ee2257-control system lab mannual

M.KUMARASAMY COLLEGE OF ENGINEERINGDEPARTMENT OF EEE

II YEAR/IV SEMESTEREE2257 – CONTROL SYSTEMS LABORATORY

LAB MANUAL

PREPARED BYMs.K.MARULIYA BEGAM,Mr.M.RAMESH,Ms.K.UMA MAHESWARI,

LECT/EEE

M.KUMARASAMY COLLEGE OF ENGINEERING ******EE2257- CONTROL SYSTEMS LABORATORY 1

M.KUMARASAMY COLLEGE OF ENGINEERING, KARUR.DEPARTMENT OF EEE

II EEE / IV SEM

EE 2257 – CONTROL SYSTEMS LABORATORY

LIST OF EXPERIMENTS:

1. DETERMINATION OF TRANSFER FUNCTION OF DC SERVO MOTOR

2. DETERMINATION OF TRANSFER FUNCTION OF AC SERVO MOTOR

3. ANALOG SIMULATION OF TYPE-0 AND TYPE-1 SYSTEM

4. DETERMINATION OF TRANSFER FUNCTION OF DC GENERATOR

5. DETERMINATION OF TRANSFER FUNCTION OF A) ARMATURE CONTROLLED DC MOTOR B) FIELD CONTROLLED DC MOTOR

6. STABILITY ANALYSIS OF LINEAR SYSTEM

7. DC AND AC POSITION CONTROL SYSTEMS

8. STEPPER MOTOR CONTROL SYSTEM

9. DIGITAL SIMULATION OF FIRST ORDER SYSTEM

10.DIGITAL SIMULATION OF SECOND ORDER SYSTEM


TRANSFER FUNCTION OF AC SERVO MOTOR

AIM :

To derive the transfer function of AC Servo motor.

APPARATUS REQUIRED :

1.AC Servomotor trainer kit 2.Multimeter 3.patch cards

THEORY :

It is an electromechanical device.Which convert electrical signal into angular displacement.An AC servomotor basically a two phase induction motor except for certain special design features.The rotor of the servomotor is built with high resistance ,so that X / R ratio is small whichResult in linear speed-torque characteristics . The stator consists of two pole pairs mounted on the inner pheriphery of the stator,such thatTheir axes are at an angle of 90o in space.Each pole pairs carries a winding.One winding is calledReference winding and the other is called control winding. The rotor construction is usually squirrel cage .The squirrel cage rotor is made of laminations.The rotor bars are placed on the slots and short circuited at both ends by end rings .

The diameter of the rotor is small in order to reduce inertia and to obtain good accelerating characteristics.The Drag cup construction is employed for very low inertia application.In this type Of construction the rotor will be in the form of hollow cylinder made of aluminium.The aluminium cylinder itself act as short circuited rotor conductors.

TRANSFER FUNCTION OF AC SERVOMOTOR :

Let Tm = Torque developed by servomotor Q = Angular displacement of rotor W = Angular speed


Tl = Torque required by the load J = Moment of inertia B = Viscous frictional coefficient

K1 = Slope of control phase voltage vs torque characteristic K2 = Slope of speed torque characteristics

Torque developed by motor , Tm = K1ec – K2 d / dt ……………………….. 1 Load torque, Tl = J d2 / dt + B d / dt………………………. 2

Equating the equation 1 & 2 J d2 / dt + B d / dt = K1ec – K2 d / dt …………………………. 3

On taking laplace transform of above equation,we get Js2(s) + Bs(s) = K1Ec(s) – K2s(s) ( Js2+ Bs+K2 ) (s) = K1Ec(s) (s) K1

= Ec(s) s( Js+ B+K2s )

(s) K1 / (B+K2 )

= Ec(s) s( J S/B+K2 + 1)

(s) Km =

Ec(s) s(ms + 1)

Where , Km = K1 / B+K2 = Motor gain constant m = J / B+K2 = Motor time constant

PROCEDURE :1.Connections are made asper the circuit diagram.2.Determination of K1

(a) Connect G1 K1 of pulse isolation output to G1 K1 OF SCR1.(b) Connect G2 K2 of pulse isolation output to G2 K2 OF SCR2(c) Connect the power card to the backside of trainer kit


(d) Motor pin is connected to the trainer kit(e) Switch on the supply(f) Measured the initial speed and add the load gradually.(g) AC voltmeter is connected across the windings(h) Take the following readings Vc,speed and load(i) Plot the graph phase voltage vs torque

3.Determination of K2

(a) Switch on the supply(b) Switch on the pulse S2

(c) Apply phase voltage to control phase using potentiometer.(d) Note down the load value(e) Plot the graph torque vs phase voltage(f) Switch off the power supply.

