C O N T R O L S Y S T E M EX-602/ EE 801

Transcription

1 PRACTICAL WORK BOOK C O N T R O L S Y S T E M EX-602/ EE 801 Name: Enrollment No: Branch: Semester: Batch: Department of Electrical Engineering

2 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering S No List of Experiments/ Programs I N D E X 1 (A) Obtain the zeros, poles and direct term in partial-fraction expansion for given transfer function using MATLAB. Consider the following transfer function H(s)= ( ) = ( ) (B) Obtain zeros (z), poles (p) and gain (k) for given transfer function using MATLAB. Consider the following transfer function H(s)= ( ) = ( ) (C) Obtain the transfer function from the given data- poles at -1-1j,-1+1j and -2;zero at 0 and gain(k)=[5]. 2 Suppose the following transfer functions are connected as shown in Figure: G 1 (s) = = 10 s 2 G +2s+10 2 (s) = = (a) (b) (c) (d) (a) Cascade (series) system, (b) parallel system and (c) feedback system 3 To digitally simulate the response characteristics of a second order system without linearity and to verify it manually. 4 Construct a simulink diagram to calculate the response of mass spring damper system, input force increases from 0 to 8 N in t=1 sec. The parameter values are mass(m)=2 kg, spring constant(k)=16 N/m, damping force(f)=4 N-sec/m 5 To simulate the different responses by creating the third order transfer function 6 Write a program to compare the change in dynamic behavior of closed loop system by changing its gain 7 The open loop transfer function of a servo system with unity feedback is given by G(s) = 10/(s+2) (s+5). Determine the damping ratio, undamped natural frequency of oscillation. What is the percentage overshoot of the response to a unit step input 8 Design a controller using Bode Plot for the following system:

3 Where Gc(s) is the controller and G(s) is:. The design must meet the following specifications: Zero steady state error. Maximum overshoot must be less than 40%. Settling time must be less than 2 sec. 9 Find the given state space model or transfer function is controllable and observable or not using MATLAB. 10 To Study the Operation of a - TYPE 1 CONTROL SYSTEM, 11 To Study the Operation of a - TYPE 2 CONTROL SYSTEM 12 To Study the principle and operation of a BASIC FEED BACK CONTROL SYSTEM

4 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering EXPERIMENT NO 1 SYSTEM MODELLING OBJECT: - (A) Obtain the zeros, poles and direct term in partial-fraction expansion for given transfer function using MATLAB. Consider the following transfer function (B) Obtain zeros (z), poles (p) and gain (k) for given transfer function using MATLAB. Consider the following transfer function (C) Obtain the transfer function from the given data- poles at -1-1j,-1+1j and -2;zero at 0 and gain(k)=[5]. HARDWARE-SOFTWARE REQUIRED: - Intel(R), Pentium(R) 4 CPU, 2.4 GHz, and 1 GB of RAM and MATLAB software. THEORY: - A. Partial Fraction Expansion of H(s) MATLAB has a command to obtain the partial-fraction expansion of a transfer functionh(s). Consider the following transfer function: Where ak and bk are the kth coefficients of the transfer-function polynomials in descending powers of the complex variable s. Note that some of these coefficients may be zero. In MATLAB, the row vectors, num and den, specify the coefficients of the numerator and denominator of the transfer function. That is, The command [r, p, k] = residue(num, den) finds the residues (or zeros), the poles and direct terms of a partial-fraction expansion

5 of the discrete-time, transfer function, H(s), and places them in the column vectors r, p and k, respectively. If there are no multiple roots, then the partial-fraction expansion of H(s) is given by: If pk = pk+1 =.= pk+m-1, the pole pk is a pole of multiplicity m. In this case, the expansion includes terms of the form: B. The Zeros and Poles of H(s) One way of obtaining the poles, zeros and gain of a transfer function in MATLAB is through the use of the function: [z, p, k] = tf2zp(num, den). This function returns the vectors z and p containing the poles and zeros, as well as a real number, k, which is the gain factor of the transfer function. C. Creation of Zero-Pole-Gain Models sys = zpk(z,p,k) creates a continuous-time zero-pole-gain model with zeros z, poles p, and gain(s) k. The output sys is a zpk model object storing the model data. In the SISO case, z and p are the vectors of real- or complex-valued zeros and poles, and k is the real- or complex-valued scalar gain: h(s)=k (s-z(1))(s-z(2))...(s-z(m)) (s-p(1))(s-p(2))...(s-p(n)) Set z or p to [] for systems without zeros or poles. These two vectors need not have equal length and the model need not be proper (that is, have an excess of poles). You can also use rational expressions to create a ZPK model. To do so, use either: s = zpk('s') to specify a ZPK model from a rational transfer function of the Laplace variable, s. z = zpk('z',ts) to specify a ZPK model with sample time Ts from a rational transfer function of the discrete-time variable, z.

6 Once you specify either of these variables, you can specify ZPK models directly as real- or complex-valued rational expressions in the variable s or z. PROCEDURE: Start-up procedure 1. Click on the MATLAB icon. 2. Click on the control system tool box. 3. Open new M-file to write a program. This can be done by click file, new, M-file or ctrl+n. 4. After writing the program save it. It will be saved in work. 5. To run the program, click debug, save and run. 6. To end any current executing operation press ctrl+c. 7. For any help, go to MATLAB help.

