CONTROL SYSTEMS LAB MANUAL - Anurag College Of Engineering
EEE Deptartment Control Systems Lab Manual CONTROL SYSTEMS LAB MANUAL Anurag College of Engineering Page 1
EEE Deptartment Control Systems Lab Manual LIST OF CONTROL SYSTEM LAB EXPERIMENTS 1. TRANSFER FUNCTION OF D.C.SHUNT GENERATOR 2. CHARACTERISTICS OF MAGNETIC AMPLIFIER 3. SPEED-TORQUE CHARACTERISTICS OF SERVOMOTOR. 4. TIME RESPONSE OF SECOND ORDER SYSTEM. 5. LAG-LEAD COMPENSATORS 6. SIMULATION OF TRANSFER FUNCTION USING OP-AMP. 7. STATE SPACE MODEL OF TRANSFER FUNCTION USING MATLAB 8. VERIFICATION OF ROOT LOCUS USING MATLAB. 9. TRANSFER FUNCTION MODEL FOR STATE SPACE USING MATLAB Anurag College of Engineering Page 2
EEE Deptartment Control Systems Lab Manual 1. TRANSFER FUNDTION OF DC GENERATOR AIM: To determine the transfer function of dc generator. NAME PLATE DETAILS: Rated voltage Rated current Speed Output Power APPARATUS: Dc motor –generator set, motor starter, field rheostat, rheostat as potential differentiator for excitation of generator, ammeters –MC&MI, voltmeters–MC&MI, tacho generator, variac, connecting wires. CIRCUIT DIAGRAM: MC- Mechanical coupling Fig(i) Anurag College of Engineering Page 3
EEE Deptartment Control Systems Lab Manual Fig(ii) Fig (iii) THEORY: The transfer function of a dc generator is derived as follows Vg(t) KgIf(t) dIf(t) dt generated voltage generator constant field current Vf(t) RfIf(t) Lf Vg(t) Kg If(t) Anurag College of Engineering Page 4
EEE Deptartment Control Systems Lab Manual Applying L.T with initial conditions as zero Vg(s) KgIf(s) Vf(s) RfIf(s) Lf sIf(s) Vf(s) [Rf sLf]If(s) If(s) Vf(s) [Rf sLf] Kg generated EMF constant Block diagram representation for the above two equations Vf(s) 1 [Rf sLf ] If(s) Kg Vg(s) Kg [Rf sLf] In this equation, the values of Kg, Rf & Lf have to be obtained. Transfer Function PRECAUTIONS: 1. The motor should run at rated speed while conducting OCC test. 2. During the conduct of field impedance and resistance drop tests only the field windings should be energized. PROCEDURE: 1. Connect the circuit as per the circuit diagram shown in fig (i).Ensure that the motor field rheostat and the P.D in the generator field circuit should be minimum. 2. Start the motor with the help of a starter and adjust the speed of the motor to the rated value by varying the field rheostat. 3. Vary the P.D in the generator circuit in small steps and note down the field current of the generator (If) and generator emf (Eg) and tabulate it in table (i). 4. To determine Kg ,magnetization characteristics Eg Vs If of a separately excited dc generator has to be plotted as shown in fig(iν) and use the straight line position to determine Kg Eg / If. Anurag College of Engineering Page 5
EEE Deptartment Control Systems Lab Manual 5. The field resistance of the generator Rf is determined by the field resistance drop test as shown in figure in fig(iii)Vary the P.D in steps ,note down the Ammeter and voltmeter values and tabulate it in table(ii). 6. To determine inductance Lf of a generator first the impedance Zf has to determined by field impedance drop test as shown in fig (ii). 7. Vary the variac in fig (ii). Note down the ammeter and voltmeter values and tabulate it in table (iii). OCC Characteristic: Field Current If(A) Generated Voltage Eg(V) Table (i) Field resistance drop test: Sl.No Vf (V) Rf Vf/If (Ω) If (A) Average Rf Ω Table (ii) Field Impedance drop test: Sl.No Vf (V) If (mA) Zf Vf/If (Ω) Average Zf KΩ Table (iii) Anurag College of Engineering Page 6
