LMECE325

1 LABORATORY MANUAL ECE 325 CONTROL SYSTEM LAB Name of the Student : Registration Number/Roll No : Section and Group : School of Electrical and Electronics Engineering 2 Table of Content S. No.Title of ExperimentPage No. 1.Error Detector Characteristics: Error Detector Characteristics and Control Applications of the following.(i) LVDT(ii) Potentiometer 3 2. Servomotor: To obtain the Transfer Function and Control Characteristics of DC/AC Servo Motor 11 3.Operational Characteristic of Stepper Motor: To obtain the Operational Characteristics for the Control Application of Stepper Motor 17 4.Operational Characteristic of Temperature Detectors.: To obtain the Operational Characteristics for the Control Application of Temperature Detectors (Thermisters, Thermocouple etc.) 21 5.Step Response: To Study the Step Response and Feed Back Properties for Ist and 2nd order system. 24 6.Simulation Using MATLAB: Simulation of control systems using MATLAB for Controllers and different Plots 27 7.Comparision of different Control action: Comparisons of different Control Action (P/I/D/Relay) on Industrial Process (Pneumatic/ Simulated System 30 8.Design of Compensator: To obtain the Frequency Response Characteristics and Design of Compensator for a given system 35 9.Position Control Performances: To obtain the Position Control performance of DC Servo Motor. 38 10.Performance Analysis: Performance Analysis of Thermal System and Design using PID/Relay Control 44 3 EXPERIMENT NO. 1 (a) Aim : To study the performance characteristics of an angular position error detector using two potentiometers. Apparatus: Set up comprises of : Signal Sources : There are two built in sources for operating the error detector. These are, d.c. : IC regulated +5Va.c. : 400Hz, 1.2V p-p Measurement : A 312digit DVM is available on the panel for the measurement of d.c. signals. For a.c. measureements an external CRO will be required. Building Blocks: (a)Error detector : the basic error detector consists of two servo-potentiometers with calibrated dials of 10 resolution mounted on the panel. A common a.c./d.c. (selected by a switch) signal is internally connected to these, and the potentiometer outputs are permanently wired to a unity gain instrumentation amplifier. The poutput of the instrumentation amplifier is brought out on the panel. This constitutes the error detector. (b) Demodulator : this block is neede during the operation of the potentiometer. The a.c. output of the potentiometer may be connected to the demodulator input and the output obtained is a phase-sensitive d.c. signal. Power supply : the unit has an internal 12V I.C. regulated supply which is permanently connected to all the circuits. The power supply and the circuits are short-circuit protected. No external a.c. or d.c. supply may be connected to the sockets on the front panel.Theory : Potentiometer is an important component of a feedback position control. Potentiometers are also used in open loop system for the purpose of monitoring the angular position of a shaft. Other devices which find similar application include optical encoders, synchros, electromagnetic transducers and specialized potentiometers like sine-cosine potentiometer etc., although a good quality linear potentiometer is perhaps the most common. A potentiometer is an electromagnetic transducer which converts angular or linear displacement into a proportional electrical voltage. When a reference voltage is applied across the fixed terminals of the potentiometer, the output voltage measured at the variable terminal is proportional to the input displacement Rotary potentiometers are commonly available in single turn or 3 turn/10 turn varieties. These have restricted motion, with mechanicals stops at both ends. Special servo-potentiometers are also available with unrestricted motion, however, they have a gap of about 50 in their electrical 4 circuits. These potentiometers are normally wire wound for long rotational life but have finite resolution. The resistance tolerance and linearity are also excellent. Output voltagee(t) may be written ase(t) = Ke () (1) where () is the shaft position and Ke is the constant of propeortionality, Ke = , ,(2) Use of two potentiometers in parallel, supplied from the same source, enables a comparison of two shaft positions a reference shaft and a controlled shaft. The output voltage taken across the variable points of the two potentiometers maybe expressed as e(t) = Ke [1() 2()] = Ke

() (3) and the circuit is also represented as an error detector block. On the other hand, in potentiometer error detector supplied with a.c. signal (carrier) v(t) = V sin

, the error output is given bye(t) =Ke

(4) where

is the angular error between reference and controlled potentiometers. It may be seen from above that whenever

changes sign there is a 1800 phase shift in e(t). Again considering a sinusoidal angular error,

() = sin

e(t) may be represented as a suppressed carrier signal given by e(t) = 12

[cos(

) cos (

+

)] (5) when the above signal is applied to a 2-phase servomotor, the motor acts as a demodulator and the direction of shaft movement is in accordance with the sign of

. A d.c. motor may be used instead, provided a balanced demodulator is used to extract the direction information from the signal of equation (5). An integrated circuit balanced modulator/demodulator type LM1496 has been used in the present unit for this purpose. In this circuit, the modulating signal e(t) = Ks

, is multiplied by the carrier signal of amplitude V to yield, e (t) = Ks

V sin

The above signal is passed through a low pass filter to remove the 2

component to yield the output 5 eo(t) =

2

this may then be amplified by a d.c. amplifier before feeding to a d.c. motor Procedure :(A) Linearity and Range of potentiometer The linearity of a potentiometer may be defined as the maximum percentage deviation of the output voltage from its ideal value. This may be better appreciated from a graph between the potentiometer output and shaft position. Again, the range of the potentiometer indicates the angle through which a proportional output is available in the potentiometer.1.Set the excitation switch to DC 2.Keep POT 2 fixed at any position and do not disturb its position. Let this position be 2 3.Turn POT 1 in steps of 200 (at 10 interval when there is a sudden change in voltage). Record angular position 1 and the output V0 4.Plot V0 vs 1. Observe linearity and range. 5.Repeat for another position of POT 2 6.From the readings, plot V0 versus

(=12) . If this plot is not a straight line, draw a straight line approximation. Calculate the slope of this line as, Slope = Ke = = 0

Sr. No.1

2V0 Table 1 (B) A.C. excitation 1. Display the CARRIER on the CRO and measure its amplitude and frequency. 2. Switch the EXCITATION to AC. Now observe Vo on a CRO while turning either POT 1 or POT 2 very slowly. Use the internal CARRIER for external triggering of the CRO. Notice and record how phase of V0 changes when

(= 1 2) changes sign. 3. Record and plot peak-to-peak (or r.m.s) V0 as a function of

. Note that the information about the sign of

is lost. 4. Next connect V0 to the input of the BALANCED DEMODULATOR and its output to the DVM. 6 5. Record and plot the demodulator output VDEM as a function of