MODEL GRAPH :

TABULAR COLUMN :

RADIUS r= Control voltage Vc1=

Angular velocity ω in rad/sec

Speed(rpm) Load(kg) Torque(Nm)


Control voltage Vc2=Angular velocity ω in rad/sec

Speed(rpm) Load(kg) Torque(Nm)

RESULT :


Thus the transfer function of AC Servomotor is obtained .

TRNSFER FUNCTION OF SELF EXITED DC GENERATOR

AIM To derive the transfer function of self exited DC Generator.


S.no Name of the apparatus Range Type Quantity1 Rheostat 290,2A - 12 Rheostat 360,1.4A - 13 Voltmeter (0-300)v mc 14 Voltmeter (0-300)v mI 15 Ammeter (0-10)A mI 16 Ammeter (0-2)A mc 17 Tachometer - - 18 Connecting wires - - few9 1 auto transformer (0-230)/270v - 110 1 Resistive Load - - 1

THEORY :

Generator is an electrical machine which convert mechanical energy into electrical energy .Depending upon the field winding excitation,it can be classified into two types.

i) Self Exited Generatorii) Separately Exited Generator

The field windings are energized from generator itself is called self exited generator.HereOur aim is determine the transfer function of self exited generator.Let Vf = Field input voltage If = Field current

Rf = Field Resistance Lf = Field Inductance Eg = Generated emf in the armature


P = no of poles N = Speed in rpm

= Flux in webKg = Generator constant

Applying kvl for field equivalent circuit Vf = If Rf+Lfdi / dt ………………………… 1The generator output voltage is given by Eg = pzn / 60*A From above equvation generator voltage is directly proportional to the flux. Eg , If , Eg = KgIf …………… 2 Taking laplace transform of equ 1 & 2 Vf (s) = If (s) Rf+s If Lf(s)…………………… 3 Eg(s) = KgIf(s) ………………. …………… 4 If(s) = Eg(s) / Kg ……………………………………….. 5

Equation 5 values substitute in equ 3 Vf (s) = (Eg(s) / Kg) Rf+ (Eg(s) / Kg) sLf

Vf (s) = (Eg(s) / Kg) (Rf+ sLf ) Eg(s) Kg

= Vf (s) (Rf+ sLf )

FORMULA USED (1) Field impedence Zf = Vf / If

(2) Field inductance Xf = Zf2 – Rf

2

(3) Lf = Xf / 2f

(4) Tf = Lf / Rf

(5) Kg = Eg / If

PROCEDURE : 1.The connection are made asper the circuit diagram.2.Switch on the main supply3.Motor is started by using 3 point starter4.To vary the motor field rheostat and set the rated speed5.To vary the Generator field rheostat .6.Note the various readings and enter into the tabular column7.Switch off the supply8.Disconnect the circuit and return the compnonents


TABULAR COLUMN :

(1) To find Kg :

S.No Generated voltage (Eg) Field current ( If)

( II ) To find Rf :

S.no Field current( If)

Field voltage (Vf)

Field Resistance ( Rf)

(I11) To find Zf :

S.no Field current( If)

Field voltage (Vf)

Field Impedence ( Zf)


MODEL GRAPH :

MODEL CALCULATION:


RESULT :

Thus the transfer function of self exited DC generator is obtained .

TRANSFER FUNCTION OF SEPARATELY EXITED DC GENERATOR

AIM : To derive the transfer function of separately exited DC Generator.


S.no Name of the apparatus Range Type Quantity1 Rheostat 290,2A - 12 Rheostat 360,1.4A - 13 Voltmeter (0-300)v mc 14 Voltmeter (0-300)v mI 15 Ammeter (0-10)A mI 16 Ammeter (0-2)A mc 17 Tachometer - - 18 Connecting wires - - Few9 1 auto transformer (0-230)/270v - 110 1 Resistive Load - - 1

THEORY :

Generator is an electrical machine which convert mechanical energy into electrical energy .Depending upon the field winding excitation,it can be classified into two types.

iii) Self Exited Generatoriv) Separately Exited Generator

The field windings are energized from Eeternal DC source is called separately exited generator.Here Our aim is determine the transfer function of self exited generator.