EEE Deptartment Control Systems Lab Manual CALCULATIONS Field resistance Rf 1.2* Rf avg Ω Impedance Zf KΩ Xf [Zf R f ]1 2 2 2 Xf 2 f From graph Lf Kg Eg If Transfer Function T.F Vg ( s ) Vf (s) Kg [ R f sL f ] MODEL GRAPH: Fig (iν) RESULT: The transfer function of dc generator was determined by conducting OCC test on the given dc generator and the T.F of the system is found to be T.F Anurag College of Engineering Kg R L f f Page 7
EEE Deptartment Control Systems Lab Manual 2. Magnetic Amplifier AIM: To Study the control characteristics of a Magnetic Amplifier APPARATUS: 1. Magnetic Amplifier having laminated core. Ammeters D.C (0-100ma), Ammeters A.C (0-500ma) are arranged in unit itself 2. Patch cards 3. Low Bulb THEORY: 1. Magnetic amplifier is a device consisting of saturable reactors, rectifiers and conventional transformers, used to secure control or amplication. 2. The load current in magnetic amplifier is cotrolled by a D.C.magnetizing current. 3. A large current value is controlled by a small current value; hence such type of circuits is termed as current amplifiers. 4. To control the load current, a saturable reactor is used.The reactance of the reactor depends upon magnetic coupling and magnetism induced depends upon the D.C.control current. 5. The load current is controlled by using magnetic property and hence the term magnetic amplifier. 6. The most common basic saturable reactor which is used in magnetic amplifier circuits consists of a three legged closed laminated core with coils wound on each leg. 7. The coils wound on central limb are called as control winding and coils wound on outer limbs are called as load winding. 8. Due to D.C.current in the control winding, the degree of magnetization in the core is changed. 9. Hence the flux density changes, i.e.reactance of the core by changing the D.C.current in the control winding. 10. If the load winding is connected in series with the load, one can control the current in the load by changing reactance of the coil with the help of D.C.control current. Anurag College of Engineering Page 8
EEE Deptartment Control Systems Lab Manual CIRCUIT DIAGRAMS: SERIES CONNECTED MAGNETIC AMPLIFIER: Fig (i) PARALLEL CONNECTED MAGNETIC AMPLIFIER: Fig(ii) SELF-SATURATED MAGNETIC AMPLIFIER: Fig (iii) Anurag College of Engineering Page 9
EEE Deptartment Control Systems Lab Manual PROCEDURE: SERIES CONNECTION: 1. Connected the circuit as per the circuit diagram shown in fig (i). 2. Keep the slide switch on ‘D’ position which will be indicated by an indicator after circuit is switched on 3. Keep control switch knob at its extreme position which ensure zero control current at starting. 4. With the help of patch cards connect the following terminals on the front panels of the unit a) Connect AC to A1 b) Connect B1 to B2 c) Connect B2 to L 5. Connect a 100w fluorescent lamp in the holder and switch on the unit. 6. Now gradually increase the control current by rotating control current setting knob clockwise in steps and note down control current and corresponding load current and tabulate it in table (i). 7. Plot the graph of load current Vs control current. B.PARALLEL CONNECTION: 1. Connect the circuit as per the circuit diagram shown in fig (ii) 2. Keep slide switch in position ‘D’ which will be indicated by an indicator after unit is switched on. 3. Keep control current setting knob at its extreme left position which ensures zero control current at starting. 4. With the help of plug in links, connect following terminals on the front panel of the unit. a) Connect AC to A1 b) Connect A1 to A2 c) Connect B1 to B2 d) Connect B2 to L Anurag College of Engineering Page 10