. Note that the information about the sign of

is restored. Sr. No.1

2VDEM Table 2 Graph : Plot between V0 and

has to be plotted. 7 EXPERIMENT NO 1 (b) Aim : To study the characteristics of synchros error detector Apparatus Required: Various components of synchros error detector are: The unit has one pair of transmitter-receiver synchros motors, powered by an isolated 60 volt ac inbuilt supply. Socketsarebroughtuponthepaneltomakeconnectionswithattenuatedcompensatedoutputin ratio 1:10 for waveform observation.The synchro pair is well mounted inside steel cabinate and dials printed in degrees with resolution of 20 provided to study phase/displacement errors.ThebottomofcabinateiscoveredwithseethroughPerspexsheetfordemonstrationpurposes. Thecontrolknobsarefactoryadjustedforelectricalzero.Completeunitis220voltacmain operable. Theory:Synchrosaresmallmotorswhichareusedforremotetransmissionofshaftangular positioninACservosystems.Thebasicstructureofsynchroiswoundrotorandwoundstator. The windings are mutuallycoupled in such a waythat itgives substantially sinusoidal variation as a function of shaft angular position. The signal transmission unit is mechanically coupled with anothermotorcalledcontroltransformer.Displacementoftransmitterunitdevelopsanoutput error voltage that are in proportion to the the misalignment between both shafts. If the receiving endhasnorotationthenitwillgenerateerrorvoltagewhichareamplifiedandsendtoservo motor to re-correct the position.The synchros has major advantages over potentiometric error detector as a)There is no wear from rotation except non-critical wear at slip ring. b)The operating speed can be much higher than pot. c)Synchro has full 3600 rotation with no electrical break. d)System is highly reliable and possibilities of multispeed operatione)Resolution is better since no stepping effect There are some demerits also a)Synchros has useful range in order of 300 b)Linearity is not much better than modern servo potentiometers. Thesynchrotransmitterhasdumbbellshapedmagneticstructurehavingprimarywindingupon rotor which is connected with the reference voltage Vr , through set of slip rings and brushes. The secondary windings are wound in slotted stator and are distributed around its periphery. Although thewindingsaredistributedbutitactsaspositioned1200apart.Inschematicsthewindingsare 8 shownasthreephaseconfigurationbutonlysinglephasevoltageappearsacrossthem.The magnitude and polarity of these voltages/phase depends upon the angular position of the rotor. Let Vs1n, Vs2n, Vs3n represent the voltages induced in stator coils S1, S2, S3 respectively with respect to the neutral then Vs1n = KVr sinwct cos(+ 2400) ..1 Vs2n = KVr sinwct cos()..2 Vs3n = KVr sinwct cos(+ 1200) 3 The terminal voltages across the stator coil are V23 = 3 KVr sinwct sin(+ 2400) ..4 V31 = 3 KVr sinwct sin().5 V12 = 3 KVr sinwct sin(+ 120)6 Where Vr sinwct is the reference voltage , is the respected angle in degree, K is a constant Thesynchrotransmitter/receiver:Thesynchrotransmitterisconstructedliketwopole alternatorinwhichrotorcoiliswoundonlaminatedcore.Theendsofthecoilarebroughtout throughslipringsandbrushesforelectricalconnectionsanddesignatedasR1,R2.Thestator portion has three coils which are spaced 1200 apart of rotor magnetic meridian. The ends of each coil is connected internally and starts are brought out for electrical connections as S1, S2 and S3. The receiver motor is similar to transmitter. Procedure: 1.Connect CRO one channel with the provided sockets COM and REF in observation block. The reference socket as attenuated 1:10, voltage of Tx, R2 with respect to R1 2.ConnectCROotherchannel,sayBchannelwithoutputsofS1,S2andS3alternately given in observation block, while kept Tx dial to certain position say 00. Note the output inVppanditsphaseanglewithrespecttoREFoutputwaveform.TheS1,S2andS3 sockets are also 1:10 attenuated. 3.Measure the voltage difference between stator sockets S1, S2 and S3 directly(meter range 200VAC) such V12 between S1 and S2, V31 between S3 and S1, V23 between S2 and S3 4.Rotate Tx dial in 300 incremental steps and note voltage magnitude and phase w.r.t input at REF 5.Prepare a table as given in reference from observations. Tx (in degree)S1S2S3 MagnitudePhaseMagnitudePhaseMagnitudePhase 0V180V0V180 9 300V0V180 60V0V0V180 90V000V180 120V0V180V180 150V0V18000 180V0V180V0 21000V180V0 240V180V180V0 270V1800V0 300V180V0V0 330V180V00

