# CHAPTER 1 Basic Concepts of Control System. CHAPTER 6 Hydraulic Control System

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1 CHAPTER 1 Basic Concepts of Control System 1. What is open loop control systems and closed loop control systems? Compare open loop control system with closed loop control system. Write down major advantages and disadvantages of open loop control systems. 2. Write Requirements of a good control system. Is an automatic electric iron an open loop or closed loop control system? 3. Explain concept of superposition for linear system with examples. CHAPTER 6 Hydraulic Control System 1. Compare hydraulic and pneumatic control system. State the different applications of pneumatic control system. 2. Write short note on Dashpots. 3. Attempt : (i) Essential elements of hydraulic circuit and (ii) Working of Directional Control Valve 4. State the various components of any hydraulic circuits. Name the various types of pumps commonly used for hydraulic power purposes. 5. State the different types of hydraulic pumps and explain the factors affecting selection it. Explain the construction and working of vane pump with neat sketch. 6. Describe proportional plus integral plus derivative (PID) control action type automatic industrial controller. Write down equation of the system. Write down expression for the transfer function. 7. Compare hydraulic and electrical control system. CHAPTER 7 Pneumatic Control System 1. Sketch and explain pneumatic nozzle-flapper amplifier. 2. State the various types of Industrial controllers and describe any two of them. 3. Explain the construction and working of 4 land rotary spool valve with neat sketches. 4. What is FRL unit in pneumatic system? Write about pneumatic power sources. State various components used in pneumatic circuit. 5. Describe the working of a force distance type pneumatic proportional controller and its transfer function. Control Engineering ( ) Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1

2 Chapter 2 Mathematical modelling of systems 1 What do you mean by mathematical modeling of a control system? Explain its importance. Given as part of Tutorial 2 2 Derive transfer function of Armature controlled DC motor. Tutorial 2 3 Derive transfer function of field controlled DC motor. Tutorial 2 4 Derive transfer function of Gear train. Tutorial 3 5 Derive a transfer function for a liquid level system. Explain resistance and capacitance of any liquid level system. Also derive transfer function of interacting and non-interacting liquid level systems. Tutorial 3 6 Derive transfer function of a thermal system. Tutorial 3 7 Draw equivalent mechanical and electrical systems to relate force voltage or force current analogy 8 What does a block diagram represent? Explain it in detail. List its salient characteristics. Explain the following: Summing point, take off point. Tutorial 3 Tutorial 4 9 Enlist various rules of block diagram algebra. Tutorial 4 10 What are signal flow graphs? Write down the rules for signal flow graphs reduction? Write down Mason s gain formula for signal flow graphs. Explain Mason s gain formula with the help of one example. 11 Define node, transmittance, branch, source, sink, path, loop, and loop gain. Write down important properties of signal flow graphs. Chapter 4 Frequency response analysis Tutorial 5 Tutorial 5 1 What is the need of frequency response analysis? Explain in detail. Tutorial 10 2 Enlist various frequency domain specifications and define each. Tutorial 10 3 Derive correlation between time domain and frequency domain specifications. Tutorial 10 Control Engineering ( ) Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2

3 Chapter 5A Stability 1 What do you mean by stability of a control system? Explain Routh s stability criterion. 2 Explain the difference between Open loop and Close loop control system with examples. Compare their merits and demerits. 2 What do you understand by Transient and steady state response and hence discuss the various types of input test signals used for time response analysis of a control system 3 Explain standard Test signals & derive equation of steady state error constant Kp, Kv, and Ka. Unit 3 Time response Given as part of Tutorial 8 Tutorial 1 Tutorial 8 Tutorial 8 1 Explain unit step response of first order linear time invariant systems. Tutorial 5 2 Define transient response specifications of second order system using neat Tutorial 5 sketch: OR Explain the performance indices second order system. 3 Derive the unit impulse response of second order system for all value of Tutorial 5 damping factor (ξ). 4 Derive the step response of second order system for all value of damping Tutorial 6 factor (ξ). 5 Explain in detail about P-I, P-D, and P-I-D control action. Tutorial 6 Unit 5B Root Locus 1 Explain Rules for construction of Root Locus. Tutorial 9 Unit 8 SSA 1 Write a short note on state space representation of a control system. Tutorial 10 2 Write definitions of state and state variables. Explain the fact that for any system, the set of state variables are non-unique. Discuss the limitations of transfer functions and advantages of analysis of control systems using state space. Tutorial 10 Control Engineering ( ) Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3

