CS notes

SELVAM COLLEGE OF TECHNOLOGY,NAMAKKAL DEPT OF EEE

SUB: CONTROL SYSTEMS. UNIT I

TWO MARKS 1. Define System. A system is a combination or an arrangement of different physical components which act together as an entire unit to achieve certain objective. 2. Define Control system. To control means to regulate, to direct or to command. Hence a control system is an arrangement of different physical elements connected in such a manner so as to regulate, direct or command itself or some other system. 3. Define Plant. The portion of a system which is to be controlled or regulated is called the plant or the process. 4. Define Controller. The element of the system itself or external to the system which controls the plant or the process is called controller. 5. Define Input. It is an applied signal or an excitation signal applied to a control system from an external energy source in order to produce a specified output. 6. Define Output. It is the particular signal of interest or the actual response obtained from a control system when input is applied to it. 7. Define disturbance. Disturbance is a signal which tends to adversely affect the value of the output of a system. 8. Define internal disturbance. If such a disturbance is generated within the system itself, it is an internal disturbance. 9. Define external disturbance. The disturbance generated outside the system acting as an input to the system in addition to its normal input, affecting the output adversely is an external disturbance. 10. Write any four major classification of control system. 1. Open loop and closed loop control system. 2. Time varying and time-invariant system. 3. Linear and nonlinear system. 4. Lumped parameter and distributed parameter control system.

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11. What is mean by Principle of superposition? Principle of superposition means the response to several inputs can be obtained by considering one input at a system and the algebraically adding the individual results. 12. What is mean by Deterministic control system? A control system is said to be deterministic when its response to input as well as behaviour to external disturbance is predictable and repeatable. 13. Write short notes about SISO and MIMO. A system having only one input and one output is called single input and single output system. Some systems may have multiple input and multiple outputs, these are called multiple input and multiple output systems. 14. Define Open loop system. A system in which output is dependent on input but controlling action is totally independent of the output or changes in input of the system, is called an open loop system. 15. Define closed loop system. A system in which controlling action or input is somehow dependent on the output or changes in output is called closed loop system. 16. Write any four advantages of open loop system. 1. Such systems are simple in construction. 2. Very much convenient when output is difficult to measure. 3. Such systems are easy when maintenance point is view. 4. Such systems are economical. 17. Write any four disadvantages of open loop system. 1. Such systems are inaccurate and unreliable because accuracy of such system is totally dependent on the accurate precalibration of the controller. 2. Such systems give inaccurate results if there are variations in the external environment. 3. Similarly they cannot sense internal disturbances in the system, after the controller stage. 4. To maintain the quality and accuracy, recalibration of the controller is necessary, time to time. 18. Give any four real time application of open loop system. 1. Sprinkler used to water a lawn. 2. Stepper motor positioning system. 3. Automatic toaster system. 4. Traffic light controller. 19. Give any four real time application of closed loop system. 1. Human being. 2. Home heating system. 3. Ship stabilization system. 4. Voltage stabilizer.



20. Define feedback. Feedback is a property of the system by which it permits the output to be compared with the reference input to generate the error signal based on which appropriate controlling action can be decided. 21. What are called feedback systems? Systems in which the effect of the disturbance must show up in the error before the controller can take proper corrective action are called feedback systems. 22. Define Laplace Transform. The Laplace transform is defined as below, Let f (t) be a real function of a real variable t defined for t>0, then

F(s) =L [f (t)] =

0

).( dtetf st

Where F (s) is called Laplace transform of f (t). And the variable s which appears in F(s) is frequency dependent complex variable. It is given by, js += Where =real part of complex variable s. = Imaginary part of complex variable s. 23. Define Linearity of Laplace transform. The transform of a finite sum of time functions is the sum of the Laplace transforms of the individual functions. So if F1(s), F2(s), , Fn(s) are the laplace transforms of the time functions f1 (t), f2(t),, fn(t) respectively then, L{f1(t)+f2(t)+..+fn(t)}=F1(s)+F2(s)+Fn(s). 24. Define scaling Theorem. If K is a constant then the Laplace transform of k(t) is given as K times the Laplace transform of f(t). L [K f (t)] =K F(s) where K is constant. 25. Define Real translation or shifting theorem. This theorem is useful to obtain the Laplace transform of the shifted or delayed function of time. If F(s) is the Laplace transform of f (t) then the Laplace transform of the function delayed by time T is L {f (t-T)} =e-Ts F(s). 26. Define Initial value theorem. The Laplace transform is very useful to find the initial value of the time function f (t). Thus if F(s) is the Laplace transform of f (t) then, )()()0(