The voltage/phase are Vpp measured on CRO with respect to input magnitude and polarity. Tx (in degree)V12V31V23 MagnitudePhaseMagnitudePhaseMagnitudePhase 0 30 60 90 120 150 180 210 240 270 300 330 The voltages should be measured on multimeter (200VAC) with respect to S1-S2, S3-S1 and S2-S3 6.From table 1, plot graphical curves between the voltage/phase of stator terminal 7.Plot another graphical representation between the voltage difference measured in table 2, Vs displacement in . Note the ve number show the out of phase voltage. 10 Worksheet of the student Date of PerformanceRegistration Number: Aim: S.NoTheoreticalSimulationError ValuesValues 1 2 3 4 Calculations: Result and Discussion Graph/Plot: Error Analysis Learning Outcomes (what I have learnt) S.NoParameterMarksMax. Marks 1Understanding of the student about the20 procedure/apparatus. 2Observations and analysis including20 learning outcomes 3Completion of experiment, Discipline and10 Cleanliness Signature of Faculty 11 Experiment No. 2 Aim : : To obtain the Transfer Function and Control Characteristics of DC/AC Servo Motor Apparatus : AC servomotor set up description is as follows: AnAcservomotorisbasicallyatwophaseinductionmotorexceptforcertaindesign feature.Thetwophaseinductionmotorconsistsoftwostatorwindingsoriented900 electricalapartinspaceandexcitedbyACvoltagewhichdifferintime-phaseby900.In figure 1, the schematic diagram for balanced operation of motor is shown where voltages of equalrmsmagnitudeand900phasedifferenceareappliedtothetwophasestator,thus making their respective filed 900 apart in both time and space, resulting in a magnetic field ofconstantmagnituderotatingatsynchronousspeed.Thedirectionofrotationdepends uponphaserelationshipofinputvoltageV1andV2Asthefieldsweepsovertheshort-circuitedrotor,voltagesinducedinitproducingcurrentinit.Therotatingmagneticfield interacts with these currents produce a torque on the rotor in the direction of field rotation. Figure 1 Theshapesoftorque-speedcharacteristicsoftwo-phaseinductionmotorareshownin figure2.Theuseofsuchmotor(a)incontrolapplicationisintolerablebecauseofthe positiveslopewhichprevailsovermostoftheoperatingspeeds.Thepositiveslopecause negative damping to lead instability in control system. In control applications the motor is modified in a way to ensure positive damping over full speed range. A convenient way to obtain the result shown in curve (b) is to design the motor with very high rotor resistance. Wheneverthetwophaseinductionmotorisdesignedwithhighrotorresistanceitis referred as a two-phase AC servomotor. 12 Figure 2 :Torque Speed characteristics of induction motor, 3 = AC servomotor Infeedback control applications phase a is energized with fixed rated voltage oftencalled as Reference, while phase b is energized by variable control voltage called control voltage. Moreover the arrangement is made in this configuration such that the control voltage is set exactly 900 out of phase with the reference voltage. In these instances unbalance operation is really an unbalance in voltage and amplitudes only. If assumption is made both voltages are always at 900 apart in time phase than the quantity p can be defined as p = V1/V2 .(1) where p is the ratio between both voltages. Then the phasor expression for the control voltage becomes, V2 = - j p V1 (2) Thejfactoraccountsforthe900lagbetweenthetwostatorvoltagesandpexpressthe magnitudeofV2asperunitratioofthereferencevoltageV1.Uponinsertingrelation1 into 2 V1a = (V1 + j V2) The expression for the positive sequence voltage becomes V1a = (V1 + j V2) = V1/2(1+ p) (3) 13 Similarly V1b = (V1 - j V2) = V1/2(1+ p) (4) The AC servomotor construction : Two phase AC servomotors are available in a wide variety of the configurations. The most popular type has a squirrel cage rotor with a low ratio of rotor to frame diameter and high rotorresistance.Thistypeofmotorgivesbestoverallperformanceandefficientin convertinginputpower(watts)toshafttorque.Thereareothermotorconfigurationsthat areusedinthespecificapplications,whichincludedrag-cuprotorandsolidironrotor basicallyusedinACtachometerapplication.Themotorusedinthissetuphasfollowing specifications: Two phase AC servomotor ACM DT 15/120 : E (rated) 120 VAC/0.1Amp/phase. Phase split capacitor 1 / 440VAC . Rotor: squirrel cage type, dia 15 mm shaft dia 5 mm. Speed 2500 RPM/100 volts Thecoilswithsimilarconstructionarewired/placedsuchthatthefluxdeveloped900 electrically apart. Under a balanced condition, the windings are excited with equal voltage 900 apart in a time phase with the help of a capacitor seriesed with one of the winding. The motorcurrentthereforegeneratemagneticfieldinanairgapwhichisalsoinaspaceand timequadrature.Therotatingfluxfieldinducesavoltageintherotorconductorswitha magnitude proportional to the relative speed. A P pole, 50 hz winding causes the resultant field to rotate at n rpm, and similar one at 400 Hz will rotate at 8n rpm. The rotor voltage in turn causes currents as a result a torque is developed by interaction of the current carrying conductors and the rotating field. This drags the rotor along after the synchronous field of the stator. Since the rotor must overcome friction, it cant reach synchronous speed. About the set up: ThegivenACservomotorismountedandmechanicallycoupledwithasmallpermanent magnet field DC motor for loading purpose. The AC servomotor is excited by a step down isolatedacsupplyof100volt.Thereferencewindingisconnectedthroughaphasesplit capacitorof1withthesevoltage.Thecontrolwindingisfedthroughaphasecontrol circuitwhichprovidevariablevoltagetoitthroughaphasecontrolcircuitwhichprovide variablevoltagetoitthroughacontrolP1(provideduponthepanel)AswitchS1isalso provided to cut-off the motor from the supply. A pair of sockets is given across the control winding to measure AC applied voltage (E). TheDCmotorwhennotconnectedwiththeprovideddcsupply(switchS2isinoff condition)itgeneratesspeedproportionalvoltageacrossitsterminalsasbackemfEb. Another pair of sockets is given across the motor terminal for this measurement. 14 When DC supply is fed to the DC motor it run in reverse direction of servomotor direction inresultaloadisimposed.TheresultanttorquedevelopedbyDCmotortoovercomeit increases the current through it which is indicated by panel meter. The expression used to determine the developed torque is givenT = 1.019 104 602 gm cm Where P is the power IaEb in watts, N is the speed in RPM Thespeedismeasuredwiththehelpofopto-interruptertransducer.A6holediscis mounted upon the motor shaft interrupt the light falling upon a photo diode which result in generating a narrow pulse train, which is used to trigger a mono-flop circuit. The width of theoutputpulsesofmono-flopisasubjectofthesetriggerpulsesrepetition,whichare rectified, averaged and fed to an analog meter calibrated in terms of RPM.Procedure:1.Switch off the switches S1 and S2. Keep both controls P1 and P2 to minimum (fully counter-clockwise) 2.Switchonthepowersupply,switchesONS1.SlowlyincreasecontrolP1sothat AC servomotor starts rotating.3.Connectdigitalmultimeter(20VDCrange)acrosstheDCmotorsocketsgivenin RED and BLCK color 4.VarythespeedofservomotorgraduallyandnotethespeedNrpmfromthepanel meter,andcorrespondingbackemfdevelopedacrosstheDCmotor.Recordthe observations in table 1. Table 1Sr. No.Speed N in rpmEb in volts 1 2 3 4 5.Connect digital multimeter (range 200 VAC) across the servomotor control winding sockets.NowadjustACservomotorvoltageto80voltAC,E1=80V.Notethe speed in rpm in table 2 6.Switch on S2 to impose load upon the motor. The DC supply although at zero volt but it short out the DC motor armature and fall in speed observed. Note the current Ia and speed from panel meters in steady state condition. 