7 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering EXPERIMENT No - 2 OBJECT: - SYSTEM MODELING Suppose the following transfer functions are connected as shown in Figure 1: (a) (b) (c)

8 (d) Figure 1: (a) Cascade (series) system, (b) parallel system and (c) feedback system. HARDWARE-SOFTWARE REQUIRED: - Intel(R), Pentium(R) 4 CPU, 2.4 GHz, and 1 GB of RAM and MATLAB software. THEORY: - Block Diagrams and Step Response In control systems analysis, we frequently need to simplify a network of interconnected transfer functions and into a single transfer function which is then used in subsequent calculations for analysis purposes. There are three different types of connections between transfer function that are usually encountered in practice: cascade-connected, parallel-connected and feedback-connected (closed-loop) transfer functions. MATALB has convenient commands to obtain these transfer functions. To obtain the transfer functions of the cascaded, parallel, feedback and unity feedback systems, the following commands are used, respectively: [num, den] = series(num1, den1, num2, den2) [num, den] = parallel(num1, den1, num2, den2) [num, den] = feedback(num1, den1, num2, den2) [num, den] = cloop(num1, den1, -1) PROCEDURE: Start-up procedure 1. Click on the MATLAB icon. 2. Click on the control system tool box. 3. Open new M-file to write a program. This can be done by click file, new, M-file or ctrl+n.

9 4. After writing the program save it. It will be saved in work. 5. To run the program, click debug, save and run. 6. To end any current executing operation press ctrl+c. 7. For any help, go to MATLAB help.

10 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering EXPERIMENT No - 3 DIGITAL SIMULATION OF SECOND ORDER SYSTEMS OBJECT: - To digitally simulate the response characteristics of a second order system without linearity and to verify it manually. HARDWARE-SOFTWARE REQUIRED: - Intel(R), Pentium(R) 4 CPU, 2.4 GHz, and 1 GB of RAM and MATLAB software. THEORY: - The time characteristics of control system are specified in terms of time domain specifications. System with energy storage element cannot respond instantaneously and exhibit transient response whenever they are subjected to a disturbance. The transient response characteristics of the control system to a step input are specified in terms of the following time domain specifications. (i) Delay time (ii) Rise time (iii) Peak time (iv) Maximum peak overshoot (v) Settling time

11 ALGORITHM : Step1: Declare the numerator and denominator for the transfer function. Step2: Assign value for zeta, wn, t & r Step3: Write the mat lab program to calculate the time domain specifications Step4: Execute the program Step5: Note down the output waveform &values of time domain specifications. PROCEDURE: Start-up procedure 1. Click on the MATLAB icon. 2. Click on the control system tool box. 3. Open new M-file to write a program. This can be done by click file, new, M-file or ctrl+n. 4. After writing the program save it. It will be saved in work. 5. To run the program, click debug, save and run. 6. To end any current executing operation press ctrl+c. 7. For any help, go to MATLAB help.

12 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering OBJECT:- EXPERIMENT No:- 4 MODELLING OF A MECHANICAL SYSTEM Construct a simulink diagram to calculate the response of mass spring damper system,input force increases from 0 to 8 N in t=1 sec.the parameter values are mass(m)=2 kg, spring constant(k)=16 N/m,damping force(f)=4 N-sec/m HARDWARE-SOFTWARE REQUIRED: - Intel(R), Pentium(R) 4 CPU, 20 GHz, and 120 MB of RAM and MATLAB software THEORY:- TRANSLATIONAL SYSTEMS:- The motion takes place along a straight is known as translational system.there are three types of force that resist motion. 1.Inertia force:-consider a body of mass M and acceleration (a),then according to newtons law of motion the inertia force will be equal to the product of mass M and acceleration a F M (t)=ma(t)..(1) In terms of velocity the equation (1) becomes F M (t)=m dv(t)/dt..(2) In terms of displacement the equation 1 can be expressed as F M (t)=md 2 x(t)/dt 2.(3) X(t) M F(t) 2.Damping force:-for viscous friction we assume that the damping force is proportional to the velocity.

13 F D (t)=bv(t)=bdx(t)/dt Where, B=damping coefficient Unit of B=N/m/sec We can represent B by a dashpot,consist of a piston and cylinder x F D (t) 3.Spring force:-a spring stores the potential energy.the restoring force of a spring is proportional to the displacement. F k (t) ax(t)=k x(t) F k (t)=k v(t)dt, where k=spring constant or stiffness Unit of k=n/m The stiffness of a spring can be defined as the restoring force per unit displacement PROCEDURE:- Start-up procedure 1. Click on the MATLAB icon. 2. Click on the control system tool box. 3. Open new M-file to write a program. This can be done by click file, new, M-file or ctrl+n. 4. After writing the program save it. It will be saved in work. 5. To run the program, click debug, save and run. 6. To end any current executing operation press ctrl+c. 7. For any help, go to MATLAB help

14 SIMULINK MODEL:-

15 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering OBJECT:- EXPERIMENT No:- 5 TIME RESPONSE OF THIRD ORDER SYSTEM To simulate the different responses by creating the third order transfer function HARDWARE-SOFTWARE REQUIRED: - Intel(R), Pentium(R) 4 CPU, 20 GHz, and 120 MB of RAM and MATLAB software THEORY:- TIME RESPONSE OF A THIRD ORDER CONTROL SYSTEM:- A Third order control system is one wherein the highest power of s in the denominator of its transfer function equals 3.Thus a third order control system is expressed by a transfer function given below. C(S) R(S) = k s + as + bs + c.. (1) In the above transfer function a,b and c are constants. The denominatror of equation(1) can be factorised as follows: (s + as + bs + c) = (s + d)(s + b1s + c1) The constant d,b 1 and c 1 can be determined in terms of a,b and c.thus the transfer function of a third order control system is given by equation (1) can be expressed as C(S) R(S) = k (s + d)(s + b1s + c1).. (2) The denominator of expression equation 2 is composed of product of first order term and quadratic term. The unit step Time response of a third order control system is given by expression equation(2) is determined as follows:- As input is r(t)=1,therefore,r(s)=1/s,hence