0ssFLimtfLimf

st

+ ==+

.

The only restriction is that f (t) must be continuous or at the most, a step discontinuity at t=0.



27. Define Final value theorem. The Laplace transform is very useful to find the final value of the time function f (t). Thus if F(s) is the Laplace transform of f (t) then, )()(

0ssFLimtfLim

st =

.

The only restriction is that the roots of the denominator polynomial of F(s) i.e. poles of F(s) have negative or zero real parts. 28. What is called Transfer function? The effect of system parameters, role of system parameters in the performance of system can be expressed as ratio of output to input. Mathematically such a function explaining the effect of such parameters on input to produce output is called transfer function. 29. Define Transfer function. Mathematically it is defined as th ratio of laplace transform of output (response) of the system to the laplace transform of input (excitation or driving function), under the assumption that all initial conditions are zero. 30. Define impulse function. The impulse function is defined as, F (t) = A for t=0 = 0 for t=0 31. Define poles of a transfer function. The values of s, which make the T.F. infinite after substitution in the denominator of a T.F. are called Poles of that T.F. 32. Define characteristic equation of a transfer function. The equation obtained by equating denominator of a transfer function to zero, whose roots are the poles of that transfer function is called characteristic equation of that system. F(s) = b0sn+b1sn-1+b2sn-2+ + bn = 0 is called the characteristic equation. 33. Define Zero of a transfer function. The value of s which make the T.F. zero after substituting in the numerator are called zeros of the T.F. 34. Define order of a transfer function. The highest power of s present in the characteristic equation i.e. in the denominator polynomial of a closed loop transfer function of a system is called order of a system. 35. What is the basic concept of block diagram representation? If a given system is complicated, it is very difficult to analyse it as a whole. With the help of transfer function approach, we can find transfer function of each and every element of the complicated system. And by showing connection between the elements, complete system can be splitted into different blocks and can be analyzed conveniently. This is the basic concept of block diagram representation.



36. Define Pole Zero plot. Plot obtained by locating all poles and zeros of a T.F. in s-plane is called pole-zero plot of a system. 37. What is called functional block? To draw the block diagram of a practical system, each element of practical system is represented by a block. The block is called functional block. 38. What is called branches? The connection between the blocks is shown by lines called branches of the block diagram. An arrow is associated with each and every branch which indicates the direction of flow of signal along the branch. 39. What are the basic elements of block diagram? 1. Blocks, 2. Transfer functions of elements shown inside the blocks, 3. Summing points, 4. Take off points, 5. Arrows. 40. What are the advantages of block diagram? 1. Very simple to construct the block diagram for complicated systems. 2. The function of individual element can be visualized from block diagram. 41. What are the disadvantages of Block diagram? 1. Block diagram does not include any information about the physical construction of the system. 2. Source of energy is generally not shown in the block diagram. So number of different block diagrams can be drawn depending upon the point of view of analysis. So block diagram for given system is not unique. 42. What is simple or canonical form of closed loop system? A block diagram in which, forward path contains only one block, one summing point and one take off point represents simple or canonical form of a closed loop system. 43. What is called signal flow graph representation? The graphical representation of the variables of a set of linear algebraic equations representing the system is called signal flow graph representation. 44. Write about branches? All the dependent and independent variables are represented by the nodes. The relationships between various nodes are represented by joining the nodes as per the equations. The lines joining the nodes are called branches. 45. What are called nodes of a graph? As variables are important elements of the set of equations for the system, these are represented first in signal flow graph by small circles called nodes of signal flow graph. Each node represents a separate variable of the system. 46. Define forward path. A path from the input to output node is defined as forward path.



