Second Order Sys_mal

VS

ERR

+_ S VF

Pragna MICRODESIGNS

INSTRUCTION AND OPERATION MANUAL FOR

SECOND ORDER SYSTEM STUDY UNIT

Designed and Manufactured by:

PRAGNA MICRODESIGNS No. 34, Karekallu, Kamakshipalya, Basaveshwaranagar post, Bangalore – 560 079. Telefax; 23285123 E-mail: [email protected] SECOND ORDER SYSTEM STUDY UNIT

This unit consists of two parts: a) Signal source for second order system. b) Second order systems using opamp and RLC. a)

Signal Source: The signal source generates the necessary input excitation supply for testing the second order system under different damping factors and time constant. This part generates a square wave of 15Hz approximately. A switch is provided to select square wave or step (DC) source. ON/OFF switch is provided for signal source. Amplitude of the signal source can be varied from 0V to 15V approximately for square wave and 0V to 10V approximately for DC source.

b)

Second order system: This part consists of a second order system built using Op-amp. In order to study the behavior of a second order system with various damping factors, facility has been provided to select the damping factor – 0.3, 0.7, 1 and 2. In order to study the behavior of a second order system with different time Constants, facility has been provided to choose the time constant at 3 msec or 5sec. The input & output terminals of the second order system are brought out on the front panel independently. So, we can also use external signal source to study the frequency response of the system.

Front Panel Details: -

1.

Power

:

Mains ON/OFF switch to the unit with builtin indicator.

2.

Amplitude

:

Potentiometer to vary the amplitude of signal source.

3.

Sq/Step

:

Switch to select square wave or step (DC) input.

4.

ON/OFF

:

ON/OFF switch for signal.

5.

OUTPUT

:

Signal output points.

6.

Damping factor:

Switch to select damping factor 0.3/0.7/1 & 2.

7.

INPUT

:

Second order system input points to connect signal source.

8.

OUTPUT

:

Second order system output points

9. Time constant 3m sec / 5 sec :

Switch to select time constant.

Procedure: Switch ON the mains supply to the unit, observe the signal source output by selecting square wave or step input and by varying amplitude potentiometer. Make sure that the signal source is correct before connecting the input of the second order system. Now select square wave signal and 3 msec time constant. Draw the input square wave signal. Connect signal output to second order system input. Draw the second order system o/p for different values of damping factors 0.3, 0.7, 1 and 2. Compare this with the theoretical wave forms. Select step input, adjust the amplitude potentiometer to get %Volts DC and select 5 sec time constant. Switch off the signal. Now switch ON the signal, monitor the second order system o/p using a multimeter. Note down the o/p voltage for every second. Draw the graph of time v/s voltage. Repeat the same for different damping factor. When testing a second order system with large time constant – 5 sec, it is essential to supply a DC as a step voltage. This source provides a DC step input to the system by selecting step signal and by switch ON the signal source from OFF to ON.

When testing a second order system with low time constant – 3 msec, the response of the system for a step input stabilizers to its final value within about 50 – 75m sec. In such case, the system response for a step can be studied by giving a repeated step, which is effectively, a square wave. Input level to the system should be chosen so as to obtain the output response within the saturable voltage of opamp + or – 15V. The amplitude should be within 5 to 8V. If a much lower input voltage is selected, then the other interference’s such as mains picks up can be become relatively higher & the response obtained may not be satisfactory. The parameters of a second order system such as delay time, rise time, peak time, settling time and peak overshoot are important parameters to be understood. For zeta less than 1, the system is under damped and the system response shows overshoot for very low damping factor, the step response is DC superimposed with an exponentially dying cosine waveform. For zeta less than 1, the system said to have over damped response. In practical systems, the damping factor is set between 0.7 and 1. Note : Use 3 pin grounded mains supply to the unit avoid line interference. Use proper CRO probe to see the output wave forms.

FIG: STEP RESPONSE OF AN UNDERDAMPED STSTEM.

td tr Mp tp ts

ess

= = = = = =

delay time Rise time Max. Overshoot peak time Setting time Steady state error.

CIRCUIT DIAGRAM

SECOND ORDER SYSTEM USING R L C Procedure: -

Switch ON the mains supply to the unit, observe the signal source output by selecting square wave or step input and by varying amplitude potentiometer. Make sure signal source is correct before connecting the input of the second order system. Now select square wave signal. Draw the input square wave signal. Connect the output of square wave signal source to second order system using RLC. Draw the second order system o/p for different values of damping factors from 0 to 2 in steps of 0.1 by varying R. Compare this with the theoretical wave forms. Measure the R values using Digital DC voltmeter or multi meter between the I/P terminals marked ‘R’ with main switch in OFF position. R-10K

L- 2H

C-0.32 µF

Square wave signal

L = 2H

C = 0.32 µF

Calculation 1 Wn

1

=

= LC

2 X 0.32 x 10¯

1250 f

=

= 200Hz 2Π

R = 2δ L/C δ = 0.3 -- R = 2δ L/C = 2X0.3 /0.3X10ֿ 2X0.3X2.5X10³ 0.3 δ = 0.7 δ = 1 δ = 2

= = = =

1500 ohms 3500 ohms 5000 ohms 10000 ohms

6

= 1250

Tabular Column

Sl No

R in Ohm

L in Henry

C in Micro Farad

1 2 3 4

500 1000 1500 2000 _ _ _ _ _ _ 10000

2H 2H 2H 2H _ _ _ _ _ _ 2H

0.32mF 0.32mF 0.32mF 0.32mF _ _ _ _ _ _ 0.32mF

δ (Dampin g Factor)

td

tr

Mp

tp

ts ess