EEE Deptartment Control Systems Lab Manual 5. Connect 100 watt fluorescent lamp in the holder provide for this purpose and switch on the unit 6. Now gradually increase control current by rotating control current setting knob clockwise in steps and note down control current and corresponding load current and tabulate it in table (ii). 7. Plot the graph of load current vs control current. C. SELF SATURATED CONNECTION: 1. Connect the circuit as per the circuit diagram shown in fig(iii). 2. Keep slide switch in position ‘E’ which will be indicated by an indicator, after unit is switched on. 3. Keep control switch knob at its extreme position which ensures zero control current at staring. 4. With the help of patch cards connect the following terminals on the front panel of the unit. a) Connect Ac to C1 b) Connect A3 to B3 c) Connect B3 to L 5. Connect a 100W fluorescent lamp in the holder provide for this purpose and witch on the unit. 6. Now gradually increase control current by rotating control current setting knob clockwise in steps and note down control current and corresponding load current and tabulate it in table (iii). 7. Plot the graph of load current Vs control current. PRECAUTIONS: 1. For series and parallel connections of the magnetic amplifier the switch should be in D mode. 2. For self saturation connection the switch is thrown to position E. Anurag College of Engineering Page 11
EEE Deptartment Control Systems Lab Manual TABULAR COLUMNS: SERIES CONNECTION: Sl.No Ic (mA) IL (mA) Table (i) PARALLEL CONNECTION: Sl.No Ic (mA) IL (mA) Table (ii) SELF SATURATION CONNECTION: Sl.No Ic (mA) IL (mA) Table (iii) MODEL GRAPHS: SERIES CONNECTION: Anurag College of Engineering Page 12
EEE Deptartment Control Systems Lab Manual PARALLEL CONNECTION: SELF SATURATION CONNECTION: OBSERVATIONS: 1. In series connection of the magnetic amplifier the load current is zero owing to high reactance. 2. In parallel connection the load current is not zero, even though the control current is zero due to low reactance. RESULT: The magnetic amplifier control characteristics were studied and drawn. 3. SPEED- TORQUE CHARACTERISTICS DC SERVO MOTOR Anurag College of Engineering Page 13
EEE Deptartment Control Systems Lab Manual AIM: To draw the speed - torque characteristics of a dc-servomotor. APPARATUS: Dc Servo Motor Multimeter (Or) Voltmeter Connecting Wires CIRCUIT DIAGRAM:- THEORY: Servo motors are used in automatic control systems. When the objective of the system is to control the position of an object then the system is called servo system. The dc motor can be controlled by varying either the field current (or) the armature current. Dc servo motor gives high efficiency than from ac servo motor of same size. The types of dc servo motors are the series ,shunt and permanent magnet (PM)motor Anurag College of Engineering Page 14
EEE Deptartment Control Systems Lab Manual .the ease of controllable speed along with linear torque speed control curve makes the PM motor ideal for servo mechanism applications PRECAUTIONS: 1. The speed control knob is always in the most anti clock wise position before switching on the position. 2. In order to increase the armature voltage, rotate the knob in the clock wise direction in a gentle fashion. 3. In order to increase the load on the motor, adjust the knob K in a gentle fashion. PROCEDURE: 1. Adjust T1 to 40gm with the help of knob K. 2. Ensure the pot P1 is in maximum position, switch on the supply. 3. Connect the voltmeters across the terminals of armature and field. 4. Adjust P1 so that Va 10v and P2 such that V f 20v. 5. Note down T1and T2 and speed values in tabular column. 6. Keeping Va 10v, adjust T1 up to 150gm in steps of readings. 7. Now for Va 15, 20, 25 and 30v repeat step 6. 8. From the table plot the speed –torque characteristics. 9. Repeat the above step for various values of Vf by controlling P2 . TABULAR COLUMNS: FIELD CONTROL: Va Vf1 T1(gm) T2(gm) Anurag College of Engineering (T1-T2)XK (mN-m) Where K rg Ia(amp) (N)rpm Page 15