7.IncreasetheloadcurrentbymeansofcontrolP2inslowmannerandnotethe corresponding speed and Ia in steady state condition. Record all the observations in table 2 15 Table 2 : E = ..Vac. No load speed = ..rpm Sr. NoIa AmpereEb VoltSpeedN rpm P wattTorque 8.Preparetable2,fillingtheEbdatafromtable1forthecorrespondingspeeds. Calculate P as P = Ia Eb in watts. Calculate the torque given by the expression T = 1.019 104 602 gm cm 9.Adjust servomotor voltage to another value say E2 = 70 Vac. Repeat the steps 5 to 8 and prepare another table. Prepare more tables for different E. 10. Draw the speed torque characteristics curves. Graph : Draw the plots between torque T and speed N, voltage Eb and speed N. 16 Worksheet of the student Date of PerformanceRegistration Number: Aim: S.NoTheoreticalSimulationError ValuesValues 1 2 3 4 Calculations: Result and Discussion Graph/Plot: Error Analysis Learning Outcomes (what I have learnt) S.NoParameterMarksMax. Marks 1Understanding of the student about the20 procedure/apparatus. 2Observations and analysis including20 learning outcomes 3Completion of experiment, Discipline and10 Cleanliness Signature of Faculty 17 EXPERIMENT NO.3 AIM: - To obtain the Operational Characteristics for the Control Application of Stepper Motor APPARATUS USED: - Stepper Motor Kit, P Kit, Interface Cord and Connecting Leads. THEORY:- Thesteppermotorisaspecialtypeofmotorwhichisdesignedtorotate throughaspecificanglecalledstepforeachelectricalpulsereceivedfromitscontrol unit.Itisusedindigitallycontrolledpositioncontrolsysteminopenloopmode.The input command is in form of a train of pulses to turn the shaft through a specified angle. the main unit is designed to interface with P 8085 kit. The stepper motor controller card remainsactivewhilethepulsesequencegeneratordisabledasgivenplugisconnected with p interface socket. The following program enables the stepper motor to run with p 8085 kit. For two phases four winding stepper motor only four LSB signals are required. CIRCUIT DIAGRAM:- DIRECTION12 V CWCCW PHASE FIELD PULSESTEPPER and PHASEMOTOR SEQ ROTOR DRIVER GEN. Y GRD TRIG PROCEDURE:- Connect the stepper motor with p 8085 kit as shown in fig. press EXMEM key to enter the address as given then press NEXT to enter data . 18 ADDRESSDATA 20003E 80MVIA, 80Initialize port A as output port. 2002D3 03OUT03OB 20043E F9Start MVIAFA 2006D3 00OUT00Output code for step o. 2008CD 3020 call delaydelay between two steps. 200B3E F5MVIA, F6Location reserve for current Delay. 200dD3 OO OUTOOOutput code for step 1. 200FCD 3020 Call delaydelay between two steps. 20123E F6 MVIA, F5 2014D3 OO OUTOOOutput code for step 2. 2016CD 3020calls delaybetween two steps. 20193E FAMVIA, F9.201BD3 OOOUTOOOutput code for step 3. 201DCD 3020 call delaydelay between two steps. 2020C3 04 20JMP STARTStart. PressFILLkeytostoredatainmemoryarea.Thiswillcompletethepulsesequence generation. To delay programme route, first press EXMEM to start, a dot sign will appear in address field then enter the start address. Press NEXT to enter data. ADDRESSDATA 203011 00 00LXID 00 00Generates a delay. 2033CD BC 03 CALLDELAY 203611 00 00LXID 00 00Generates a delay. 2039CD BC 03 CALLDELAY 203CC9RET Press FILL to save data to execute the programmed press the key GO .The above program istorotatethemotorataparticularasdefinedbythegivenaddress.Changingthe following contents will change the motor speed. ADDRESSDATA 203011 00 20AND 2036TO SIMILAR 11 00 20 CHANGE11 00 10TO11 00 10 CHANGE11 00 05TO11 00 05 19 CHANGE11 00 03TO11 00 03. 20123EF6TO3EF5 20193EFATO3EF9. SrNo. of PulsesDisplacementStep Angle No. RESULT:- The stepper motor runs as per fed program. PRECAUTION:- 1.Make the connection of motor with p kit properly.2.Feed the program carefully and correctly.3.Donotchangethemotordirectionathighspeed. 20 Worksheet of the student Date of PerformanceRegistration Number: Aim: S.NoTheoreticalSimulationError Values Values 1 2 3 4 Calculations: Result and Discussion Graph/Plot: Error Analysis Learning Outcomes (what I have learnt) S.NoParameterMarksMax. Marks 1Understanding of the student about the20 procedure/apparatus. 2Observations and analysis including20 learning outcomes 3Completion of experiment, Discipline and10 Cleanliness Signature of Faculty 21 EXPERIMENT NO. 4 Aim: To obtain the Operational Characteristics for the Control Application of Temperature Detectors Apparatus: Resistance temperature detector (PT-100), signal conditioner module, beaker, immersion rod, thermometer. Theory : The resistivity of metals increases with an increase in temperature (i.e. the temperature coefficient is positive), where as in some semiconductors the resistance decreases with an increase in temperature(i.e the temperature coefficient is negative). The resistance thermometer based on the above phenomenon is one of the most accurately reproducible temperature-sensing device. Pt 100 is unduly used as a RTD Sr. NoTemperature (0C)Resistance () 1.00100.00 2.10103.90 3.20107.79 4.30111.67 5.40115.54 6.50119.40 7.60123.24 8.70127.07 9.80130.89 10.90134.70 11.100138.50 Table 1 Signal conditioner module : AC constant current signal is applied on the RTD to make it operative. The output of the RTD is directly fed to the input of D.C. differential amplifier and then is fed to a summing amplifier with some gain and zero adjustment to obtain the output directly in engineering unit of temperature. SET GAIN pot (VR2) is given for the adjustment of amplifier gain and SET ZERO pot (VR1) is given for zero adjustment. Fixed Resistance Source : A 100 and 138.5 fixed resistance is provided with the set-up to calibrate the signal conditioners module for measurement of temperature directly in 0C. Procedure : 1. Throw the SPDT switch towards RTD position given on the front panel. 2. Place a beaker containing water. Place an immersion rod in the beaker. Keep the thermometer and RTD in the beaker. 22 3. Connect the OUTPUT terminals of the signal conditioner (DPM Output) with the digital panel meter. 4. Connect a digital multimeter across the OHMS socket, set the mode of digital multimeter to resistance measurement and set output of fixed resistance at 100 with selector switch. 5. Connect output to the RTD INPUT of signal conditioner. 6. Switch ON the instrument and adjust SET ZERO pot (VR1) so that display will show 00.0 7. Remove output of fixed resistance i.e. OUTPUT from the RTD INPUT. 8. Switch OFF the instrument and select fixed resistance at 138.5 with a selector switch. 9. Connect fixed resistance ( output) to RTD INPUT of signal conditioner. 10. Again switch on the instrument and adjust SET GAIN pot (VR2) so that display wills show 100.0 11. Repeat step 3 to 10 one or two times. 12. Remove resistance lead from the RTD INPUT and connect RTD probe across RTD INPUT. 13. Heat the RTD kept in water and note down the reading of the thermometer. For reference compare the reading with table no. 1 14. To note down the resistance of RTD, throw the OHM/ RTD switch towards OHMS positions. Connect a digital multimeter across OHMS socket and set the mode of DMM to resistance. In this case the DPM of demonstration unit will show infinite reading. 15. Plot the graph between temperature (in 0C) and resistance. Note : For better results take reading in reverse order i.e. from 1000C to 00C (or room temperature) RESULT :Linear curve is obtained between temperature and resistance. 23 Worksheet of the student Date of PerformanceRegistration Number: Aim: S.NoTheoreticalSimulationError ValuesValues Calculations: Result and Discussion Graph/Plot: Error Analysis Learning Outcomes (what I have learnt) ToParameterMarksMax. Marks 1Understanding of the student about the20 procedure/apparatus. 2Observations and analysis including20 learning outcomes 3Completion of experiment, Discipline and10 Cleanliness Signature of Faculty 24 EXPERIMENT NO 5 Aim: To Study the Step Response and Feed Back Properties for 1st and 2nd order system APPARATUS REQUIRED: Computer with MATLAB Theory:First order system These are characterized by one pole and/or a zero. A pure integrator and a single time constant, having transfer function of the form K/s and K/(sT+1), are the only two commonly studied representatives of this class of system.If ()()= () = /then for R(s) = 1/s C(s) = K/ s2 and c(t) = Kt If ()()= () =