16 C(s) = 1 s k (s + d)(s + b1s + c1).. (3) The R.H.S of the equation can be expanded using partial fraction technique and the corresponding time response is obtained by taking inverse laplace transform.therefore, C(S) = K1 S + K2 S + d + k3s + k4 s + b1s + c1 (4) PROCEDURE:- Start-up procedure C(t) = (L ) { K1 S + 1. Click on the MATLAB icon. 2. Click on the control system tool box. K2 S + d + k3s + k4 s + b1s + c1 } (5) 3. Open new M-file to write a program. This can be done by click file, new, M-file or ctrl+n. 4. After writing the program save it. It will be saved in work. 5. To run the program, click debug, save and run. 6. To end any current executing operation press ctrl+c. 7. For any help, go to MATLAB help

17 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering OBJECT:- EXPERIMENT NO-6 COMPARING SYSTEM Write a program to compare the change in dynamic behavior of closed loop system by changing its gain.hardware-software REQUIRED:- Intel(R), Pentium(R) 4 CPU, 2.4 GHz, and 1 GB of RAM and MATLAB software. THEORY:- TRANSIENT RESPONSE SPECIFICATIONS OF A SECOND ORDER SYSTEM:- Due to change in the gain of a closed loop system its dynamic behavior or its characteristics changes but its shape remains same. By changing gain of a system its change characteristics are compared here. RISE TIME:- The definition of rise time is "that time taken for a linear network's output to rise from 10% to 90% of its final value when stimulated by a step input". This measurement is useful because it is easy to measure on an oscilloscope and can be applied to any linear network. SETTLING TIME:- The time required for a component, circuit, device, instrument, piece of equipment, or system, to settle and remain at a given value once an input signal or pulse is received. Settling time is defined as "the time required for the response curve to reach and stay within a range of certain percentage (usually 5% or 2%) of the final value." PEAK TIME:- The peak time is the time required for the response to reach the first peak of the overshoot. STEADY STATE:- The steady state response is that part of the total response which does not approach zero as time approaches zero as time approaches infinity.

18 PROCEDURE:- Start-up procedure 1. Click on the MATLAB icon. 2. Click on the control system tool box. 3. Open new M-file to write a program. This can be done by click file, new, M-file or ctrl+n. 4. After writing the program save it. It will be saved in work. 5. To run the program, click debug, save and run. 6. To end any current executing operation press ctrl+c. 7. For any help, go to MATLAB help.

19 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering OBJECT:- EXPERIMENT No:- 7 SERVO SYSTEM The open loop transfer function of a servo system with unity feedback is given by G(s)=10/(s+2)(s+5).Determine the damping ratio,undamped natural frequency of oscillation.what is the percentage overshoot of the response to a unit step input HARDWARE-SOFTWARE REQUIRED: - Intel(R), Pentium(R) 4 CPU, 20 GHz, and 120 MB of RAM and MATLAB software THEORY: - A second order control system is one wherein the highest power of s in the denominator of its transfer function equals 2. A general expression for transfer function of a second order control system is given by C(s)/R(s)= ωn ^2/s^2+2 ζ ωn s + ωn ^2. ζ:- the damping ratio of the system ωn-: the (undamped) natural frequency of the system Natural Frequency(ωn):- The natural frequency of a second order system is the frequency of oscillation of the system without damping.for example,the frequency of oscillation of a series RLC circuit with the resistance shorted would be the natural frequency Damping Ratio(ζ):- The damping ratio of a second-order system, denoted with the Greek letter zeta(ζ), is a real number that defines the damping properties of the system. More damping has the effect of less

20 percent overshoot, and slower settling time. Damping is the inherent ability of the system to oppose the oscillatory nature of the system's transient response. Larger values of damping coefficient or damping factor produces transient responses with lesser oscillatory nature. The ratio of actual damping to the critical damping is known as damping ratio (ζ), Three cases: ζ = 1, critically damped case ζ > 1, overdamped case 0 < ζ < 1, underdamped case TRANSIENT RESPONSE SPECIFICATIONS OF A SECOND ORDER SYSTEM:- Delay Time(Td):- The delay time is the time needed for the response to reach half of its final value the very first time. Rise Time(tr):- It is the time required for the response to rise from 10% to 90% of its final value.for overdamped systems and 0 to 100% for underdamped systems Peak Time(tp):- The peak time is the time required for the response to reach the first peak of the time response or first peak overshoot Maximum Overshoot(Mp):- It is the normalized difference between the peak of the time response and steady output.the maximum percent overshoot is defined by:- Settling Time(ts):- The settling time is the time required for the response to reach and stay within specified range(2% to 5%) of its final value. PROCEDURE:- Start-up procedure

21 1. Click on the MATLAB icon. 2. Click on the control system tool box. 3. Open new M-file to write a program. This can be done by click file, new, M-file or ctrl+n. 4. After writing the program save it. It will be saved in work. 5. To run the program, click debug, save and run. 6. To end any current executing operation press ctrl+c. 7. For any help, go to MATLAB help.