EEE Deptartment Va T1(gm) Va T1(gm) Control Systems Lab Manual Vf2 T2(gm) (T1T2)K(mN-m) Vf3 T2(gm) (T1-T2)K(mNm) Ia(amp) Ia(amp) N(rpm) N(rpm) ARMATURE CONTROL: Va1 T1(gm) Vf T2(gm) (T1-T2)K(mN-m) Ia(amp) N(rpm) Va2 T1(gm) Vf T2(gm) (T1-T2)K(mN-m) Ia(amp) N(rpm) Va3 T1(gm) Vf T2(gm) (T1-T2)K(mN-m) Ia(amp) N(rpm) Anurag College of Engineering Page 16
EEE Deptartment Control Systems Lab Manual MODEL GRAPHS: ARMATURE CONTROL Va1 Va2 Va3 Vf3 Vf2 Vf1 CONCLUSIONS: 1. In armature control the speed of the servo motor is increased with increase in armature voltage. 2. The speed of the servomotor decreases with the increase in field voltage. RESULT: The speed- torque characteristics of a dc servo motor is plotted for both armature control and field control. 4. TIME RESPONSE OF SECOND ORDER SYSTEM Anurag College of Engineering Page 17
EEE Deptartment Control Systems Lab Manual AIM: 1. To obtain the time response of second order system 2. To determine time domain specifications. APPARATUS: Decade resistance box Decade inductance box Decade capacitance box Function generator CRO probes Connecting wires. . CIRCUIT DIAGRAM: Fig (i) THEORY: The time response of second order system is defined as the response of the system as the function of time. Apply the KVL to the circuit, Anurag College of Engineering Page 18
EEE Deptartment Control Systems Lab Manual Ei (t ) Ri t L di (t ) 1 i (t )dt dt c 1 i (t )dt c ApplyingLaplace transform to the above equations 1 E i ( s ) RI ( s ) LsI ( s ) I ( s ) cs 1 2 Ei ( s ) s LC sRC 1 I ( s ) Cs 1 Eo ( s ) I ( s) Cs Eo (t ) T.F 1 LC E o (s) 1 2 2 Ei ( s ) s LC sRC 1 s R L s 1 LC Characteristic Equation is s 2 R L s 1 LC 0 Comparing the above transfer function with standard second order transfer function i.e, n 2 2 s 2 2 n s n 1 LC 1 n LC where n 2 damping ratio R 2 C L 1 2 damping natural frequency d n 1 2 12 PROCEDURE: 1. Connect the circuit as per the circuit diagram shown in fig (i). 2. A square wave of amplitude 1V and frequency of 100Hz is given as input to the circuit by using a function generator. 3. Connect the CRO probes across the capacitor terminals. 4. The various time domain specifications are measured from the output waveform Anurag College of Engineering Page 19
EEE Deptartment Control Systems Lab Manual PRECAUTIONS: i) Set the R, L and C values before switch on the supply. ii) Set the input signal voltage equal to 1V and frequency as 100HZ THEORITICAL CALCULATIONS: For the given R, L and C parameters n 1 LC R Damping ratio 2L n M aximum peak over shoot, M p Peak Time t p c(t p ) c ( ) c ( ) d Delay Time t d 1 0.7 n Settling Time t s 4 n 3 n ( ) Rise Time t r d for 2% Error for 5% Error 1 2 2 1 where tan -1 d n 1 2 2 1 Anurag College of Engineering Page 20
EEE Deptartment Control Systems Lab Manual MODEL GRAPH: PRACTICAL OBSERVATIONS: Max % peak over shoot, %Mp Delay time, td Rise time, tr Peak time, tp Settling time, ts TABULAR COLUMN: Time domain specifications Practical observations Theoretical calculations Max % peak over shoot, %Mp Delay time, td Rise time, tr Peak time, tp Settling time, ts Anurag College of Engineering Page 21
EEE Deptartment Control Systems Lab Manual OBSERVATIONS: 1. In the output response tolerance errors can not be observable. 2. Settling time in the output response can be observed only at the 5% tolerance. RESULT: The response of second order system was obtained and time domain specifications were obtained from the response. The time domain specifications are : % Mp td tr tp ts 5. LAG COMPENSATOR AIM: To study the electrical lag compensator network experimentally and to draw bode plots for improvement of steady state and transient behavior of system. APPARATUS: 1. CRO with 2 channels 2. frequency generator to supply a variable frequency sinusoidal source 3. lag compensator kit (R1 20kΩ,R2 25kΩ& C 0.2nf) 4. 1:1 CRO probes -2 Nos CIRCUIT DIAGRAM: Anurag College of Engineering Page 22