Let Vf = Field input voltage


If = Field current

Rf = Field Resistance Lf = Field Inductance Eg = Generated emf in the armature P = no of poles N = Speed in rpm

= Flux in webKg = Generator constant

Applying kvl for field equivalent circuit Vf = If Rf+Lfdi / dt ………………………… 1The generator output voltage is given by Eg = pzn / 60*A From above equvation generator voltage is directly proportional to the flux. Eg , If , Eg = KgIf …………… 2 Taking laplace transform of equ 1 & 2 Vf (s) = If (s) Rf+s If Lf(s)…………………… 3 Eg(s) = KgIf(s) ………………. …………… 4 If(s) = Eg(s) / Kg ……………………………………….. 5

Equation 5 values substitute in equ 3 Vf (s) = (Eg(s) / Kg) Rf+ (Eg(s) / Kg) sLf

Vf (s) = (Eg(s) / Kg) (Rf+ sLf ) Eg(s) Kg

= Vf (s) (Rf+ sLf )

FORMULA USED (1) Field impedence Zf = Vf / If

(2) Field inductance Xf = Zf2 – Rf

2

(3) Lf = Xf / 2f

(4) Tf = Lf / Rf

(5) Kg = Eg / If

PROCEDURE :

1.The connection are made asper the circuit diagram.2.Switch on the main supply3.Motor is started by using 3 point starter


4.To vary the motor field rheostat and set the rated speed5.To vary the Generator field rheostat .6.Note the various readings and enter into the tabular column7.Switch off the supply8.Disconnect the circuit and return the compnonents

TABULAR COLUMN :(1) To find Kg :

S.No Generated voltage (Eg) Field current ( If)

( II ) To find Rf :

S.no Field current

( If)Field voltage (Vf)

Field Resistance ( Rf)

(I11) To find Zf :

S.no Field current Field voltage Field Impedence


( If) (Vf) ( Zf)

MODEL GRAPH :

MODEL CALCULATION


RESULT :

Thus the transfer function of separately exited DC generator is obtained .

TRANSFER FUNCTION OF ARMATURE CONTROLLED DC MOTOR AIM : To derive the transfer function of armature controlled DC motor.


S.no Name of the apparatus Range Type Quantity1 Rheostat 50,5A - 22 Rheostat 360,1.4A - 13 Voltmeter (0-300)v mc 14 Voltmeter (0-75)v mc 15 Ammeter (0-10)A mc 16 Ammeter (0-2)A mc 17 Tachometer - - 18 Connecting wires - - few9 1 auto transformer (0-230)/270v - 110 1 Resistive Load - - 1

THEORY :

In armature controlled DC motor,the desired speed is obtained by varying armature Voltage and keeping field current is constant. We know that Eb = pzn / 60*A From above equation DC motor speed is directly propotional to the armature voltage.Let Ra = Armature Resistance


La = Armature Inductance Eb = Back emf Ia = Armature current T = Torque developed in the motor J = Momemt of inertia B = Dashpot

= Angular DisplacementKt = Torque constantKb = Back emf constant

From equivalent circuit Differential equation of equivalent circuit can be written as ia +La dia/dt + eb = Va …………………………………….. 1

Differential equation of mechanical system can be written as J d2 /dt2 + B d / dt = T……………………….. 2 Torque is directly propotional to the armature current T Ia , T Ia T = Kt Ia……………………. 3

Motor back emf is directly propotional to the speed ( Angular velocity ) Eb = Kb d / dt ………………….. ……………… 4Taking laplace transform froom equ 1 , 2 & 3 RaIa(s) + LsIa(s) + Eb(s) = Va(s) ………………. 5 Js2(s) + Bs(s) = T ( s)………………………… 6 T(s) = KtsIa(s)……………………………………. 7 Eb(s) = Kbs(s)…………………………………... 8 Equvating equvation 6 & 7 KtsIa(s) = Js2(s) + Bs(s) Ia(s) = Js2(s) + Bs(s) / Kts ………………. 9Equation 9 & 8 values substitute in equ 5 ( Ra + Ls)Ia(s) + Eb(s) = Va(s) ( Ra + Ls) Js2(s) + Bs(s) / Kts + Kbs(s) = Va(s) (s )( Ra + Ls) Js2) + Bs + Kbs / Kts = Va(s) (s ) Kts = Va(s) ( Ra + Ls) Js2) + (B + Kbs

Retardation Test ( To find moment of inertia )