22 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering EXPERIMENT NO.:- 8 DESIGNING A CONTROLLER USING BODE PLOT OBJECT:- Design a controller using Bode Plot for the following system: Where Gc(s) is the controller and G(s) is: s + 1 The design must meet the following specifications: Zero steady state error. Maximum overshoot must be less than 40%. Settling time must be less than 2 sec. HARDWARE-SOFTWARE REQUIRED: - Intel(R), Pentium(R) 4 CPU, 20 GHz, and 120 MB of RAM and MATLAB software THEORY: - There are two ways of solving this problem: one is graphical and the other is numerical. Within MATLAB, the graphical approach is best, so that is the approach we will use. First, let's look at the Bode plot. There are several characteristics of the system that can be read directly from this Bode plot. First of all, we can see that the bandwidth frequency is around 10 rad/sec. Since the bandwidth frequency is roughly the same as the natural frequency (for a first order system of this type), the rise time is 1.8/BW=1.8/10=1.8 seconds. This is a rough estimate, so we will say the rise time is about 2 seconds.

23 The phase margin for this system is approximately 95 degrees. The relation damping ratio = pm/100 only holds for PM < 60. Since the system is first-order, there should be no overshoot. The last major point of interest is steady-state error. The steady-state error can be read directly off the Bode plot as well. The constant (Kp, Kv, or Ka) is found from the intersection of the low frequency asymptote with the w=1 line. Just extend the low frequency line to the w=1 line. The magnitude at this point is the constant. Since the Bode plot of this system is a horizontal line at low frequencies (slope = 0), we know this system is of type zero. Therefore, the intersection is easy to find. The gain is 20dB (magnitude 10). What this means is that the constant for the error function it 10. The steady-state error is 1/(1+Kp)=1/(1+10)= Let's check our predictions by looking at a step response plot. This can be done by adding the following two lines of code into the MATLAB command window As you can see, our predictions were very good. The system has a rise time of about 2 seconds, has no overshoot, and has a steady-state error of about 9%. Now we need to choose a controller that will allow us to meet the design criteria. We choose a PI controller because it will yield zero steady state error for a step input. Also, the PI controller has a zero, which we can place. This gives us additional design flexibility to help us meet our criteria. Recall that a PI controller is given by: K*(s+a) Gc(s) = S The first thing we need to find is the damping ratio corresponding to a percent overshoot of 40%. Plugging in this value into the equation relating overshoot and damping ratio (or consulting a plot of this relation), we find that the damping ratio corresponding to this overshoot is approximately Therefore, our phase margin should be at least 30 degrees. From our Ts*Wbw vs damping ratio plot, we find that Ts*Wbw ~ 21. We must have a bandwidth frequency greater than or equal to 12 if we want our settling time to be less than 1.75 seconds which meets the design specs. Now that we know our desired phase margin and bandwidth frequency, we can start our design. Remember that we are looking at the open-loop Bode plots. Therefore, our bandwidth frequency will be the frequency corresponding to a gain of approximately -7 db. Our phase margin and bandwidth frequency are too small. We will add gain and phase with a zero. Let's place the zero at 1. It turns out that the zero at 1 with a unit gain gives us a satisfactory answer. Our phase margin is greater than 60 degrees (even less overshoot than expected) and our bandwidth frequency is approximately 11 rad/s, which will give us a satisfactory response. Although satisfactory, the response is not quite as good as we would like. Therefore, let's try to get a higher bandwidth frequency without changing the phase margin too much. Let's try to increase the gain to 5 and see what happens. This will make the gain shift and the phase will remain the same. As you can see, our response is better than we had hoped for. However, we are not always quite as

24 lucky and usually have to play around with the gain and the position of the poles and/or zeros in order to achieve our design requirements. PROCEDURE:- Start-up procedure 1. Click on the MATLAB icon. 2. Click on the control system tool box. 3. Open new M-file to write a program. This can be done by click file, new, M-file or ctrl+n. 4. After writing the program save it. It will be saved in work. 5. To run the program, click debug, save and run. 6. To end any current executing operation press ctrl+c. 7. For any help, go to MATLAB help.

25 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering OBJECT: - EXPERIMENT No:- 9 TEST OF CONTROLLABILITY AND OBSERVABILITY Find the given state space model or transfer function is controllable and observable or not using MATLAB. HARDWARE-SOFTWARE REQUIRED: - Intel(R), Pentium(R) 4 CPU, 20 GHz, and 120 MB of RAM and MATLAB software. THEORY: - Controllability:- A control system is said to be completely state controllable if it is possible to transfer the system from any arbitrary initial state to any desired state (also an arbitrary state) in a finite time period. That is, a control system is controllable if every state variable can be controlled in a finite time period by some unconstrained control signal. If any state variable is independent of the control signal, then it is impossible to control this state variable therefore the system is uncontrollable. Observability:- A control system is said to be completely observable if every initial state x(t0) can be determined from the observation of y(t) over a finite time interval, t0<=t<=t1. The system, therefore, is completely observable if every transition of the state eventually affects every element of the output vector. The concept of observability is useful in solving the problem of reconstructing unmeasurable state variables from measurable variables in the minimum

26 possible length of time. PROCEDURE:- Start-up procedure 1. Click on the MATLAB icon. 2. Click on the control system tool box. 3. Open new M-file to write a program. This can be done by click file, new, M-file or ctrl+n. 4. After writing the program save it. It will be saved in work. 5. To run the program, click debug, save and run. 6. To end any current executing operation press ctrl+c. 7. For any help, go to MATLAB help.