4 CONTROL ENGINEERING EXPERIMENT NO. 01 DATE : Definition of Laplace Transform: Laplace transform F( of a function f(t) is defined as MATHEMATICAL PRELIMINARIES FOR CONTROL THEORY: LAPLACE TRANSFORMS & DIFFERENTIAL EQUATIONS 1 Where, f(t) = a function of time t such that f(t) = 0, for t <0 s = a complex variable of the form Standard Laplace Transform Pair:

5 EXPERIMENT NO. 01 DATE : MATHEMATICAL PRELIMINARIES FOR CONTROL THEORY: LAPLACE TRANSFORMS & DIFFERENTIAL EQUATIONS 2

6 EXPERIMENT NO. 01 DATE : Properties of Laplace Transform: MATHEMATICAL PRELIMINARIES FOR CONTROL THEORY: LAPLACE TRANSFORMS & DIFFERENTIAL EQUATIONS 3 Initial Value Theorem: Final Value Theorem:

7 EXPERIMENT NO. 01 DATE : MATHEMATICAL PRELIMINARIES FOR CONTROL THEORY: LAPLACE TRANSFORMS & DIFFERENTIAL EQUATIONS 4 Using Standard Laplace Transform pairs and its properties to solve following problems 1) Obtain LT of the function defined as 2) Obtain LT of the function defined as 3) Obtain LT of the function defined as Obtain the inverse LT of the function defined below: 1 2 3

8 EXPERIMENT NO. 01 DATE : MATHEMATICAL PRELIMINARIES FOR CONTROL THEORY: LAPLACE TRANSFORMS & DIFFERENTIAL EQUATIONS Obtain the solution of the differential equation defined below: NOTE: Verify all above examples using MATLAB and list the command used for the same with small description. GRADE LAB-INCHARGE H.O.D

9 CONTROL ENGINEERING EXPERIMENT NO. 02 DATE : (1) Define the following giving one suitable example. (a) Transfer function (b) Order of the system (c) Type of the system (d) Characteristic equation (e) Pole & zero of the system TO STUDY OF SYSTEM & SYSTEM TRANSFER FUNCTION 1 DOC. CODE : DIET/EC (2) Find transfer function of following system. Also find characteristic equation order and type of there system. (3) Find transfer function of the following system and identity its poles & zeros.

10 EXPERIMENT NO. 02 DATE : TO STUDY OF SYSTEM & SYSTEM TRANSFER FUNCTION 2 DOC. CODE : DIET/EC (4) Find the transfer function of the following system and verify if the transfer function is equal to the product of transfer functions giving appropriate reason. CONCLUSION: GRADE LAB-INCHARGE H.O.D.

11 CONTROL ENGINEERING EXPERIMENT NO. 03 DATE : 1. Explain Force-Voltage Analogy & Force-Current Analogy MODELLING OF MECHANICAL SYSTEMS 1 2. Draw the equivalent mechanical system of the given system. Hence write the set of equilibrium equations for it and obtain electrical analogous circuits using (i) F-V Analogy (ii) F-I Analogy (a) (b) (c) 3. Consider Rotational system shown in the following figure, Where J = Moment of inertia of disk B = Friction Constant K = Torsional Spring Constant And disk subjected to torque T(t) as shown. Draw its analogous network based on (i) F V Analogy (ii) F I Analogy

12 EXPERIMENT NO. 03 DATE : MODELLING OF MECHANICAL SYSTEMS 2 4. For the mechanical system shown, obtain the analogous electrical network based on F V Analogy 5. The figure shows F I Analogous Electrical Network for translational mechanical system. Draw the mechanical system.

13 CONTROL ENGINEERING TO STUDY BLOCK DIAGRAM REDUCTION TECHNIQUE 1 EXPERIMENT NO. 04 DATE : REV. R NO.: 3.00/JAN-2013 (1) Explain the block diagram reduction rules with the block diagram before and after the transformation. (2) Simplify the block diagram showing in the below figure. (3) Assume that linear approximations in the form of transfer functions are available for each block of the Supply and Demand System of given problem, and that the system can be represented by given figure. Determine the overall transfer functionn of the system. (4) Simplify the block diagram showing in the below figure. And obtain the transfer function relating R( and c(.