+1 , for R(s) = 1/s C(s) = K/(s(sT+1)) and c(t) = 1 e-t/T Second order system 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 the transfer function of a second order system is given by () =

2

2+2

+

2 where is called the damping ratio and

the undampednatural frequency. Depending upon the value of , the poles of the system may be real, repeated or complex conjugate which is reflected in the nature of its step response. Results obtained for various cases are: -Undamped case (0 < < 1) C(t)=

12 sin(

+ 11 2/)Where,

=

1 2 is termed the damped natural frequency. A sketch of the unit step response for various values of is available in the text books. -Critically damped case( = 1) ;c(t)=1-

(1 +

) -Overdamped case ( > 1) : c(t)= 1 -

221 (

21

21

21

+ 21) 25 Delay time , is defined as the time needed for the response to reach 50% of the final value. Rise time,

, is the time taken for response to reach 100% of the final value for the first time. This is given by

=

,where =

112

Peak time,

, is the time taken for the response to reach the first peak of the overshoot and is given by

=

1 2 Maximum overshoot, Mp, is defined by Mp= c (tp)-c()x 100% Setting time, ts, is the time required by the system response to reach and stay within a prescribed tolerance band which is usually taken as 2% or 5%. Procedure : Consider a first order and second order system.Using MATLAB, plot the unit-step response curveofthissystem.Obtaintherisetime,peaktime,maximumovershoot,andsettling time. Result : DISCUSSION:- The Step Response indicates how the system behaves in Transient as well as Steady States. The slope indicates the fastness of the system to reach the required value. The settling time indicates how long the system is going to take to reach steady state value 26 Worksheet of the student Date of PerformanceRegistration Number: Aim: S.NoTheoreticalSimulationError ValuesValues 1 2 3 4 Calculations: Result and Discussion Graph/Plot: Error Analysis Learning Outcomes (what I have learnt) S.NoParameterMarksMax. Marks 1Understanding of the student about the20 procedure/apparatus. 2Observations and analysis including20 learning outcomes 3Completion of experiment, Discipline and10 Cleanliness Signature of Faculty 27 EXPERIMENT NO. 6 AIM: Simulation of control systems using MATLAB for Controllers and different Plots APPARATUS REQUIRED: System with MATLAB THEORY: Frequency Response: The frequency response is the steady state response of a system when the inputto thesystemisasinusoidalsignal.Frequencyresponseanalysisofcontrolsystemcanbe carriedeitheranalyticallyorgraphically.Thevariousgraphicaltechniquesavailablefor frequency response analysis are 1. Bode Plot 2. Polar plot (Nyquist plot) 3. Nichols plot 4. M and N circles 5. Nichols chart Bodeplot:Thebodeplotisafrequencyresponseplotofthetransferfunctionofasystem.A bodeplotconsistsoftwographs.Oneisplotofthemagnitudeofasinusoidaltransferfunction versus log w. The other is plot of the phase angle of a sinusoidal transfer function versus logw. Themainadvantageofthebodeplotisthatmultiplicationofmagnitudecanbeconvertedinto addition. Also a simple method for sketching an approximate log magnitude curve is available. Polar plot: The polar plot of a sinusoidal transfer function G (jw) on polar coordinates as w is varied from zero to infinity. Thus the polar plot is the locus of vectors [G (jw) ] G (jw) as w is varied from zero to infinity. The polar plot is also called Nyquist plot. Nyquist Stability Criterion: If G(s)H(s) contour in the G(s)H(s) plane corresponding to Nyquist contour in s-plane encircles the point 1+j0 in the anti clockwise direction as many times as the number of right half s-plain of G(s)H(s). Then the closed loop system is stable. Root Locus: The root locus technique is a powerful tool for adjusting the location of closed loop poles to achieve the desired system performance by varying one or more system parameters. The path taken by the roots of the characteristics equation when open loop gain K is varied from 0 to infinity are called root loci (or the path taken by a root of characteristic equation when open loop gain K is varied from 0 to infinity is called root locus.) 28 Frequency Domain Specifications: The performance and characteristics of a system in frequency domain are measured in term of frequency domain specifications. The requirements of a system to be designed are usually specified in terms of these specifications. The frequency domain specifications are 1. Resonant peak, Mr 2. Resonant Frequency, wr. 3. Bandwidth. 4. Cut off rate 5. Gain margin 6. Phase margin Resonant Peak, Mr The maximum value of the magnitude of closed loop transfer function is called the resonant peak, Mr. A large resonant peak corresponds to a large over shoot in transient response. Resonant Frequency, wr The bandwidth is the range of frequency for which the system gain is more than -3db. The frequency at which the gain is -3db is called cut off frequency. Bandwidth is usually defined for closed loop system and it transmits the signals whose frequencies are less than cut-off frequency. The bandwidth is a measured of the ability of a feedback system to produce the input signal, noise rejection characteristics and rise time. A large bandwidth corresponds to a small rise time or fast response. Cut-Off Rate: The slope of the log-magnitude curve near the cut off frequency is called cut-off rate. The cut-off rate indicates the ability of the system to distinguish the signal from noise. Gain Margin, Kg The gain margin, Kg is defined as the reciprocal of the magnitude of open loop transfer function at phase cross over frequency. The frequency at with the phase of open loop transfer function is 180 is called the phase cross over frequency, wpc. Phase Margin, g The phase marging, is that amount of additional phase lag at the gain cross over frequency required to bring the system to the verge of instability, the gain cross over frequency wgc is the frequency at which the magnitude of open loop transfer function is unity (or it is the frequency at which the db magnitude is zero). PROCEDURE: 1. Enter the command window of the MATLAB. 2. Create a new M file by selecting File New M File. 3. Type and save the program. 4. Execute the program by either pressing F5 or Debug Run. 5. View the results. 6. Analysis the stability of the system for various values of gain. 29 Worksheet of the student Date of PerformanceRegistration Number: Aim: S.NoTheoreticalSimulationError ValuesValues Calculations: Result and Discussion Graph/Plot: Error Analysis Learning Outcomes (what I have learnt) ToParameterMarksMax. Marks 1Understanding of the student about the20 procedure/apparatus. 2Observations and analysis including20 learning outcomes 3Completion of experiment, Discipline and10 Cleanliness Signature of Faculty 30 EXPERIMENT NO. 7 Aim: To study the characteristics of an analogue PID controller using simulated systems Apparatus:The experimental set up has the following description: ProcessorPlant:Inpracticalsituationtheprocessorplantisthatpartofthesystemwhich produces the desired response under the influence of command signal. Usual processes are higher order,nonlinearfunctionshavingdeadtimeorpuretimedelay.Inprocesscontrolstudiessuch plants are commonly modeled by transfer functions of the form

() =

+1 Where is the time delay in sec, is the effective time constant and K is the dc gain In the present system, the process is an analogue simulation through a few basic building blocks which may be connected suitably to from a variety of processes or plants. These blocks are, (a)Integrator having an approximate transfer function of 10/s (b) Simple pole two identical units, each having a transfer function of 1/(1+0.0155s) (c)Pure time delay a time delay of about 5.64 msec generated by a high order multiple pole approximation of the delay function Controller:ThecontrollerfortheprocessinananalogueProportional-Integral-Derivative(PID) circuitinwhichthePIDparametersareadjustable.Thevaluesmaybesetwithinthefollowing range through 10 turn calibrated potentiometers: Proportional gain, Kc : 0 to 20 Integral Time constant, Ti : 5 to 100 msec Derivative Time Constant, Td : 0 20 msec Error detector : The error detector is a unity gain inverting adder which adds the command signal withthefeedbacksignal.Toensurenegativefeedbackitwouldthereforebenecessarytohave (2n+1) phase shift in the forward path, for n = 0,1,2. Uncommitted Amplifier : It is a unity gain inverting amplifier. This amplifier may be inserted in the loop, if required, to ensure a proper phase angle. Signalsources:thesignalsourcescomprisesofalowfrequencysquareandtriangularwave generator having adjustable amplitude and frequency. The square wave is used as command input tothesystem,whilethetriangularwaveisusedforexternalx-deflectionintheCRO.This arrangementgivesaperfectlysteadydisplayevenuptoverylowfrequenciesandisconvenient for CRO measurements. 31 Power supply and DVM: An IC regulated circuit powers the complete unit. A 312digit DVM of 19.99 volt range mounted on the panel may be used for dc or steady state measuremnets. Also a variable dc in the range 1 (min) available on the panel may be used as a dc input or set point for the system. Theory:Anapproachtowardsimprovingtheperformanceofsystemshasbeenthrough elementarycontrolactionscalledcontroltermsinsertedintheforwardpathofanexisting control system. PID controller The equation of a PID controller is given by () =

() +

() +

()

Where e(t) = error signal m(t) = PID output or plant output Kc = Proportional gain Ki = Integral gain Kd = Derivative gain In Laplace domain the above equation is written as() =

() +

() +

() Analternativerepresentationoftheabove,whichiscommonlyusedinprocesscontrol,isas under: () =

(1 +1

+

) () Where Ti =

= Integral time constant Td =

= Derivative time constant It is easy to develop the structure of PD, PI controllers from above, by substituting Ki = 0 and Kd = 0 respectively 32 Figure 1 In the present unit, the three gains are adjustable in the following range with the help of calibrated 10-turn potentiometers. Kc : 0 to 20; Ki : 0 to 1000; Kd = 0 to 0.01 In the next section, the student finds out the maximum values of Kc, Ki and Kd or in other words the full scale values of these parameters. The potentiometers used are 10 turn types and each turn is divided into 10 parts by the dial scale. Each part is further divided into five divisions so that the total dial range of 0 to 1 has a least count of 0.002. A full revolution of a knob corresponds to a changeof0.1indialreading.Toobtainaparametervalue,multiplythedialsettingbythe correspondingfullscalevalue.Asanexample,ifFSVforP-controlis20thenadialsettingof 0.032 will correspond to a Kc = 0.032x20 = 0.64 Procedure : Controller calibration 1.Apply a square wave signal of 100mV p-p at the input of the error detector. Connect P, I and D outputs to the summer and display controller output on the CRO 2.WithP-potentiometersettomaximumandI-andD-potentiometerssettozero,obtain maximum value of Kc as Kc (max.) = 3.WithI-potentiometersettomaximumandP-andD-potentiometerssettozero,aramp will be seen on CRO. Maximum value of Ki is then given by Ki (max.)= 4 () wherefisthefrequencyofthe input. 4.Set D-potentiometer to maximum and P- and I- potentiometers to zero. A series of sharp pulseswillbeseenontheCRO.ThisisobviouslynotsuitableforcalibratingtheD-potentiometer.Instead,applyingatriangularwaveattheinputoftheerrodetectora square wave is seen on the CRO. Kd (max.) = 4 ()