27 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering EXPERIMENT No.: 10 OBJECT: - TO STUDY THE OPERATION OF A TYPE 1 CONTROL SYSTEM APPARATUS : 1. Trainer Kit. 2. Test Signal Generator 3. Digital Multi-meters- 2 Nos. PROCEDURE: 1. Connect the required supply & the switch on the unit. See that supply LED glow on. TIME RESPONSE ANALYSIS:- A- FOR STEP SIGNAL. 1. Connect test signal generator output to the input terminal of the trainer kit. 2. Connect Digital Multi-meter each at the i/p & o/p terminals. 3. Switch on the test signal generator and select STEP SIGNAL for the o/p. 4. Adjust step signal by STEP ADJ potentiometer for 1v, 2v, 3v, & for each reading, observe & record the o/p voltage in the observation table Repeat the above procedures for different settings of T. 6. From the readings calculate steady state error per unit step i/p & plot i/p, o/p graphs. B- FOR RAMP SIGNAL. 1. Select ramp signal from the test signal generator. Keep toggle switch is in discharge position. 2. Keep digital multi-meter at the i/p & o/p terminals for 0-300mv, or 0-2v range. 3. Make toggle switch in restart position & ramp signal will be available at the i/p terminal of the trainer kit.

28 4. Input voltage will go on increasing at a predefined rate. Observe input & output meter simultaneously & the record the o/p voltage for different i/p voltage at 10mv, 20mv, 30mv,, 250mv. 5. Record your observations from the reading analyzes steady state error & plot i/p & o/p graph. C- FOR PARABOLIC SIGNAL. 1. Select parabolic signal from the test signal generator. keep the toggle switch in discharge position. 2. Connect digital multi-meter at the i/p & o/p terminals of the trainer kit. 3. Also connect the test signal generator output terminals of the trainer kit. 4. Observe the i/p & o/p meter simultaneously & the record the o/p voltage for different t i/p voltages. Record your observation in table-iii A. STEP INPUT. OBSERVATION TABLE I S.No. INPUT OUTPUT ERROR ERROR/STEP R(S) C(S) R(S) - C(S) (R(S)-C(S)) / R(S)

29 OBSERVATION TABLE II B. RAMP INPUT. S.no. INPUT OUTPUT ERROR R(S) C(S) R(S) - C(S) OBSERVATION TABLE III C. FOR PARABOLIC INPUT. S.no. INPUT OUTPUT ERROR TIME IN SECONDS R(S) C(S) R(S) - C(S)

30 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering EXPERIMENT No.: 11 OBJECT: - TO STUDY THE OPERATION OF A TYPE 2 CONTROL SYSTEM APPARATUS : 1. Trainer Kit. 2. Test Signal Generator 3. Digital Multimeteres- 2 Nos. PROCEDURE: 1. Connect the required supply & the switch on the unit see that supply LED glow on. TIME RESPONSE ANALYSIS :- A- FOR STEP SIGNAL. 1. Connect test signal generator output to the input terminal of the trainer kit. 2. Connect Digital Multimeter each at the i/p & o/p terminals. 3. Switch on the test signal generator and select STEP SIGNAL for the o/p. 4. Adjust step signal by STEP ADJ potentiometer for 1v, 2v, 3v, & for each reading, observe & record the o/p voltage in the observation table Repeat the above procedures for different settings of K.T. 6. From the readings calculate steady state error per unit step i/p & plot i/p, o/p graphs. B- FOR RAMP SIGNAL. 1. Select ramp signal from the test signal generator keep toggle switch is in discharge position. 2. Keep digital multimeter at the i/p & o/p terminals for 0-300mv, or 0-2v range. 3. Make toggle switch in restart position & ramp signal will be available at the i/p terminal of the trainer kit.

31 4. Input voltage will go on increasing at a prefined rate observe input & output meter simultaneously & the record the o/p voltage for different i/p voltage at 10mv, 20mv, 30mv,, 250mv. 5. Record your observations from the reading analyze steady state error & plot i/p & o/p graph. C- FOR PARABOLIC SIGNAL. 1. Select parabolic signal from the test signal generator keep the toggle switch in discharge position. 2. Connect digital multimeter at the i/p & o/p terminals of the trainer kit. 3. Now keep the toggle switch of test signal generator in the restart position the parabolic signal is available at the output. 4. Observe the i/p & o/p meter simultaneously & the record the o/p voltage for different i/p voltage record your observation. OBSERVATION TABLE I STEP INPUT. S.no. INPUT OUTPUT ERROR ERROR/STEP R(S) C(S) R(S) - C(S) (R(S)-C(S)) / R(S)

32 OBSERVATION TABLE II RAMP INPUT. S.no. INPUT OUTPUT ERROR R(S) C(S) R(S) - C(S) OBSERVATION TABLE II FOR PARABOLIC INPUT. S.no. INPUT OUTPUT ERROR TIME IN SECONDS R(S) C(S) R(S) - C(S)

33 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering EXPERIMENT No.: 12 OBJECT: - TO STUDY THE PRINCIPLE AND OPERATION OF A BASIC FEED BACK CONTROL SYSTEM APPARATUS: 1. Trainer Kit. 2. Digital Multimeteres- 2 Nos PROCEDURE: 1. Connect the digital multimeter at the terminals marked µa. 2. Adjust the input command Adj potentiometer P1 at the position marked A. 3. Set the disturbance Adj potentiometer P2 at the 0 point position marked A. 4. Connect the digital voltmeter at the terminals marked controlled output. 5. Connect the required supply & the switch ON the unit sees that the supply LED glows. 6. Not the changes voltages at the output of the feedback controller. You will observe that as the output voltage approach s the input voltage. 7. Note the output voltage at the instant the relay is switched off. 8. Observe the switching ON-OFF action of the relay as output voltage approaches the set voltage. 9. Very the disturbances signal & observe its effect. 10. Repeat the above procedure for different settings & conclude your results.