EEE Deptartment Control Systems Lab Manual Fig (i) THEORY: Some kind of corrective subsystems introduce in a system to force the plant to meet the desired specifications. These sub systems are known as compensators. Desired specifications mean transient response and steady state error. In general, there are two situations in which compensator are required to stabilize it as well as to achieve a specific performance. In the 2nd case the system is stable. But the compensation is required to obtain the desired performance. The lag compensation is required to improve the steady state behavior of the system of a system while nearly preserving its transient response. THEORITICAL CALCULATIONS: The general form of the T.F of lag compensator is s zc Gc ( s ) s pc 1 s Z c 1 1 pc s From the electrical lag- network Anurag College of Engineering Page 23
EEE Deptartment Control Systems Lab Manual Eo ( s ) R2 1 sC Ei ( s ) R1 R2 1 sC E0 ( s ) R2 sC 1 Ei ( s ) ( R1 R2 ) sC 1 R 2C s 1 CR2 ( R1 R2 )C s 1 ( R1 R2 ) 1 C R2 s 1 CR2 (R 1 R2 ) s R2 R1 R2 1 R2C 1 s 1 s 1 (R 1 R2 ) R2 1 R 2C 1 s 1 s The sinusoidal T.F of the lag- network is Gc ( j ) 1 j Gc ( j ) Gc ( j ) 1 j REPRESENTATION OF S- PLANE: Zc -1/ τ Pc -1/ τ β PROCEDURE: Anurag College of Engineering Page 24
EEE Deptartment Control Systems Lab Manual 1. Connections are made as per the circuit diagram shown in fig (i). Apply a variable frequency of constant amplitude through frequency generator to input terminals of the lag compensation network. 2. Connect both the input and output terminals of CRO and record the input and output sinusoidal signals on the CRO screen. 3. For every value of input frequency, record corresponding lagging phase angle Ф from the CRO. 4. τ and β values are calculated from the known values R1,R2&C.and determine Gc(jω)for every value of ω. 5. Gc (jω) is converted into polar form and bode plots are sketched. TABULAR COLUMN: S.NO Frequency(Hz) A CALCULATIONS: B Xo Yo Gain Ф 20log(B/A) Sin-1(-Xo/A) R1 R2 R2 R2C n 1 MODEL GRAPH: Anurag College of Engineering Page 25
EEE Deptartment Control Systems Lab Manual RESULT: The electrical lag compensator network was studied experimentally and the bode plot is plotted. 5. LEAD COMPENSATOR AIM: To study the electrical lead compensatory network experimentally and to draw bode plots for improvement of steady state and transient behavior of system or plant APPARATUS: 5. CRO with 2 channels 6. frequency generator to supply a variable frequency sinusoidal source 7. lag compensator kit (R1 20kΩ,R2 25kΩ& C 0.2μf) 8. 1:1 CRO probes -2 Nos CIRCUIT DIAGRAM: Anurag College of Engineering Page 26
EEE Deptartment Control Systems Lab Manual Fig (ii) THEORY: A lead compensator speeds up the transient response and increases the margin of stability of system .it also helps to increase the system error constant through to a limited extent. THEORITICAL CALCULATIONS: The general form of the T.F of lag compensator is Anurag College of Engineering Page 27
EEE Deptartment Control Systems Lab Manual s Zc Gc ( s ) s Pc s 1 , Z c Pc 1 s 1 For the Electrical lead - network E 0 (s) R2 Ei ( s ) R2 R1 1 Cs ( R1 1 Cs ) R 2 R1Cs 1 R2 R1 R2Cs R1 R 1 R2C s 1 CR1 R1 R2C s R1 R2 R1 R2C s 1 CR1 s R1 R2 R2 1 R1C s 1 , R2 R1 R2 1, R1C s 1 1 s 1 s The sinusoidal transfer function of a lag network is 1 j G c ( j ) 1 j Gc ( j ) Gc ( j ) REPRESENTATION OF S- PLANE: Anurag College of Engineering Page 28