where f is the frequency of the input signal. 33 5.Set all the three potentiometers- P, I and D to maximum values and apply a square wave input of 100mV (p-p). Observe and trace the step response of the PID controller. Identify the effects of the P, I and D control individually on the shape of this response. Proportional Control 1.Makeconnectionasshowninfigurewiththeprocessmadeupoftimedelayandtime constantblocks.NoticethattheCROoperationintheX-Ymodeensuresstabledisplay even at low frequencies. 2.Set input amplitude to 1 V(p-p) and frequency to a low value. 3.ForvariousvaluesofKc=0.2,0.4measurefromthescreenthevaluesofpeak overshoot and steady state error and tabulate Proportional Integral Control 1.Make connections for the 1st order type-0 system with time delay2.Set input amplitude to 1 V p-p, frequency to a low value and Ki to zero 3.For Kc = 0.6 (say), observe and record the peak overshoot and steady state error. 4.WiththeKcasabove,increaseKiinsmallstepsandrecordpeakovershootandsteady state error. Proportional Integral Derivative Control 1.Makeconnectionsasshowninfigurewithproportional,integralandderivativeblocks connected. 2.Set input amplitude to 1V (p-p), frequency a low value Kc = 0.6, Ki = 54.85 (scale setting of 0.06) and KD = 0 3.Thesystemshowsafairlylargeovershoot.Recordthepeakovershootandsteadystate error. 4.Repeat the above step for a few non-zero values of Kd Figure 2 :CRO display of step response using triangular time base 34 Worksheet of the student Date of PerformanceRegistration Number: Aim: S.NoTheoreticalSimulationError ValuesValues Calculations: Result and Discussion Graph/Plot: Error Analysis Learning Outcomes (what I have learnt) ToParameterMarksMax. Marks 1Understanding of the student about the20 procedure/apparatus. 2Observations and analysis including20 learning outcomes 3Completion of experiment, Discipline and10 Cleanliness Signature of Faculty 35 EXPERIMENT NO. 8 AIM: To obtain the Frequency Response Characteristics and Design of Compensator for a given system APPARATUS REQUIRED: System employed with MATLABTHEORY:Thecontrolsystemsaredesignedtoperformspecifictasks.Whenperformance specificationaregivenforsingleinput.Singleoutputlineartimeinvariantsystems.Thenthe system can be designed by using root locus or frequency response plots. Thefirststepindesignistheadjustmentofgaintomeetthedesiredspecifications.Inpractical system. Adjustment of gain alone will not be sufficient to meet the given specifications. In many cases,increasingthegainmayresultpoorstabilityorinstability.Insuchcase,itisnecessaryto introduceadditionaldevicesorcomponentinthesystemtoalterthebehaviorandtomeetthe desired specifications. Such a redesign or addition of a suitable device is called compensations. A deviceinsertedintothesystemforthepurposeorsatisfyingthespecificationsiscalled compensator. The compensator behavior introduces pole & zero in open loop transfer function to modify the performance of the system. Thedifferenttypesofelectricalorelectroniccompensatorsusedareleadcompensatorandlag compensator. In control systems compensation required in the following situations. 1.Whenthesystemisabsolutelyunstablethencompensationisrequiredtostabilizethesystem and to meet the desired performance. 2. When the system is stable. Compensation is provided to obtain the desired performance. LAG COMPENSATOR: Figure 1 Acompensatorhavingthecharacteristicsofalagnetworkiscalledalagcompensator.Ifa sinusoidal signal is applied to a lag network, then in steady state the output will have a phase lag with respect input. Lagcompensationresultinimprovementinsteadystateperformancebutresultinslower response due to reduced bandwidth. The attenuation due to the lag compensator will shift the gain crossoverfrequencytoalowerfrequencypointwherethephasemarginisacceptable.Thusthe lagcompensatorwillreducethebandwidthofthesystemandwillresultinslowertransient 36 response.Lagcompensatorisessentiallyalowpassfilterandhighfrequencynoisesignalsare attenuated.Ifthepoleintroducebycompensatoriscancelledbyazerointhesystem,thenlag compensator increase the order of the system by one. LEAD COMPENSATOR: Figure 2 Inaleadnetworkzeroisnearertooriginascomparedtopole,hencetheeffectsofzerois dominant, therefore, the phase lead network, when introduced in cascade with forward-path of a transfer function, the phase shift is increased. The bode plot of phase-lead network reveals that the lead network allows to pass high frequencies and low frequencies are attenuated. As thegain isreduced at low frequencies additional gain is needed in the system toaccount for the reduction in gain. PROCEDURE: Without compensator: 1. Write the transfer function of system in command window. 2. Obtain its bode plot and step response. 3.Calculategainmarginandphasemarginfrombodeplot.Calculatetimespecificationsfrom step response. With compensator: 1. Write the appropriate transfer function of compensation network. 2. Obtain the closed loop transfer function with compensator using MATLAB command. 3. Draw its bode plot and step response. 4. Compare the values of gain margin, phase margin and time specifications. 37 Worksheet of the student Date of PerformanceRegistration Number: Aim: S.NoTheoreticalSimulationError ValuesValues Calculations: Result and Discussion Graph/Plot: Error Analysis Learning Outcomes (what I have learnt) ToParameterMarksMax. Marks 1Understanding of the student about the20 procedure/apparatus. 2Observations and analysis including20 learning outcomes 3Completion of experiment, Discipline and10 Cleanliness Signature of Faculty 38 EXPERIMENT NO. 9 Aim : To obtain the Position Control performance of AC Servo Motor Apparatus: The set up comprises two parts, the motor unit and control unit. Motor unit: It consists of two phase ac servomotor. It has the following specifications: (a)Operating voltage : 120 Vac, maximum current 0.15 Amp (b) Rated shaft speed: 2400 rpm, Inertia 4.6 x 10-4 kg/cm2 (c)Torque : 0.085 x 10-2 kg/m The motor drives a potentiometric load throughgear train. Thegear ratio is 1:40 hence the load shaft rotation is 2400/40 = 60 rpm The angular displacement is sensed by a 3600 servo potentiometer. A graduated disc is mounted uponthepotentiometertoindicateangularpositionwith10resolution.Thecompleteunitis housedinseethroughcabinate.Acableisattachedtotheunitwith9pinDtypeconnectorfor connection with the control unit. Controlunit:Itconsistsofpowersupply,servo-amplifier,errordetectorandcommand potentiometer.Thereisfacilitygiventorecordthetransientperiodofpositioncontrolsystem under step signal. The description is as follows: 1.Command signal there are two command signals provided in the control unit. One is the continuouscommandwhichisgivenbyreferencepotentiometer.Thereference potentiometer is also a 3600 servo potentiometer of same value as fitted in the motor unit. Boththepotentiometersareconnectedwithsamereferencesourceof3Vppac,50Hz obtainedfrombuiltintransformer.Socketsareprovidedforboththeoutputsfor measurement purposes. A graduated dial is fitted with the reference potentiometer with 10 resolution. Other command signal is in the form of a step signal of 11 second duration which is activated by briefly pushing upon step key. This signal is added with the reference signal through a relay and quantity is subject to reference dial position. The step command is used for quantative study. 2.ErrordetectorItisatwoinputandoneoutputblock.Oneofthemispositiveoriented for command signals and one negative oriented for feedback. The error detector produces aphasesensitivesignalwithrelativeamplitude.Thissignalformanenvelopease(t), which is followed by an amplifier with variable gain setting. 3.Gain block The gain settings provided upon the panel. This block provide forward path gain KA in equal steps from 3 to 10, selected by a rotary switch provided upon the panel. 39 4.Servo amplifier block the servo amplifier is a push-pull transistorized amplifier operate from 36 V dc supply. Its voltage gain is 20 and its output gas quadrature phase with motor reference winding voltage phase. 5.Waveformcapture/displayblockThetimeresponseofthesystemistooslowfor convenient display upon CRO. This card can capture the event, store it in a RAM and then display the stored contents on CRO for detailed studies. The stored data is erased when a newcapturecycleismade.Thetimeforcapturecycleisabout3.2seconds.InmodeA transient response is recorded, while in mode B error detector envelope is recorded. The unit has built in dc regulated power supplies for all blocks and motor unit reference winding operate upon 110 volt isolated ac supply . Theory : Second order systems are studied in great detail in any course in linear control system. The reason for this is that a large number of higher order practical systems may be approximated asasecondordersystemwhileneglectinglessdominantmodes,nonlinearitieslikedeadzone, saturation,hysteresisetc.assumingthesetohavelittleeffectontheperformance.Alsosecond ordersystemslendthemselvestoasimpleandaccuratemathematicalanalysis.Inthefollowing descriptionweshallfollowtheabovestrategy.Attheendhowever,theimperfectionsdueto nonlinearities must be pointed out. Position Control- a second order system A second order system is represented in the standard form as, () =