34 Name of Laboratory : Control System Lab Subject Code : EX 602 Name of Department : Electrical Engineering Lab-Quiz 1. In an open loop control system (a) Output is independent of control input (b) Output is dependent on control input (c) Only system parameters have effect on the control output (d) None of the above 2. For open control system which of the following statements is incorrect? (a) Less expensive (b) Recalibration is not required for maintaining the required quality of the output (c) Construction is simple and maintenance easy (d) Errors are caused by disturbances 3. A control system in which the control action is somehow dependent on the output is known as (a) Closed loop system (b) Semiclosed loop system (c) Open system (d) None of the above 4. In closed loop control system, with positive value of feedback gain the overall gain of the system will (a) decrease (b) increase (c) be unaffected (d) any of the above 5. Which of the following is an open loop control system? (a) Field controlled D.C. motor (b) Ward leonard control (c) Metadyne (d) Stroboscope 6. Which of the following statements is not necessarily correct for open control system? (a) Input command is the sole factor responsible for providing the control action (b) Presence of non-linearities causes malfunctioning (c) Less expensive (d) Generally free from problems of non-linearities 7. In open loop system (a) the control action depends on the size of the system (b) the control action depends on system variables (c) the control action depends on the input signal (d) the control action is independent of the output 8 has tendency to oscillate. (a) Open loop system

35 (b) (c) (d) Closed loop system Both (a) and (b) Neither (a) nor (b) 9. A good control system has all the following features except (a) good stability (b) slow response (c) good accuracy (d) sufficient power handling capacity 10. A car is rtyining at a constant speed of 50 km/h, which of the following is the feedback element for the driver? (a) Clutch (b) Eyes (c) Needle of the speedometer (d) Steering wheel (e) None of the above 11. The initial response when tne output is not equal to input is called (a) Transient response (b) Error response (c) Dynamic response (d) Either of the above 12. A control system working under unknown random actions is called (a) computer control system (b) digital data system (c) stochastic control system (d) adaptive control system 13. An automatic toaster is a loop control system. (a) open (b) closed (c) partially closed (d) any of the above 14. Any externally introduced signal affecting the controlled output is called a (a) feedback (b) stimulus (c) signal (d) gain control 15. A closed loop system is distinguished from open loop system by which of the following? (a) Servomechanism (b) Feedback (c) Output pattern (d) Input pattern 16 is a part of the human temperature control system. (a) Digestive system (b) Perspiration system (c) Ear (d) Leg movement

36 17. By which of the following the control action is determined when a man walks along a path? (a) Brain (b) Hands (c) Legs (d) Eyes 18 is a closed loop system. (a) Auto-pilot for an aircraft (6) Direct current generator (c) Car starter (d) Electric switch 19. Which of the following devices are commonly used as error detectors in instruments? (a) Vernistats (b) Microsyns (c) Resolvers (d) Any of the above 20. Which of the following should be done to make an unstable system stable? (a) The gain of the system should be decreased (b) The gain of the system should be increased (c) The number of poles to the loop transfer function should be increased (d) The number of zeros to the loop transfer function should be increased 21 increases the steady state accuracy. (a) Integrator (b) Differentiator (c) Phase lead compensator (d) Phase lag compensator 22. A.C. servomotor resembles (a) two phase induction motor (b) Three phase induction motor (c) direct current series motor (d) universal motor 23. As a result of introduction of negative feedback which of the following will not decrease? (a) Band width (b) Overall gain (c) Distortion (d) Instability 24. Regenerative feedback implies feedback with (a) oscillations (b) step input (c) negative sign (d) positive sign 25. The output of a feedback control system must be a function of (a) reference and output (b) reference and input (e) input and feedback signal (d) output and feedback signal

37 26 is an open loop control system. (a) Ward Leonard control (b) Field controlled D.C. motor (c) Stroboscope (d) Metadyne 27. A control system with excessive noise, is likely to suffer from (a) saturation in amplifying stages (b) loss of gain (c) vibrations (d) oscillations 28. Zero initial condition for a system means (a) input reference signal is zero (b) zero stored energy (c) ne initial movement of moving parts (d) system is at rest and no energy is stored in any of its components 29. Transfer function of a system is used to calculate which of the following? (a) The order of the system (b) The time constant (c) The output for any given input (d) The steady state gain 30. The band width, in a feedback amplifier. (a) remains unaffected (b) decreases by the same amount as the gain increase (c) increases by the sane saaaajajt as the gain decrease (d) decreases by the same amount as the gain decrease 31. On which of the following factors does the sensitivity of a closed loop system to gain changes and load disturbances depend? (a) Frequency (b) Loop gain (c) Forward gain (d) All of the above 32. The transient response, with feedback system, (a) rises slowly (b) rises quickly (c) decays slowly (d) decays quickly 33. The second derivative input signals modify which of the following? (a) The time constant of the system (b) Damping of the system (c) The gain of the system (d) The time constant and suppress the oscillations (e) None of the above 34. Which of the following statements is correct for any closed loop system? (a) All the co-efficients can have zero value (6) All the co-efficients are always non-zero

38 (c) Only one of the static error co-efficients has a finite non-zero value (d) None of the above 35. Which of the following statements is correct for a system with gain margin close to unity or a phase margin close to zero? (a) The system is relatively stable (b) The system is highly stable (c) The system is highly oscillatory (d) None of the above 36. Due to which of the following reasons excessive bond width in control systems should be avoided? (a) It leads to slow speed of response (b) It leads to low relative stability (c) Noise is proportional to band width (d) None of the above 37. In a stable control system backlash can cause which of the following? (a) Underdamping (b) Overdamping (c) Poor stability at reduced values of open loop gain (d) Low-level oscillations 38. In an automatic control system which of the following elements is not used? (a) Error detector (b) Final control element (c) Sensor (d) Oscillator 39. In a control system the output of the controller is given to (a) final control element (b) amplifier (c) comparator (d) sensor (e) none of the above 40. A controller, essentially, is a (a) sensor (b) clipper (c) comparator (d) amplifier 41. Which of the following is the input to a controller? (a) Servo signal (b) Desired variable value (c) Error signal (d) Sensed signal 42. The on-off controller is a system. (a) digital (b) linear (c) non-linear (d) discontinuous

