1.3 Sensitivity With Respect to Input Elements (K)... 2.110 3.10.2 Sensitivity of Open Loop Control System... 2.111 3.11 PERFORMANCE INDICES... 2.111 Short Questions and Answers... 2.118-2.121 Expected University Questions with Solutions... 2.122-2.124
viii UNIT - III [CH.. - 4] ] [ST STABILITY ANALYSIS AND ROOT T LOCUS TECHNIQUE].. 3.1-3.62 4.1 INTRODUCTION TO STABILITY ABILITY... 3.2 4.2 STABILITY CRITERION... 3.2 4.2.1 Different Types of Systems Based on Stability... 3.3 4.2.2 Significance of Characteristic Equation in Stability Analysis... 3.4 4.3 ROUTH CRITERIA (OR) ROUTH STABILITY CRITERIA... 3.7 4.3.1 Special Cases of Routh Hurwitz Criterion... 3.10 4.3.1.1 Case 1 (Zero in the First Column)... 3.10 4.3.1.2 Case 2 (All the Elements in any One of the Rows are Zero)... 3.12 4.3.2 Relative Stability Analysis... 3.14 4.3.3 Limitations of Routh Criterion... 3.17 4.3.4 Solved Problems on Routh Criterion... 3.17 4.4 ROOT T LOCUS METHOD... 3.23 4.4.1 Rules for Construction of Root Locus... 3.25 4.4.2 Procedure for Constructing Root Locus... 3.28 4.4.3 Advantages of Root Locus... 3.30 4.4.4 Solved Problems on Root Locus Technique... 3.30 4.4.5 Effect of Adding Poles and Zeros on Root Locus ocus... 3.55 Short Questions and Answers... 3.58-3.60 Expected University Questions with Solutions... 3.61-3.62 UNIT - III [CH.. - 5] ] [FREQUENCY DOMAIN ANALYSIS YSIS]... 3.63-3.144 5.1 INTRODUCTION... 3.64 5.2 ADVANT ANTAGES AND DISADVANT ANTAGES OF FREQUENCY DOMAIN ANALYSIS YSIS... 3.64 5.3 FREQUENCY RESPONSE AND SINUSOIDAL TRANSFER FUNCTION... 3.65
ix 5.4 FREQUENCY DOMAIN SPECIFICATIONS TIONS... 3.66 5.4.1 Definitions of Frequency Domain Specifications... 3.66 5.5 CORRELATION BETWEEN TRANSIENT AND FREQUENCY RESPONSE... 3.68 5.6 FREQUENCY DOMAIN SPECIFICATIONS OF SECOND ORDER SYSTEM... 3.69 5.6.1 Resonant Peak (M r ) and Resonant Frequency (ω r )... 3.69 5.6.2 Band Width (ω b )... 3.71 5.6.3 Phase Margin (γ)... 3.72 5.6.4 Solved Problems... 3.74 5.7 BODE PLOTS TS FOR FREQUENCY RESPONSE... 3.77 5.7.1 Conversion of Multiplication of Magnitudes into Addition... 3.78 5.7.2 Basic Factors of Transfer Function G(jω)... 3.79 5.7.3 Procedure to Draw Bode Plot... 3.92 5.7.4 Gain Margin and Phase Margin in Bode Plot... 3.94 5.7.5 Gain Adjustment in Bode Plot... 3.94 5.7.6 Solved Problems... 3.96 5.8 POLAR PLOTS TS FOR FREQUENCY RESPONSE... 3.112 5.8.1 Starting and End Points of Polar olar-plot -Plot... 3.113 5.8.2 Procedure to Draw Polar Plots... 3.113 5.8.3 Polar Plots of Standard Functions... 3.113 5.8.4 Gain Margin and Phase Margin in Polar Plot... 3.120 5.8.5 Gain Adjustment in Polar Plot... 3.122 5.8.5.1 Determination of K for Specified Gain Margin... 3.122 5.8.5.2 Determination of K for Specified Phase Margin... 3.123 5.8.6 Stability of Polar Plot... 3.123 5.8.7 Solved Problems... 3.124 5.8.8 Advantages and Limitations of Polar Plots... 3.132