EEE Deptartment Control Systems Lab Manual Pc Zc -1/ τ α -1/ τ PROCEDURE: 6. Connections are made as per the circuit diagram shown in fig (ii). 7. Apply a variable frequency of constant amplitude is applied through frequency generator to input terminals of the lead compensation network. 8. Connect both the input and output terminals of CRO and record the input and output sinusoidal signals on the CRO screen. 9. For every value of input frequency, record corresponding phase angle Ф from the CRO. 10. τ and α values are calculated from the known values R1, R2&C.and determine Gc(jω)for every value of ω. 11. Gc(jω) is converted into polar form and bode plots are sketched. TABULAR COLUMN: S.NO Frequency(Hz) A B Xo Yo Gain Ф 20log(B/A) Sin-1(-Xo/A) CALCULATIONS: Anurag College of Engineering Page 29
EEE Deptartment Control Systems Lab Manual R2 R1 R2 R1C n 1 MODEL GRAPH: RESULT: The electrical lead compensator network was studied experimentally and the bode plots are plotted. 6. SIMULATION OF TRANSFER FUNCTION USING OP-AMPS AIM: To simulate the transfer function using Op-Amps, by using the circuits Integrator, Non inverting amplifier and summing amplifier. APPARATUS: Op- Amps IC -741 -3 NO’S Capacitor 0.1μF -1 No. Resistor 10 KΩ -5 No’s Anurag College of Engineering Page 30
EEE Deptartment Control Systems Lab Manual 2 KΩ- 2 No.’s 100KΩ- 1 No. Function Generator, CRO & probes, connecting wires. THEORY: 1. Op-amp is a operational amplifier, which performs arithmetic operations. 2. Op-amp pin configuration contains 8-pins, generally it is IC 741 3. In 741 second and third pins are inverting and non-inverting pins, it is operated in conduction mode by giving biasing voltages - VEE and VCC to the 4th and 7th pins respectively. 4. It is a high gain amplifier. 5. In inverting mode the phase shift between input and output is 1800, where as in non-inverting mode the input and output signals are in phase. 6. In integrator circuit output is integration of input signal. CIRCUIT DIAGRAM: Fig (i) PROCEDURE: 1. Connect the circuit as per the circuit diagram shown in fig (i). 2. A square wave input is given to both the integrator and non inverting amplifier circuits. Anurag College of Engineering Page 31
EEE Deptartment Control Systems Lab Manual 3. Vcc and –Vee are applied as 10v and -10v at 7 and 4 pins respectively for every circuit shown in the circuit diagram. 4. Individual out puts V01 and V02 of integrator and non inverting amplifier are summed by using a summing amplifier which is shown in figure. 5. The output waveform of integrator, non-inverting amplifier and summing amplifier are observed and plotted on the graph THEORITICAL CALCULATIONS:-. For the integrator circuit, R - f R K 10 T1 1 1 sR f C (1 sR f C ) (1 .01s) For the Non- inverting amplifier, T2 1 R f R1 2 For summing amplifier T T1 T2 2- 10 (1 .01s) MODEL GRAPH: Anurag College of Engineering Page 32
EEE Deptartment Control Systems Lab Manual RESULT: The transfer function of the op-amp was simulated. 7. STATE SPACE TO TRANSFER FUNCTION USING MATLAB AIM: To determine the transfer function for the given state space representation. Anurag College of Engineering Page 33
EEE Deptartment Control Systems Lab Manual 5 10 2 A 1 0 0 1 0 0 C 1 4 11 1 B 0 0 D 0 PROGRAM: The program to convert state space representation to transfer function A [-5 -10 -2; 1 0 0; 0 1 0]; B [1; 0;0]; C [1 4 11]; D [0]; [num ,den] ss2tf (A, B, C, D) THEORY: This experiment is done to convert the state space representation into transfer function model by using MATLAB. 5 10 2 A 1 0 0 1 0 0 C 1 4 11 Transfer Function Anurag College of Engineering 1 B 0 0 D 0 C.Adj[SI - A]B D SI - A Page 34