Retardation test is used to find the moment of inertia ( j ). The motor is made to run at rated speed. Interchange the position 1 to 2 and 1i to 2i

Measure the speed ,voltage ,current & time

PROCEDURE :

1.The connection are made asper the circuit diagram.2.Switch on the main supply3.Motor is started by using 3 point starter4.To vary the motor field rheostat and set the rated speed5.To vary the armature field rheostat by keeping field is constant6.Note the various readings and enter into the tabular column7.Switch off the supply8.Disconnect the circuit and return the compnonents

TABULAR COLUMN :

( I ) To find Kb

S.no Armature current( Ia)

Armature voltage ( Va)

Speed ( N ) =2N/60 Eb =Va - IaRa

( I I ) To find moment of inertia ( j ) :

S.no N1

(Rpm)

N2

(Rpm)

I1

( A)

I2

( A)

T1

(Sec)

T2

(Sec)

V1

( volts)

V2

( volts)


( III ) To find Ra :



Armature Resistance ( Ra)

(IV) To find Zf :



Armature Impedence ( Za)


MODEL GRAPH :

MODEL CALCULATION :


RESULT :

Thus the transfer function of armature controlled DC motor is obtained .

TRANSFER FUNCTION OF FIELD CONTROLLED DC MOTOR

AIM : To derive the transfer function of field controlled DC motor.


S.no Name of the apparatus Range Type Quantity1 Rheostat 50,5A - 22 Rheostat 360,1.4A - 13 Voltmeter (0-300)v mc 14 Voltmeter (0-75)v mc 15 Ammeter (0-10)A mc 16 Ammeter (0-2)A mc 17 Tachometer - - 18 Connecting wires - - few9 1 auto transformer (0-230)/270v - 110 1 Resistive Load - - 1

THEORY :

In Field controlled DC motor,the desired speed is obtained by varying field current and keeping armature is constant. We know that Eb = pzn / 60*A From above equation DC motor speed is inversly propotional to the field current.


Let Rf = Armature Resistance Lf = Armature Inductance Ra = Armature Resistance La = Armature Inductance Ia = Armature current T = Torque developed in the motor J = Momemt of inertia B = Dashpot

= Angular DisplacementKt = Torque constantKb = Back emf constant

From equivalent circuit Differential equation of equivalent circuit can be written as ia +La dia/dt + = Vf …………………………………….. 1

Differential equation of mechanical system can be written as J d2 /dt2 + B d / dt = T……………………….. 2 Torque is directly propotional to the armature current T Ia , T Ia T = Kt Ia……………………. 3

Taking laplace transform froom equ 1 , 2 & 3 RaIa(s) + LsIa(s) = Va(s) ………………. 4 Js2(s) + Bs(s) = T ( s)………………………… 5 T(s) = KtsIa(s)……………………………………. 6 Equvating equvation 6 & 7 KtsIa(s) = Js2(s) + Bs(s) Ia(s) = Js2(s) + Bs(s) / Kts ………………. 7Equation 7 values substitute in equ 4 ( Ra + Ls)Ia(s) + Eb(s) = Va(s) ( Ra + Ls) Js2(s) + Bs(s) / Kts) = Va(s) (s )( Ra + Ls) Js2) + Bs / Kts = Va(s) (s ) Kts = Va(s) ( Ra + Ls) Js2) + (Bs

Retardation Test ( To find moment of inertia )


Retardation test is used to find the moment of inertia ( j ). The motor is made to run at rated speed. Interchange the position 1 to 2 and 1i to 2i

Measure the speed ,voltage ,current & time

PROCEDURE :

1.The connection are made asper the circuit diagram.2.Switch on the main supply3.Motor is started by using 3 point starter4.To vary the motor field rheostat and set the rated speed5.To vary the field rheostat by keeping armature is constant6.Note the various readings and enter into the tabular column7.Switch off the supply8.Disconnect the circuit and return the compnonents

TABULAR COLUMN :

( I ) To find Kb



Speed ( N ) =2N/60 Eb =Va - IaRa

( II ) To find Ra :



Armature Resistance ( Ra)


(III) To find Za :



Armature Impedence ( Za)

MODEL GRAPH :

MODEL CALCULATION :


RESULT :

Thus the transfer function of Field controlled DC motor is obtained.

STABILITY ANALYSIS OF LINEAR SYSTEM

AIM:

To analyze the stability of linear system using Root locus. APPARATUS REQUIRED:

1. Computer system with MATLAB software 2. Power supply

THEORY:

MATLAB is software package for high performance numerical computation and visualization .It provides an interacting environment with hundred of built in fun for technicalComputation, graphics and animation. The name MATLAB stands for matrix laboratory. The user can write their own function in the MATLAB language.