14 TO STUDY BLOCK DIAGRAM REDUCTION TECHNIQUE 2 EXPERIMENT NO. 04 DATE : (5) Simplify the block diagram showing in the below figure. (6) Simplify the block diagram showing in the below figure. (7) Simplify the block diagram showing in the below figure with unity feedback.

15 TO STUDY BLOCK DIAGRAM REDUCTION TECHNIQUE 3 EXPERIMENT NO. 04 DATE : (8) Simplify the block diagram showing in the below figure. (9) Simplify the block diagram showing in the below figure. (10) Simplify the block diagram showing in the below figure. GRADE LAB-INCHARGE H.O.D.

16 CONTROL ENGINEERING EXPERIMENT NO. 05 DATE : TIME RESPONSE ANALYSIS - I 1 1. What are Standard Test signals? Explain each of them with a sketch and its mathematical expression in both time and Laplace domain. 2. Define the following (a) Time response analysis and Frequency response analysis (b) Transient response and Steady state response. 3. (For Even roll numbers in the batch). Derive a general expression showing unit ramp response of a first order system. Sketch input and output with respect to time. Also comment on the error signal and value of steady state error. (For Odd roll numbers in the batch). Derive a general expression showing unit step response of a first order system. Sketch input and output with respect to time. Also comment on the error signal and value of steady state error. 4. (For Even roll numbers in the batch). Derive a general expression showing unit impulse response of a second order system. Sketch response for different values of damping ratio. (For Odd roll numbers in the batch). Derive a general expression showing unit impulse response of a second order system. Sketch response for different values of damping ratio. 5. Define the following terms related to step response of a second order system. (a) Delay time (b) Rise time (c) Peak time (d) Maximum peak overshoot (d) Settling time. 6. Write the expression of response of a second order system to a unit step input and derive expression of the following (For Even roll numbers in the batch). (a) Rise time (b) Maximum peak over shoot (For Odd roll numbers in the batch). (a) Peak time (b) Settling time 7. Obtain the response of a unity feedback system whose open-loop transfer function is 3 = +4 for a unit step input.

17 EXPERIMENT NO. 05 DATE : TIME RESPONSE ANALYSIS - I 2 8. Obtain the unit step response of a system whose forward path and feed back path transfer function are given as = 10 +3, = The open loop transfer function of a unity feedback system is 4 G s = s s+1 Determine the nature of response of the closed-loop system for a unit-step input. Also determine the damping ratio, natural frequency of oscillation, damped frequency of oscillation, rise time, peak time, peak overshoot and settling time. 10. A second order system is represented by a transfer function given below C s R s = 1 Js +fs+k When this system is excited with a step input of magnitude 10 units, following results were measured from the system response. (a) Peak overshoot 6% (b) Peak time = 1 s (c) Steady state value of output = 0.5 Determine the values of J, f and K

18 CONTROL ENGINEERING EXPERIMENT NO. 06 DATE : 1. Define a) Signal flow graph. b) Node c) Multiplication factor/ Transminattance. d) Branch e) Source SIGNAL FLOW GRAPH 1 g) Mixed node h) Path i) Loop and loop gain j) Nontouching loop k) Forward path and Forward path gain f) Sink 2. Mention the properties of SFG. 3. Consider the signal flow graph given in Fig and 4. Find the transfer function for the fig. using signal flow graphs.

19 EXPERIMENT NO. 06 DATE : SIGNAL FLOW GRAPH 2 5. Find the transfer function for the fig. using signal flow graphs. 6. Find the transfer function for the fig. using signal flow graphs. 7. Find the transfer function for the fig. using signal flow graphs.