47. Define Source node source node and chain node. The node having only outgoing branches is known as source or input node. The node having an only incoming branch is known as sink node or output node.A node having incoming and outgoing branches is known as chain node. 48. Define feedback loop. A path which originates from a particular node and terminating at the same node, traveling through at least one other node, with out tracing any node twice is called feedback loop. 49. Define self loop. A feedback loop consisting of only one node is called self loop. A self loop cannot appear while defining a forward path or feedback loop as node containing it gets traced twice which is not allowed. 50. Define path gain and loop gain. The product of branch gains while going through a forward path is known as path gain. This can be also called as forward path gain. The product of all the gains of the branches forming a loop is called loop gain. 51. Define dummy node. If there exists incoming and outgoing branches both at first and last node representing input and output variables then as per definition these cannot be called as source node or sink node. In such a case a separate input and output nodes can be created by adding branches with gain 1. Such nodes are called dummy nodes. 52. Define non-touching loops. If there is no node common in between the two or more loops, such loops are said to be non- touching loops. 53. State masons formula. The formula can be stated as

= KK

TFOverallT . .

Where k= no. of forward paths 54. What are the two methods of obtaining electrical analogous network? 1. Force-voltage analogy (Direct) 2. Force-current analogy (indirect) 55. Write short notes about servomotors. The servo system is one in which the output is some mechanical variable like position, velocity or acceleration. Such systems are generally automatic control systems which work on the error signals. The error signals are amplified to drive motors used in such systems. These motors used in servo systems are called servomotors.




SUB:CONTROL SYSTEMS. UNIT II

TWO MARKS 1. Define Zero. The zero of a function, F(s) is the value at which the function, F(s) becomes zero, Where F(s) is a function of complex variable s. 2. What is the order of a system? The order of the system is given by the order of the differential equation governing the system. It is also given by the maximum power of s in the denominator polynomial of transfer function. The maximum power of s is also gives the number of poles of the system and so the order of the system is also given by number of poles of the transfer function. 3. What is called time constant form? Those elements are constant of system K and poles of G(s)H(s) at origin of G(s)H(s) is expressed in a particular form called time constant form. 4. Write any four disadvantages of static error co-efficient method. 1. Method cannot give error if inputs are other than the three standard test inputs. 2. Most of the times, method gives mathematical answer of the error as 0 or infinite and hence does not provide precise value of the error. 3. Method does not provide variation of error with respect to time, which will be otherwise very useful from design point of view. 4. The method is applicable only for stable systems 5. Define time response. The response given by the system which is function of the time, to the applied excitation is called time response of a control system. 6. Define transient response. The output variation during the time, it takes to achieve its final value is called as transient response. The time required to achieve the final value is called transient period. 7. Define steady state response. It is that part of the time response which remains after complete transient response vanishes from the system output. 8. What is called steady state error? The difference between the desired output and the actual output of the system is called steady state error which is denoted as ess. This error indicates the accuracy and plays an important role in designing the system. 9. Define step input. It is the sudden application of the signal as shown. Mathematically it can be described as, r(t) = A for t>=0 = 0 for t

10. Define ramp input. It consist of rate of change in input i.e. gradual application of input as shown. Magnitude of ramp input is nothing but the slope. Mathematically, r (t) = At for t>=0 = 0 for t=0 = 0 for t < 0 12. Define Impulse input. It is the input applied instantaneously (for short duration of time) of very high amplitude as shown.