39 43. The capacitance, in force-current analogy, is analogous to (a) momentum (b) velocity (c) displacement (d) mass 44. The temperature, under thermal and electrical system analogy, is considered analogous to (a) voltage (b) current (c) capacitance (d) charge (e) none of the above 45. In electrical-pneumatic system analogy the current is considered analogous to (a) velocity (b) pressure (c) air flow (d) air flow rate 46. In liquid level and electrical system analogy, voltage is considered analogous to (a) head (b) liquid flow (c) liquid flow rate (d) none of the above 47. The viscous friction co-efficient, in force-voltage analogy, is analogous to (a) charge (b) resistance (c) reciprocal of inductance (d) reciprocal of conductance (e) none of the above 48. In force-voltage analogy, velocity is analogous to (a) current (b) charge (c) inductance (d) capacitance 49. In thermal-electrical analogy charge is considered analogous to (a) heat flow (b) reciprocal of heat flow (c) reciprocal of temperature (d) temperature (e) none of the above 50. Mass, in force-voltage analogy, is analogous to (a) charge (b) current (c) inductance (d) resistance 51. The transient response of a system is mainly due to (a) inertia forces

40 (b) internal forces (c) stored energy (d) friction 52 signal will become zero when the feedback signal and reference signs are equal. (a) Input (b) Actuating (c) Feedback (d) Reference 53. A signal other than the reference input that tends to affect the value of controlled variable is known as (a) disturbance (b) command (c) control element (d) reference input 54. The transfer function is applicable to which of the following? (a) Linear and time-in variant systems (b) Linear and time-variant systems (c) Linear systems (d) Non-linear systems (e) None of the above 55. From which of the following transfer function can be obtained? (a) Signal flow graph (b) Analogous table (c) Output-input ratio (d) Standard block system (e) None of the above 56 is the reference input minus the primary feedback. (a) Manipulated variable (b) Zero sequence (c) Actuating signal (d) Primary feedback 57. The term backlash is associated with (a) servomotors (b) induction relays (c) gear trains (d) any of the above 58. With feedback increases. (a) system stability (b) sensitivity (c) gain (d) effects of disturbing signals 59. By which of the following the system response can be tested better? (a) Ramp input signal (b) Sinusoidal input signal (c) Unit impulse input signal (d) Exponentially decaying signal

41 60. In a system zero initial condition means that (a) The system is at rest and no energy is stored in any of its components (b) The system is working with zero stored energy (c) The system is working with zero reference signal 61. In a system low friction co-efficient facilitates (a) reduced velocity lag error (b) increased velocity lag error (c) increased speed of response (d) reduced time constant of the system 62. Hydraulic torque transmission system is analog of (a) amplidyne set (b) resistance-capacitance parallel circuit (c) motor-generator set (d) any of the above 63. Spring constant in force-voltage analogy is analogous to (a) capacitance (b) reciprocal of capacitance (c) current (d) resistance 64. The frequency and time domain are related through which of the following? (a) Laplace Transform and Fourier Integral (b) Laplace Transform (c) Fourier Integral (d) Either (b) or (c) 65. An increase in gain, in most systems, leads to (a) smaller damping ratio (b) larger damping ratio (c) constant damping ratio (d) none of the above 66. Static error co-efficients are used as a measure of the effectiveness of closed loop systems for specified input signal. (a) acceleration (b) velocity (c) position (d) all of the above 67. A conditionally stable system exhibits poor stability at (a) low frequencies (b) reduced values of open loop gain (c) increased values of open loop gain (d) none of the above 68. The type 0 system has at the origin. (a) no pole (b) net pole (c) simple pole

42 (d) two poles (e) none of the above 69. The type 1 system has at the origin. (a) no pole (b) net pole (c) simple pole (d) two poles 70. The type 2 system has at the origin. (a) no net pole (b) net pole (c) simple pole (d) two poles 71. The position and velocity errors of a type-2 system are (a) constant, constant (b) constant, infinity (c) zero, constant (d) zero, zero 72. Velocity error constant of a system is measured when the input to the system is unit function. (a) parabolic (b) ramp (c) impulse (d) step 73. In case of type-1 system steady state acceleration is (a) unity (b) infinity (c) zero (d) If a step function is applied to the input of a system and the output remains below a certain level for all the time, the system is (a) not necessarily stable (b) stable (c) unstable (d) always unstable (e) any of the above 75. Which of the following is the best method for determining the stability and transient response? (a) Root locus (b) Bode plot (c) Nyquist plot (d) None of the above 76. Phase margin of a system is used to specify which of the following? (a) Frequency response (b) Absolute stability (c) Relative stability (d) Time response