20 CONTROL ENGINEERING EXPERIMENT NO. 07 DATE : TIME RESPONSE ANALYSIS - II 1 1. Study and use following MATLAB functions for time response analysis of systems. (a) tf (b) step (c) impulse (d) residue (e) tf2zpk (Self study, no need to write in file 2. Using MATLAB obtain time response of following systems for step and impulse input C( 10 (a) = ; identify the value of system time constant R ( s ) s + 2 (b) C( = R( s ;(c) 0.2s + 1 C( = R ( s ) s (d) C( = R( s 2 1 (e) + 2s + 1 C( = R( s s + 1 For (b) to (e) identify the value of ζ and ω n and comment of the damping present in the system. (write or attaché print out of the program and response plot) 3. Define steady state response and steady state error. Derive the equation of steady state error for a general closed loop system with G( as forward path transfer function, H( as feedback path transfer function, R( as input and C( as output. 4. Define static error constant. Derive the value of steady state errors for type 0, type 1 and type 2 systems. 5. For control systems with open-loop transfer functions given below, which type of input signal will give finite, non-zero steady state error. Also calculate the error for that input ( s + 4) 20 G ( H ( =, G( H ( =, G( H ( = 2 ( s + 1)( s + 4) s( s + 1)( s + 2) s ( s + 1)( s + 4) 6. Consider a unity feedback system whose closed loop transfer function is C( Ks + b = R ( s ) s 2 + as + b Find open loop transfer function. Also show that the steady-state error with unit ramp input is given by (a-k)/b. 7. The open loop transfer function of a servo system with unity feedback is 10 G ( H ( = s(0.1s + 1) Evaluate the static error co-efficient (Kp, Kv, Ka) for the system. Obtain the steady-state error of the system when subjected to following inputs (i) 2 u(t) (ii) 2t u(t) (iii) t 2 u(t) (iv) (2 + 2t + t 2 ) u(t)

21 CONTROL ENGINEERING EXPERIMENT NO. 08 DATE : STABILITY ANALYSIS USING RH CRITERION 1 1. Define stability criteria for LTI system. 2. Show location of following poles on s-plane and sketch approximate impulse response contributed by each of them giving its approximate equation. (a) s = -5 (b) s = 5 (c) s1,s2 = ±j (d) s1,s2 = -5±j (e) s1,s2 = 5±j (f) s = 0 (g) s1,s2 = 0 (h) s1,s2 =j s3,s4 = -j 3. Using Routh Criterion, determine the stability of the system represented by following characteristic equation. For system found to be unstable identify number of roots in the right half of s-plane (a) s + 2s + 8s + 15s + 20s + 16s + 16 = (b) s + 2s + s + 2s + 3s + 4s + 5 = (c) s + 3s + 5s + 9s + 8s + 6s + 4 = 0 4. System characteristic equation is given below, looking at the equation comment on system stability. Identify number of roots in right half of the s-plane. If the roots lie on jω axis identify the frequency of sustained oscillation. s s + 24s + 48s 25s 50 = 0 5. A unity feedback system has following forward path transfer function; determine the range of K system stability. Also determine the value of K when the system exhibits sustained oscillation and also find frequency of oscillation. K (a) G ( = (b) G 2 s( s + s + 1)( s + 2) K( s 2) = ( s + 1)( s + 6s + 25) ( 2 6. Using Hurwitz stability criterion, determine the range of K for system with following characteristic equation to be stable s s + (4 + K) s + 9s + 25 = 0 7. For given characteristic equation determine the range f=of values of K such that the system poles are located on left of point s=-1. s (1 + K) s + (5 + 7K) s + (4K + 7) = 0

22 CONTROL ENGINEERING EXPERIMENT NO. 09 DATE : ROOT LOCUS 1 Root locus: It is the locus of the roots of the characteristic equation of the closed loop system as a specific parameter (usually the gain K) Is varied from zero to infinity. Condition: Roots of characteristic equation: 1+ G ( H ( = 0 G( H ( = 1 Thus, a point in s-plane will lie on root locus if it satisfies following condtions. (a) Magnitude criterion: G ( H ( = 1 o (b) Angle Criterion = G( H ( = ± 180 (2l + 1); l = 0,1,2,3... KN( Consider the open loop transfer function G ( H ( = having n poles and m zeros (n>m). D( 1. Each branch of the root locus begins at an open-loop pole (K = 0) and ends at an open-loop (finite) zero or at a zero at infinity (K ). The locus will be symmetric about real axis. 2. Starting at + and moving along the real axis toward the left, the root locus lies on the real axis to the left of an odd number of real-axis open-loop poles or zeros. 3. If n > m, there will be n-m branches of the root locus going to infinity. they will follow asymptotes that meet at a common point on the real axis and make specified angles with respect to the positive real axis. The angles of asymptotes, φ A, and the center of asymptotes, σ A, are given by 4. If G(H( has a complex conjugate pole, then the root locus branch will start from the pole making θ D angle (angle of departure) with respect to the positive real axis. θ D = ±(2q+1)+ [ θ z θ P ] ; q = 0,1,2,. θ P = net angle contributed by all other poles at give complex conjugate pole. θ z = net angle contributed by all other zeros at give complex conjugate pole. 5. If G(H( has a complex conjugate zero, then the root locus branch will end at the zero making θ A angle (angle of arrival) with respect to the positive real axis. θ A = ±(2q+1)- [ θ z θ P ] ; q = 0,1,2,. θ P = net angle contributed by all other poles at give complex conjugate pole. θ z = net angle contributed by all other zeros at give complex conjugate pole. 6. If the root locus on the real axis lies in the interval between two open-loop poles, there will always be a break-away point between the poles where the root locus leaves the real axis. Similarly If the root locus on the real axis lies in the interval between two open-loop zeros,