EEE Deptartment Control Systems Lab Manual S 5 10 2 SI - A 1 S 0 0 1 S S2 S 2 Cofactor matrix of (SI - A) (10 S 2) S 5S 2S 2 Adj ( SI A) S 2 S 1 (10 S 2) S 2 5S S 5 S 5 S 2 5S 10 1 2 S 5S 10 2S 2 S 2 Adj ( SI A).B S 1 S 2 C. Adj ( SI A).B 1 4 11 S S 2 4 S 11 1 S 5 10 SI - A 1 0 S 2 0 (S 5)S2 10( S ) S (1 0) s 3 5s 2 10 s 2 1 S T .F C.Adj[SI - 1]B D SI A S2 4 S 11 S 3 5S 2 10 S 2 RESULT: num 0 1 4 11 den 1 5 10 2 Hence the transfer function was verified for the given state space representation. T.F Anurag College of Engineering (S2 4S 11 / S3 5S2 10S 2) Page 35
EEE Deptartment Control Systems Lab Manual 8. PLOTING OF ROOT LOCUS AIM: To obtain root locus plot for a given transfer function 1/ (s2-4s 8) by using MATLAB. PROGRAM: num [1]; den [1 -4 8]; rlocus (tf (num, den)) THEORY: The root locus technique is used for stability analysis. Using the root locus the range of values of K, for a stable system can be determined. It is also easier to study the relative stability of the system from the knowledge of location of closed loop poles. The root locus can be plotted in S-plane by verifying system parameters over the complete range of values. The roots corresponding to a particular value of the system parameter can then be located on the locus ors the value of the parameter for a desired root locus can be determined from root locus. PROCEDURE: From the command window open new .M file. Write a program and save it on to the desktop and come back to the command window. Now type .M file name and observe the root locus. THEORETICAL CALCULATIONS: 1 s 4s 8 Characteristic equation is s 2 4s 8 0 Given transfer function 2 The roots are (2-j2) & (2 j2) Anurag College of Engineering Page 36
EEE Deptartment Control Systems Lab Manual MODEL GRAPH: RESULT: The root locus plot for a given transfer function was verified in MATLAB. 9. STATE SPACE REPRESENTATION OF TRANSFER FUNCTION USING MATLAB AIM: To determine the state space representation for the given transfer function PROGRAM: The program to convert transfer function in to state space representation num [a b c]; den [1 p q r]; [A B C D] tf2ss (num, den) THEORY: This experiment is done to convert the state space representation into transfer function model by using MATLAB. Anurag College of Engineering Page 37
EEE Deptartment Control Systems Lab Manual State space representation * x Ax Bu y Cx Du is the state space representation of a physical system. The function tt2ss (num, den) converts the given transfer function into state space representation. CONVERTION OF T.F INTO STATE SPACE MODEL: T.F as 2 bs c Y ( s) 3 2 s ps qsr U ( s) Y x3 Let, dy * x 3 x2 dt d2y * x 2 x1 dt 2 d3y * x1 dt 2 d3y d2y dy U (t ) 3 p 2 q ry dt dt dt * U (t ) x1 px1 qx2 rx3 * x1 px1 qx2 rx3 U (t ) * x2 x1 * x3 x2 * x*1 p q r x1 1 x 1 0 0 x2 0 u (t ) *2 1 0 x3 0 x3 0 Comparing with equation Anurag College of Engineering Page 38
EEE Deptartment Control Systems Lab Manual * x Ax Bu then p q r 1 A 1 0 0 B 0 0 0 1 0 Y (t ) as 2 bs c d2y dy b cy 2 dt dt Y (t ) ax1 bx2 cx3 Y (t ) a x1 Y a b c x2 [0]U (t ) x3 Comparing with Y CX DU C a b c D [0] There fore p q r 1 A 1 0 0 B 0 0 0 1 0 C a b c D [0] RESULT: p A 1 0 C a b q r 1 0 0 B 0 0 1 0 c D [0] The state space representation for the given transfer function was verified using MATLAB Anurag College of Engineering Page 39
anurag college of engineering page 2 list of control system lab experiments 1. transfer function of d.c.shunt generator 2. characteristics of magnetic amplifier 3. speed-torque characteristics of servomotor. 4. time response of second order system. 5. lag-lead compensators 6. simulation of transfer function using op-amp. 7.