2

2+2

+

2 where is called the damping ratio and

the undampednatural frequency. Depending upon thevalueof,thepolesofthesystemmaybereal,repeatedorcomplexconjugatewhichis reflected in the nature of its step response. Results obtained for various cases are: -Undamped case (0 < < 1) C(t)=

12 sin(

+ 11 2/)(1) Where,

=

1 2istermedthedampednaturalfrequency.Asketchoftheunitstep response for various values of is available in the text books. -Critically damped case( = 1) ;c(t)=1-

(1 +

)(2) -Overdamped case ( > 1) : c(t)= 1 -

221 (

21

21

21

+ 21) (3) 40 The transfer function G(s) of an ac servomotor may be derived as ()()=

( +1) WhereKmisthemotorgainconstantandTisthemechanicalconstant,andEisthecontrol winding voltage. Considering closed loop transfer function of the system with proportional feedback only as ()()=

()1+

()=

/

2+

+

/. (4) Thisgivesunitstepresponsesimilartoallthreecasesasdiscussedinequation1-3,depending uponthevalueofKAthegainconstant.Thereforetheresponseofthepositioncontrolcanbe altered by the alteration of the gain KA for satisfactory response. Some of the parameters should be defined in term of response curves a)Delay time , is defined as the time needed for the response to reach 50% of the final value. b)Rise time,

, is the time taken for response to reach 100% of the final value for the first time. This is given by

=

,where =

112

c)Peaktime,

,is thetimetakenfortheresponsetoreachthefirstpeakoftheovershoot and is given by

=

1 2 d)Maximum overshoot, Mp, is defined by Mp= c (tp)-c()x 100% e)Settingtime,ts,isthetimerequiredbythesystemresponsetoreachandstaywithina prescribedtolerancebandwhichisusuallytakenas2%or5%.Anapproximate calculation based on the envelops of the response for a low damping ratio system yields. Ts(5% tolerance band)= 3/

Ts(2% tolerance band)= 4/

Another important characteristic of a closed loop system is the steady state error, ess. For unity feedback systems ess is defined as Ess= lim() = lim0() = lim0()1+() 41 Procedure :(a) Position control through continuous command 1.Connect motor unit with the control unit. 2.Switch on the power. Set KA = 4 3.ConnectCROwiththeVrsocket.Startingfromonendsay300,measurethevoltage amplitude A 4.Movethereferencepotentiometerto900andmeasuretheoutputvoltagehereasB.the constant c related to command signal is = volt/0 5.Connect CRO other channel with socket V0. Move command potentiometer in steps of 300 approximatelyandnotetheR(fromcommandpotentiometer)0(fromfeedback potentiometer) , Vr and V0 from the sockets provided upon the panel. 6.SetKAforothervaluesay6,andrecordthevalues.Calculatetheerrorsfromthe results(