x 5.9 EXPERIMENTAL DETERMINATION TION OF TRANSFER FUNCTIONS... 3.133 5.9.1 Determination of Minimum Phase Transfer Function Using Bode Plot... 3.134 Short Questions and Answers... 3.140-3.142 Expected University Questions with Solutions... 3.143-3.144 UNIT - IV [CH. H. - 6] ] [NYQUIST CRITERIA]... 4.1-4.88 6.1 INTRODUCTION... 4.2 6.1.1 Nyquist Stability Criterion... 4.2 6.1.2 Principle of Argument... 4.4 6.1.3 Different Cases for Stability of the System... 4.4 6.1.4 Concept of Encircled and Enclosed... 4.4 6.1.5 Nyquist Contour... 4.5 6.1.6 Procedure to Draw Nyquist Plot... 4.6 6.1.7 Gain Margin and Phase Margin in Nyquist Plot... 4.7 6.1.8 Solved Problems... 4.8 6.2 COMPENSATION TION... 4.25 6.3 TYPES OF COMPENSATORS ORS... 4.27 6.3.1 Lead Compensator... 4.27 6.3.2 Lag Compensator... 4.31 6.3.3 Lag-Lead Compensator... 4.34 6.4 DESIGN OF COMPENSATORS ORS USING BODE PLOT... 4.36 6.4.1 Design of Lead Compensator Using Bode Plot... 4.36 6.4.2 Design of Lag Compensator Using Bode Plot... 4.45 6.4.3 Design of Lag-Lead Compensator Using Bode Plot... 4.53 6.5 CONTROLLER... 4.64
xi 6.6 PROPORTIONAL, PLUS INTEGRAL PLUS DERIVATIVE CONTROLLER (PID CONTROLLER)... 4.67 6.6.1 PID Controller Compensation... 4.68 6.6.1.1 Procedure for Design of PD/PI/PID Controller by Frequency Response Analysis... 4.69 6.6.1.2 Procedure for Design of PD/PI/PID Controller by Root Locus Method (or) Time Response Analysis... 4.74 6.7 LINEARIZATION OF NON LINEAR SYSTEMS... 4.79 6.7.1 Types of Non-Linearities... 4.79 6.7.2 Linearisation... 4.82 Short Questions and Answers... 4.83-4.85 Expected University Questions with Solutions... 4.86-4.88 UNIT - V [CH. - 7] ] [STATE SPACE REPRESENTATION OF CONTROL SYSTEMS]... 5.1-5.42 7.1 INTRODUCTION... 5.2 7.1.1 Advantages of State Space Analysis... 5.2 7.2.2 BASIC TERMS IN STATE TE SPACE CE ANALYSIS... 5.2 7.3 STATE TE SPACE CE REPRESENTATION TION OF LINEAR SYSTEM... 5.5 7.3.1 Procedure for Applying State Space Analysis to Electric Circuits... 5.9 7.4 SOLUTION OF THE STATE TE EQUATIONS TIONS... 5.13 7.4.1 Solution of Non-Homogeneous State Equations (Zero State Response)... 5.13 7.4.2 Solution of Homogeneous State Equation (Zero Input Response)... 5.14 7.5 STATE TE TRANSITION MATRIX... 5.15 7.5.1 Computation of State Transition Matrix... 5.15 7.5.2 Properties of State Transition Matrix... 5.21
xii 7.6 CONCEPT OF CONTROLLABILITY AND OBSERVABILITY... 5.24 7.6.1 Controllability... 5.25 7.6.2 Observability... 5.26 7.6.3 Solved Problems... 5.27 Short Questions and Answers... 5.36-5.40 Expected University Questions with Solutions... 5.41-5.42 PREVIOUS UNIVERSITY QUESTION PAPERS [May - 2013] [New/Main]... QP.1 - QP.3 [May - 2013] [Old/Main]... QP.4 - QP.6 [January - 2013] [Supplementary]...QP QP.7 - QP.10