23 EXPERIMENT NO. 09 DATE : ROOT LOCUS 2 there will always be a break-in point between the zeros where the root locus enters the real axis. All break points break-away points and break-in points can be determined from the dk roots of equation = 0. r branches of root locus meet at break point at an angle of ds 180 ±. r 7. The point of intersection of the root locus branches with the imaginary axis and the critical value of K can be determined by use of Routh criterion. Exercise 1. Draw Root Locus for a unit feedback system whose forward path transfer function is given as G ( = K. Also find the value of K at s = -1±2j. s( s + 1)( s + 4) 2. Sketch the Root Locus of unity feedback control system whose open-loop transfer function is given below. Determine the range of gain for stability and the point at which it crosses the imaginary axis. Determine the value of gain K at the breakaway point. K G ( =. 2 ( s 1)( s + 4s + 7) 3. Sketch Root Locus for the system shown in figure below. Also find the value of gain for the value of ζ= Sketch Root Locus for the system shown in figure below. (for odd roll nos.)

24 EXPERIMENT NO. 09 DATE : ROOT LOCUS 3 (For even roll nos.) 5. Sketch Root Locus for the system with following open loop transfer function. On basis of the root locus obtained comment on the system stability for various values of gain K. Also find value of gain at break points. K( s + 3) (a) G(H( = (For odd roll nos.) s( s + 2) K( s + 1) (b) G(H( = (For even roll nos.) s( s 3) 6. Sketch root locus for the following system 2 K( s + 2s + 10) G(H(= 2 s ( s + 2)

25 CONTROL ENGINEERING EXPERIMENT NO. 10 DATE : TO STUDY STATE SPACE REPRESENTATION 1 1. Define the following terms. a) State b) State variable c) State space d) State vector e) State trajectory 2. Derive expression of transfer function of the system which is represented in the following standard state space form and also define transfer matrix. 3. Derive the correlation between transfer function and state space analysis. 4. Obtain the transfer function of the system defined by following state-space equations. 5. Obtain the transfer function of the system defined by following state-space equations. 6. Obtain the transfer function of the system defined by following state-space equations. Dashing Institute of Engineering And Technology, Rajkot

26 EXPERIMENT NO. 10 DATE : TO STUDY STATE SPACE REPRESENTATION 2 7. Obtain the transfer function of the system defined by following state-space equations. 8. Obtain the transfer function of the system from the data given below.,, 9. Obtain the transfer function of the system defined by following state-space equations. 10. Obtain the state space representation of nth order systems given by the following linear differential equations. 11. Obtain the state space representation of the system given by the following linear differential equations. Dashing Institute of Engineering And Technology, Rajkot

27 EXPERIMENT NO. 10 DATE : TO STUDY STATE SPACE REPRESENTATION Obtain the state space representation of the system given by the following transfer function. 13. Obtain the state space model of the system shown in the figure. 14. Dashing Institute of Engineering And Technology, Rajkot

28 EXPERIMENT NO. 10 DATE : TO STUDY STATE SPACE REPRESENTATION Obtain the state space representation of nth order systems given by the following linear differential equations. 16. Obtain the state space representation of the system given by the following transfer function. 17. For a given LRC circuit, derive the state model of the system. 18. Obtain the state space model of the system shown in the figure. Dashing Institute of Engineering And Technology, Rajkot

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