MATLAB is a matrix-based system for mathematical and engineering calculation. Each variable is treated as a matrix which the only data type handled by it. The graphical output can be obtained by running different set of routines.


MATLAB can be used as an application development because of graphical user interface tools. The typical are in the field of mathematics’ and computation development of algoritm, modeling simulation and its prototyping, data analysis, scientific and engineering problems, application development tools. Several toolboxes are also available from the differentManufacture.

Tool box is a group of MATLAB function which are predefined that can be used for Obtaining solution in the different applications, control systems, neural network, fuzzy logic andDigital signal processing.

PROGRAM :

num = [ 0 0 0 0 1 ]; den = [ 1 1.1 10.3 5 0 ]; rlocus = (num,den) grid

PROCEDURE :

1.Switch on the main supply2.Open the MATLAB command window3.Create a new M file .The file that is containing MATLAB language codes are called M file.4.Type the program and check the error.5.After saving the program ,debug and run to see the output .6.Verify the output waveform obtained through MATLAB with theoretical output7.Shutdown the computer8.Switch off the supply

OUTPUT WAVEFORM :


RESULT:

Thus the Stability analysis of linear system using MATLAB was studied.

DC & AC POSITION CONTROL SYSTEM AIM: To study the characteristics of synchros as error detector.

APPARATUS REQUIRED: DC Servoposition kit Synchro transmitter and receiver – 1set. Patch cards – As required. Multimeter – 1.

PROCEDURE:

To obtain the characteristics of synchro transmitter.1. The main supply to the system is connected with the help of cable provided.2. The main supply to the unit is switched ON & supply to the transmitter is also switched

ON. The magnitude of the AC voltage supplied to the rotor is fixed as 40v.3. The magnitude of the AC voltage between each of the stator terminal Vs1s2,Vs2s3 &

Vs3s1 are measured and tabulated for different rotor positions at equal intervals.4. The graph, angular position Vs rotor voltages for all the three phases are plotted.


To obtain the input-output characteristics of Synchro Transmitter & Reveiver Pair:1. The terminals of transmitter s1,s2 & s3 are connected to s1,s2 & s3 of receiver using

patch cards respectively.2. The main supply is switched ON.3. The rotor supply of both transmitter and receiver are also switched ON.4. The rotor of receiver is tightly held at 0 degree.5. The rotor position of synchro transmitter(pointer) is moved in steps of 10 degree and the

new rotot position of receiver is observed.6. The output voltage is also observed and t varies sinusoidally with angular error.7. The plot input angular position in degrees is plotted.

MODEL GRAPH:


RESULT: Thus the characteristics of Synchro as Ac position control systems were studied.

DIGITAL SIMULATIUON OF OF IST ORDER SYSTEM

AIM :

To digitally simulate the time response characteristics of first order system for different inputs using MATLAB.

APPARATUS REQUIRED : 1.Computer system with MATLAB software 2.Power supply

THEORY :

MATLAB is software package for high performance numerical computation and visualization .It provides an interacting environment with hundred of built in fun for technicalComputation, graphics and animation. The name MATLAB stands for matrix laboratory. The user Can write their own function in the MATLAB language.





PROGRAM :

( i ) Step response of first order system num = [ 0 1 ]; den = [ 1 1 ]; step (num,den ); grid

PROCEDURE :


OUTPUT WAVEFORM :


RESULT :

Thus the unit step response of a first order system using MATLAB were studied and its curves were plotted.

DIGITAL SIMLATION OF II ORDER SYSTEM

AIM : To digitally simulate the time response characteristics of second order system for different inputs using MATLAB APPARATUS REQUIRED : 1.Computer system with MATLAB software 2.Power supply

THEORY :

MATLAB is software package for high performance numerical computation and visualization .It provides an interacting environment with hundred of built in fun for technicalComputation, graphics and animation. The name MATLAB stands for matrix laboratory. The user Can write their own function in the MATLAB language.





PROGRAM :

Step response of second order system num = [ 0 0 1 ]; den = [ 1 0.5 1 ]; step ( num,den ); grid

PROCEDURE :


OUTPUT WAVEFORM :


RESULT :

Thus the unit step response of a second order system using MATLAB were studied and its curves were plotted.


ee2257-control system lab mannual

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