It is the pulse whose magnitude is infinite while its width tends to zero i.e. t 0, applied momentarily. Mathematically, r(t) = A, for t=0 = 0, for t=0 13. Define damping ratio. The damping ratio is defined as the ratio of actual damping to critical damping. 14. Give the expression for damping ratio of mechanical and electrical system. The damping ratio of second order mechanical translational system, =B/2 MK. The damping ratio of second order mechanical rotational system, =B/2 JK. The damping ratio of second order electrical system, =R/2 L/C. 15. How the system is classified depending on the value of damping? Depending on the value of damping, the system can be classified into the following four cases Case 1: Undamped system, =0



Case 2: Underdamped system, 0< 1. 16.What is the importance of test signals? The test signals can be easily generated in test laboratories and the characteristics of test signals resembles, the characteristics of actual input signals. The test signals are used to predetermine the performance of the system. 17. Name the test signals used in control system. The commonly used test input signals in control system are impulse, step, ramp, acceleration and sinusoidal signals. 18. What is weighting function? The impulse response of system is called weighting function. It gives inverse laplace transform of system transfer function. 19. Define Pole. The pole of a function, F(s) is the value at which the function, F(s) becomes infinite, Where F(s) is a function of complex variable S. 20. How the system is classified depending on the value of damping. Depending on the value of damping, the system cen be classified into the following four cases Case 1: Undamped system Case 2: Under damped system Case 3: critically damped system Case 4: over damped system 21. What will be the nature of response of a second order system with different types of damping? For Undamped system the response is oscillatory. For Under damped system the response is damped oscillatory. For Critically damped system the response is exponentially rising. For over damped system the response is exponentially rising but the rise time will be very large. 22. Sketch the response of a second order under damped system. 23. What is damped frequency of oscillation? In under damped system the response is damped oscillatory. The frequency of damped Oscillation is given by



24. List the time domain specifications. The time domain specifications are

1. Delay time 2. Rise time 3. Peak time 4. Maximum peak overshoot 5. Settling time.

25. Define delay time. It is the time taken for response to reach 50% of the final value, for the very first time. 26. Define rise time. It is the time taken for response to raise from 0 to 100% for the very first time. For under damped system, the rise time is calculated from 0 to 100%. But for over damped system, it is the time taken by the response to raise from 10% to 90%. For critically damped system, it is the time taken for response to raise from 5% to 95%. 27. Define Peak time. It is the time taken for the response to reach the peak value for the very first time (or) It is the time taken for the response to reach peak overshoot, Mp. 28. Define Peak overshoot. It is defined as the ratio of the maximum peak value measured from final value to final value. Let final value= c( ), Maximum value=c(tp) Peak over shoot, Mp= 29. Define Settling time. It is defined as the time taken by the response to reach and stay with in a specified error and the error is usually specified as % of final value. The usual tolerable error is 2% or 5% of the final value. 30. What is type number of a system? What is its significance? The type number is given by number of poles of loop transfer function at the origin. The type number of the system decides the steady state error. 31. Distinguish between type and order of a system. 1. Type number is specified for loop transfer function but order can be specified for any transfer function. (open loop or closed loop transfer function). 2. The type number is given by number of poles of loop transfer function lying at origin of s-plane but the order is given by the number of poles of transfer function. 32. For the system with following transfer function, determine type and order of the system. Ans: 1. Type-1, Order-4 2. Type-2, Order-4 3. Type-0, Order-2 4. Type-3, Order-5



33. What are static error constants? The Kp,Kv and Ka are called static error constants. These constants are associated with steady state error in a particular type of system and for a standard input. 34. Define positional error constant. The positional error constant Kp = Lt G(s)H(s). The steady state error in type-0 system when the input is unit step is given by 1/(1+Kp). 35. Define Velocity error constant. The Velocity error constant Kv=Lt sG(s) H(s). The steady state error in type-1 system for unit ramp input is given by 1/Kv. 36. Define acceleration error constant. The acceleration error constant Ka=Lt s2G(s) H(s). The steady state error in type-2 system for unit parabolic input is given by 1/Ka. 37. What are generalized error coefficients? They are the coefficients of generalized error series. The generalized error series is given by.The Coefficients C0,C1,C2 are called generalized error coefficient or dynamic error coefficients. The nth coefficient, Cn=Lt dnF(s)/dsn, Where F(s)=1/(1+G(s)H(s)). 38. Give the relation ship between generalized and static error coefficients. The following expressions shows the relation between generalized and static error coefficient C0=1/(1+Kp), C1=1/Kv,C2=1/Ka. 39. Mention two advantages of generalized error constants over static error constants. 1. Generalized error series gives error signal as a function of time. 2. Using generalized error constants the steady state error can be determined for any type of the input but static error constants are used to determine steady state error when the input is anyone of the standard input. 40. What is the effect on system performance, when a proportional controller is introduced in a system? The proportional controller improves the steady state tracking accuracy, disturbance signal rejection and relative stability of the system. It also increases the loop gain of the system which results in reducing the sensitivity of the system to parameter variations. 41. What is the disadvantage in proportional controller? The disadvantage in proportional controller is that it produces a constant steady state error. 42. What is the effect of PI controller on the system performance? The PI controller increases the order of the system by one, which results in reducing, the steady state error. But the system becomes less stable than the original system.