43 77. Addition of zeros in transfer function causes which of the following? (a) Lead-compensation (b) Lag-compensation (c) Lead-lag compensation (d) None of the above 78. technique is not applicable to nonlinear system? (a) Nyquist Criterion (b) Quasi linearization (c) Functional analysis (d) Phase-plane representation 79. In order to increase the damping of a badly underdamped system which of following compensators may be used? (a) Phase-lead (b) Phase-lag (c) Both (a) and (b) (d) Either (a) and (b) (e) None of the above 80. The phase lag produced by transportation relays (a) is independent of frequency (b) is inverseh'proportional to frequency (c) increases linearly with frequency (d) decreases linearly with frequency 81. In a stable control system saturation can cause which of the following? (a) Low-level oscillations (b) High-level oscillations (c) Conditional stability (d) Overdamping 82. Which of the following can be measured by the use of a tacho-generator? (a) Acceleration (b) Speed (c) Speed and acceleration (d) Displacement (e) None of the above 83 is not a final control element. (a) Control valve (b) Potentiometer (c) Electro-pneumatic converter (d) Servomotor 84. Which of the following is the definition of proportional band of a controller? (a) The range of air output as measured variable varies from maximum to minimum (b) The range of measured variables from set value (c) The range of measured variables through which the air output chan ges from maximum to minimum (d) Any of the above (e) None of the above 85. In pneumatic control systems the control valve used as final control element converts

44 (a) (b) (c) (d) (e) pressure signal to electric signal pressure signal to position change electric signal to pressure signal position change to pressure signal none of the above 86. Pressure error can be measured by which of the following? (a) Differential bellows and straingauge (b) Selsyn (c) Strain gauge (d) Strain gauge and potentiometer 87. Which of the following devices is used for conversion of co-ordinates? (a) Microsyn (b) Selsyn (c) Synchro-resolver (d) Synchro-transformer 88. The effect of error damping is to (a) provide larger settling lime (b) delay the response (c) reduce steady state error (d) any of the above (e) none of the above 89 technique gives quick transient and stability response (a) Root locus (b) Bode (c) Nyquist (d) Nichols 90. A phase lag lead network introduces in the output (a) lag at all frequencies (b) lag at high frequencies and lead at low frequencies (c) lag at low frequencies and lead at high frequencies (d) none of the above 91. Which of the following is the non-linearity caused by servomotor? (a) Static friction (b) Backlash (c) Saturation (d) None of the above 92 can be extended to systems which are time-varying? (a) Bode-Nyquist stability methods (b) Transfer functions (c) Root locus design (d) State model representatives 93. When the initial conditions of a system are specified to be zero it implies that the system is (a) at rest without any energy stored in it (b) working normally with reference input (c) working normally with zero reference input

45 (d) at rest but stores energy 94. Which of the following is an electromechanical device? (a) Induction relay (b) Thermocouple (c) LVDT (d) Any of the above (e) None of the above 95. A differentiator is usually not a part of a control system because it (a) reduces damping (b) reduces the gain margin (c) increases input noise (d) increases error 96. If the gain of the critical damped system is increased it will behave as (a) oscillatory (b) critically damped (c) overdamped (d) underdamped (e) none of the above 97. In a control system integral error compensation steady state error (a) increases (b) minimizes (c) does not have any effect on (d) any of the above 98. With feed back reduces. (a) system stability (6) system gain (c) system stability and gain (d) none of the above 99. An amplidyne can give which of the following characteristics? (a) Constant current (b) Constant voltage (c) Constant current as well as constant voltage (d) Constant current, constant voltage and constant power (e) None of the above 100. Which of the following can be measured bylvdt? (a) Displacement (b) Velocity (c) Acceleration (d) Any of the above 101 directly converts temperature into voltage. (a) Thermocouple (b) Potentiometer (c) Gear train (d) LVDT (e) None of the above

46 102. The transfer function technique is considered as inadequate under which of the following conditions? (a) Systems having complexities and non-linearities (b) Systems having stability problems (c) Systems having multiple input dis turbances (d) All of the above 103. Which of the following is the output of a thermocouple? (a) Alternating current (b) Direct current (c) A.C. voltage (d) D.C. voltage (e) None of the above 104. A.C. servomotor is basically a (a) universal motor (b) single phase induction motor (c) two phase induction motor (d) three phase induction motor 105. The first order control system, which is well designed, has a (a) small bandwidth (b) negative time constant (c) large negative transfer function pole (d) none of the above 106. Which of the following is exhibited by Root locus diagrams? (a) The poles of the transfer function for a set of parameter values (b) The bandwidth of the system (c) The response of a system to a step input (d) The frequency response of a system (e) None of the above 107.A good control system has all the following features except a) good stability b) slow response c) good accuracy d) sufficient power handling capacity 108.In open loop system a) the control action depends on the size of the system b) the control action depends on system variables c) the control action depends on the input signal d) the control action is independent of the output 109.The initial response when tne output is not equal to input is called a) Transient response b) Error response c) Dynamic response d) Either of the above 110.For open control system which of the following statements is incorrect?

47 a) Less expensive b) Recalibration is not required for maintaining the required quality of the output c) Construction is simple and maintenance easy d) Errors are caused by disturbances 111.Which of the following statements is not necessarily correct for open control system? a) Input command is the sole factor responsible for providing the control action b) Presence of non-linearities causes malfunctioning c) Less expensive d) Generally free from problems of non-linearities 112.Which of the following is an open loop control system? a) Field controlled D.C. motor b) Ward leonard control c) Metadyne d) Stroboscope 113. A control system in which the control action is somehow dependent on the output is known as a) Closed loop system b) Semiclosed loop system c) Open system d) None of the above 114. The output of a feedback control system must be a function of a) reference and output b) reference and input c) input and feedback signal d) output and feedback signal 115.A control system working under unknown random actions is called a) computer control system b) digital data system c) stochastic control system d) adaptive control system 116.Regenerative feedback implies feedback with a) oscillations b) step input c) negative sign d) positive sign 117. By which of the following the control action is determined when a man walks along a path? a) Brain b) Hands c) Legs d) Eyes 118.A closed loop system is distinguished from open loop system by which of the following? a) Servomechanism b) Feedback c) Output pattern d) Input pattern 119.In closed loop control system, with positive value of feedback gain the overall gain of the system will