Contents Chapter 1 Lab Algorithms, Errors, and Testing 1 Chapter 2 Lab Java Fundamentals 9 Chapter 3 Lab Selection Control Structures 21 Chapter 4 Lab Loops and Files 31 Chapter 5 Lab Methods 41 Chapter 6 Lab Classes and Objects 51 Chapter 7 Lab GUI Applications 61 Chapter 8 Lab Arrays 67 Chapter 9 Lab More Classes and Objects 75 Chapter 10 Lab Text Processing and Wrapper Classes 87
Biology Lab Notebook Table of Contents: 1. General Lab Template 2. Lab Report Grading Rubric 3. Sample Lab Report 4. Graphing Lab 5. Personal Experiment 6. Enzymes Lab 7. The Importance of Water 8. Cell Membranes - How Do Small Materials Enter Cells? 9. Osmosis - Elodea Lab 10. Respiration - Yeast Lab 11. Cell Division - Egg Lab 12.
esty Young in IBM Almaden, Anurag Acharya in Google, and Madhu Talluri and Yousef Khalidi in Microsoft. They were all wonderful people to work with and I learned a lot in each of my internships. I especially thank Anurag and Yousef for their support and insights during my job search. I was f
In this document, "PwC" refers to PricewaterhouseCoopers Priv ate Limited (a limited liability com MS 219-September 2011 S&R .indd Designed by: PwC Brand and Communications, India www.pwc.in Contacts Shashank Tripathi Executive Director 91 98196 78900 shashank.tripathi@in.pwc.com Anurag Garg Senior Manager 91 9711701799 anurag.garg@in.pwc .
Lab 5-2: Configuring DHCP Server C-72 Lab 5-3: Troubleshooting VLANs and Trunks C-73 Lab 5-4: Optimizing STP C-76 Lab 5-5: Configuring EtherChannel C-78 Lab 6-1: Troubleshooting IP Connectivity C-80 Lab 7-1: Configuring and Troubleshooting a Serial Connection C-82 Lab 7-2: Establishing a Frame Relay WAN C-83 Lab 7
Each week you will have pre-lab assignments and post-lab assignments. The pre-lab assignments will be due at 8:00am the day of your scheduled lab period. All other lab-related assignments are due by 11:59 pm the day of your scheduled lab period. Pre-lab assignments cannot be completed late for any credit. For best performance, use only Firefox or
Lab EX: Colony Morphology/Growth Patterns on Slants/ Growth Patterns in Broth (lecture only) - Optional Lab EX: Negative Stain (p. 46) Lab EX : Gram Stain - Lab One (p. 50) Quiz or Report - 20 points New reading assignment 11/03 F Lab EX : Gram Stain - Lab Two Lab EX: Endospore Stain (p. 56) Quiz or Report - 20 points New reading .
3 For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards volume information, refer to the standard’s Document Summary page on the ASTM website. 4 Withdrawn. 5 Available fromAmerican Concrete Institute (ACI), P.O. Box 9094, Farmington