43. What is the effect of PD controller on the system performance? The effect of PD controller is to increase the damping ratio of the system and so the peak overshoot is reduced. 44. Why derivative controller is not used in control systems? The derivative controller produces a control action based on rate of change of error signal and it does not produce corrective measures for any constant error. Hence derivative controller is not used in control systems.




SUB:CONTROL SYSTEMS. UNIT III

TWO MARKS 1. What is frequency response? The frequency response is steady-state output of the system, when the input is a sinusoidal signal. 2. What are the advantages of frequency response analysis? 1. The absolute and relative stability of the closed loop system can be estimated from the knowledge of the open loop frequency response. 2. The practical testing of system can be easily carried with available sinusoidal signal generators and precise measurement equipments. 3. What are the frequency domain specifications? 1. Resonant peak 2. Resonant frequency 3. Band width 4. Cut-off rate 5. Gain margin 6. Phase Margin 4. Define resonant peak? The maximum value of the magnitude of closed loop transfer function is called resonant peak. 5. What is resonant frequency? The frequency at which resonant peak occurs is called resonant frequency. The resonant peak is the maximum value of the magnitude of closed loop transfer function. 6. Define bandwidth? The bandwidth is the range of frequencies for which the system gain is more than -3db. 7. What is cut-off rate? The slope of the log-magnitude curve near the cut-off frequency is called cut-off rate. 8. Define Gain Margin? The gain margin, kg is defined as the reciprocal of the magnitude of open loop transfer function, at phase cross over frequency, Gain Margin, Kg=1/ |G(jw)| and when expressed in decibels it is 20 log kg. 9. Define phase Margin? The phase margin, is that amount of additional phase lag at the gain cross-over frequency, required to bring the system to the verge of instability. It is given by, 180+ , where is the phase of g(jw) at the gain cross over frequency. Phase Margin, = 180+



10. What is phase and gain cross over frequency? The gain cross over frequency is the frequency at which the magnitude of the open loop transfer function is unity. The phase cross over frequency is the frequency at which the phase of the open loop transfer function is 180. 11. Write the expression for resonant peak and resonant frequency. Resonant peak, Mr = Resonant frequency, 12. Write short note on the correlation between the time and frequency response? There exists a correlation between time and frequency response of first or second order systems. The frequency domain specification can be expressed in terms of the time domain parameter and .For a peak overshoot in time domain specification there is a corresponding resonant peak in frequency domain. For higher order systems there is no explicit correlation between time and frequency response. 13. What is bode plot? The bode plot is a frequency response plot of the transfer function of a system. It consists of two plots-magnitude plot and phase plot. The magnitude plot is a graph between magnitude of a system transfer function in db and the frequency . The phase plot is a graph between the phase or arguments of a system transfer function in degrees and the frequency . Usually, both the plots are plotted on a common x-axis in which the frequencies are expressed in logarithmic scale. 14. What is approximate bode plot? In approximate bode plot, the magnitude plot of first and second order factors are approximated by two straight lines, Which are asymptotes to exact plot. One straight line is at odb, for the frequency range 0 to and other straight line is drawn with a slope of +20n db/dec for the frequency range . Here is the corner frequency. 15. Define corner frequency? The magnitude plot can be approximated by asymptotic straight lines. The frequencies corresponding to the meeting point of asymptotes are called corner frequency. The slope of the magnitude plot changes at every corner frequencies. 16. What are the advantages of bode plot? 1. The magnitudes are expressed in db and so a simple procedure is available to add magnitude of each term one by one. 2. The frequency domain specification can be easily determined. 17. What is the value of error the approximate magnitude plot of a first order factor at the corner frequency? The error in the approximate magnitude plot of a first order factor at the corner frequency is +3mdb, where m is multiplicity factor. Positive error for numerator factor and negative error for denominator factor.