0),(

0)foreachstepforeachsetofKAwhereK=gain= selected gain KA x 20 7.Keepcommandpotentiometerat1800.SetKA=4Notethepositionofthefeedback potentiometer. Rotate slowly the command potentiometer and note R, which position the motor follows the command. Repeat the step for gain KA at 7 From the observations it is found that motor follows the command signal with a finite error at low gain settings. Graphically it is shown below. At low gain K = 4 x 20 = 80, the system has some delay(themotorfollowscommandpositionaftersomedisplacement)andlargersteadystate error, where at K = 140 the system produce low error with small delay hence faster response. (b) Study of error detector. Position control through step command 1. Set gain KA = 4. Position reference potentiometer to 1200 2. Connect CRO one channel at reference socket(Vr). Note the signal amplitude in Vac pp. 3. Connect other channel with feedback socket (V0) and measure the ac pp voltage there as V0 4.NowapplystepsignalandnotethermssignalvalueatVrsocket.Afterelapseoftimewhen movetopreviousposition(11secondslater)movethereferencedialforsamereadingobtained with step signal. Note the dial position and find out the step signal actuation in degree. For example start degree is 120 and new degree is 200 then step signal actuation is 200-120 = 800 5.NowremoveCROonechannelconnectedwithfeedbacksocket,andconnectitwiththe error output socket ET 42 6.Applystepcommandandnotetheerroroutput(anoisysignalmayappearinmVorder) ess 0 = error output/constant c in deg 7.Set gain KA = 7. Apply same step and find out the ess. Connect CRO back with V0 socket and note V0 is initial value and V0 is the final value, where V0 is voltage at 1200 and V0 after applying step signal in steady state. Observation of dynamic response1.Select KA = 4. Keep command potentiometer at 1200 Connect CRO at X-Y output sockets withreferencetogroundinX-Ymode.SetYat0.5V/divandXat0.5V/div.Azig-zag curve will appear upon CRO. Select mode A. 2.Press capture key briefly, a spot will appear upon screen. Press step key briefly, the motor willberun.Waittillcapturetimeiscomplete(about4seconds).Aftercompletionof capture time the captured waveform will be displayed upon screen. 3.Connect CRO at reference socket and note the ac voltage. Apply step signal and note the acsignalvoltage.ConnecttheCROatfeedbacksocketandfindoutthedifference between both readings as error (in mV). Trace the waveform which appears upon screen, withscreengraticulesasreference.Observethewaveformshape;thecurveshowno overshoot and sluggish hence the damping factor is = or > 1 4.Apply step signals at gain settings of 6, 8 and each time capture a fresh waveform. Trace the waveforms to observe the effect of different gain in closed loop control system. 5.Selectthewaveformthatlookslikesecondorderresponsecurve.Findoutthetime specifications. 43 Worksheet of the student Date of PerformanceRegistration Number: Aim: S.NoTheoreticalSimulationError ValuesValues Calculations: Result and Discussion Graph/Plot: Error Analysis Learning Outcomes (what I have learnt) ToParameterMarksMax. Marks 1Understanding of the student about the20 procedure/apparatus. 2Observations and analysis including20 learning outcomes 3Completion of experiment, Discipline and10 Cleanliness Signature of Faculty 44 EXPERIMENT NO. 10 Aim : Performance Analysis ofThermal System and Design using PID/Relay Control Apparatus : Thermal System Kit, CRO, Power Supply Theory : In most of the chemical and biochemical processes it is of fundamental importance to control the temperature at which various processes occur.Improper temperature control may lead to loss of product quality, non-profitable operation or even create hazardous situations. Temperatureisgenerallycontrolledbymodifyingthepoweroutputofaheating/cooling device.Thistranslatesinsettingtheflowrateofaheating/coolingagentortheelectrical current applied to an electrical heater. For a continuous stirred tank, the dynamic heat balance is described by equation 1. dTR =F (T TR ) +Q dt V 0 V cp If a thermosensor is used to measure the temperature, the delay in the measurement can be described: dTsens (T T) dt=Rtsens sens The same first-order delay can describe the response of the heater: dQ = (Q0 Q) dt t Q (1) (2) (3) By introducing a temperature controller in the system, the power output of the heater will depend on the difference between the measured temperature and a set value. A proportional-integral-derivative 45 controller (PID) computes the power by considering instantaneous temperature deviation (proportional component), deviation history (integral component) and deviation trend (derivative component): E +KP t dE QPID= Q0+ K t I } Edt + KPt Ddt (4) P0 Controllerparameters(Kp,IandD)areestablishedthroughaprocesscalledcontroller tuning. Several methods are available for determining these parameters, the purpose being to reach a temperature as close as possible to the reference. Notations: TR = temperature in the tank [o0C] T = temperature of the inlet [oC] o Tsens = temperature indication (observed) [ C] Tset = set temperature [oC] E=TsensTset(temperature deviation)F=flowrate[L/h] V = tank volume [L] Q = heater power [J/h] Q0 = nominal power of the heater [J/h] QPID = controlled power output [J/h] = fluid density [kg/L] cp = specific heat [J/kg K] t = time [h] sens = time constant of the thermosensor [h] Q = time constant of the heater [h] I = time constant of the integral component [h] D = time constant of the derivative component [h] o KP = proportional constant of the controller [J/hC] 46 Experimental setup Figure 1 - Scheme of a continuous stirred tank with temperature control The experimental setup (Figure 1) consists of a stirred tank equipped with an electrical heater and amagneticstirrer.Wateriscontinuouslypumpedinthetankthroughavalvethatcontrolsthe water flow. A rotameter (FI) indicates the flow rate. The water level is maintained constant by an overflow connection to the vessel. Anelectricalcoilheaterwiththeconstantnominalpowerof1000Wissubmersedinthefilled tankandconnectedto aanalog/digital(A/D)transformingunit.Temperatureismeasuredwith a thermocouple (T), and recorded using the same A/D unit. The A/D unit transforms the continuous analogous signal into a digital signal that can be interpreted with the aid of a process computer. TheLabVIEWTMplatformisusedtocommunicatewiththemeasurementinstruments (thermocouples) and the actuators (electrical heater). The decision to turn the heater ON or OFF is taken according to an adapted model of a PID controller (Figure 2). A modulator was included to transform the continuous output of the PID (heating power in this case) in an ON/OFF command. The purpose of the controller is to maintain a steady temperature in the tank (Tset). 47 Figure 2 - Schematic representation of the adapted PID controller implemented in the process computer The control parameters (Kp, TauI, TauD) and other values (Tset, modulator frequence, etc.) can be introduced manually using sliders or input boxes. 1. Controller configuration 1.1.Calibratethetemperaturesensorusinganormalthermometerforcomparison (minimum three values). 1.2.Calibrate the rotameter by measuring the volume of water collected in 1 minute time intervals at different rotameter indications (minimum three values per indication). 1.3.Forthemeasuredinlettemperatureandagivenflowrate,determinethetheoreticalsteady state temperature in the case when the heater is ON and there is no temperature control. Use the steady- state heat balance. Is this value attainable? 1.4. Determine the time constant of the temperature sensor. a) Write down the sensor indication at time=0. b) Submerge the sensor in a well-mixed heated tank and write down the sensor indication vs. time. Use a scale of seconds. Stop after the indication shows three consecutive identical values. c)Createthesensor_data.txtfilewithtwocolumns:time[hours]and measuredtemperature[oC].UseHEAT_DELAY_FIT.mmdprogramtoestimate sensor delay (TAUsens) by fitting simulated temperature (Tsens) to data. For estimation, set the parameters to the following values: Q0=0, Tenv=initial sensor indication, T0=final sensor indication. 1.5. Determine the time constant of the electrical heater. 48 a) Write down the temperature in the tank at time=0. Make sure that agitation is ON. b)TurntheheaterON.Writedownthesensorindicationvs.time.Useascaleof seconds. Stop the heating when the temperature increases over 90 oC. c)Createtheheater_data.txtfilewithtwocolumns:time[hours]and measuredtemperature[oC].UseHEAT_DELAY_FIT.mmdprogramtoestimate heater delay (TAUQ) by fitting simulated temperature (Tsens) to data. For estimation, settheparameterstothefollowingvalues:Q0=3600,Tenv=T0=initialsensor indication. Comment on the quality of the fitting. Is estimating only TAUQ sufficient to obtain a good fit? What other parameters could be changed to improve the fitting? 1.6. Determine the parameters of the controller (tuning the controller) using the Ziegler-Nichols open-loop method. Use the TEMPERATURE_SWITCH Lab View file for monitoring the process. a) Switch the operation of the tank to continuous by switching the water flow ON. Set a flow rate indication of 25 L/h. Make sure that agitation is ON. b) For the actual flow rate (see rotameter calibration!), compute the theoretical power output (Qcomp) needed to have a steady state temperature of 40 C in the tank. In LabView, set the value of the Heater ON parameter to round(10*Qcomp/Q0). Becausetheheatercandeliveronlyonepoweroutput,smallerpowersareachievedby switching the heater ON for a fraction of a set time interval, in this case 10 seconds, and then switching it OFF. The process is then repeated. c) Turn the heater ON. Use a chronometer to make sure that the heater is switched on/off as prescribed.Waituntilthesystemreachesasteadystate(steadyTsensintheprocess monitor). Compare the steady-state temperature with the theoretical one. In case they are different, comment on the possible causes. Compare the indications of the three thermosensors. Are Tsens and Toutlet identical? If they are not, comment on the possible causes. 49 d) Performastep-changeintheflowrate(decreaseabruptlytheflowratewith15L/h). Write down the value of this step (=B). Wait for the system to reach the new steady-state. e) Byusingtheresponseplots,estimateandcomparethetimeconstantsaffectingthe behavior of the system (residence time, sensor response time, heater response time). f)UsethestepchangecollecteddataandinterpolateasmoothcurvefromTsens(time). Usingthismodifiedresponsecurve,estimatelagtimeTLandtheslope(Figure3). Establish the PI controller settings using these values. Figure Open-loop Ziegler-Nichols method for tuning the controller parameters 1.7.Testthecontrollersettingscomputedat4.6.usingthe TEMPERATURE_CONTROLLER_FINALLabViewfile.Commentonthequalityofthe control.Testthesystemtoasmall(