18. What is the value of error in the approximate magnitude plot of a quadratic factor with at the corner frequency? The error is +6db, for the quadratic factor with =1. Positive error for numerator factor and negative error for denominator factor. 19. What is polar plot? The polar plot of a sinusoidal transfer function g(j ) is a polar plot of the magnitude of G(j ) versus the phase angle/argument of G(j ) on polar or rectangular co-ordinates as is varied from zero to infinity. 20. What is minimum phase system? The minimum phase systems are systems with minimum phase transfer functions. In minimum phase transfer functions, all poles and zeros will lie on the left half of s-plane. 21. What are All-Pass systems? The all pass systems are systems with all pass transfer functions. In all pass transfer functions, the magnitude is unity at all frequencies and the transfer function will have anti-symmetric pole zero-pattern. 22. What is non-minimum phase transfer function? A transfer function which has one or more zeros in the right half s-plane is known as non-minimum phase transfer function. 23. What is Nichols plot? The Nichols plot is a frequency response plot of the open loop transfer function of a system. It is a graph between magnitude of G(j ) in db and the phase of g(j ) in degree, plotted on a ordinary graph sheet. 24. What are M and N circles? The magnitude, m of closed loop transfer function with unity feedback will be in the form of circle on complex plane for each constant value of M. The family of these circles is called M circles. Let N=tan where is the phase of closed loop transfer with unity feedback. For each constant value of N, a circle can be drawn in the complex plane. The family of these circles are called N circles. 25. How closed loop frequency response is determined from open loop frequency using M and n circles? The G(j ) locus or the polar plot of open loop system is sketched on the standard M and n circles chart. The meeting point of M circle with G(j ) locus gives the magnitude of closed loop system. The locus with N-circle gives the value of phase of closed loop system. 26. What is Nicholas Chart? The Nicholas chart consists of m and n contours superimposed on ordinary graph. Along each M contour the magnitude of closed loop system, M will be constant. Along each N contour, the phase of closed loop system will be constant. The ordinary graph consists of magnitude in db, marked on the y-axis and the phase in degrees marked on x axis. The Nicholas chart is used to find the closed loop frequency response from the open loop frequency response.



27. How the closed loop frequency response is determined from the open loop frequency response using Nicholas chart? The G(j ) locus or the Nicholas plot is sketched on the standard Nicholas chart. The meeting point of M-contour with G(j ) locus gives the magnitude of closed loop system and the meeting point with N circle gives the argument/phase of the closed loop system. 28. What are the advantages of Nicholas chart? 1. The gain of the system can be adjusted to satisfy the given specification. 2. The frequency domain specification can be easily determined. 29. In minimum phase system, how the start and end of polar plot are identified? 30. Draw the polar plot of G(s)=1(1+sT).



SELVAM COLLEGE OF TECHNOLOGY, NAMAKKAL-03 DEPARTMENT OF EEE

CLASS/SEM: III ECE/V SEM CONTROL SYSTEMS

UNIT-IV TWO MARKS

1. Define BIBO stability. A linear relaxed system is said to have BIBO stability if every bounded (finite) input results in a bounded (finite) output. 2. What is impulse response? The impulse response of a system is the inverse Laplace transform of the system transfer function. 3. What is the requirement for BIBO stability?

The requirement for BIBO stability is that, where )(m is the impulse response of the

system.

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