Experiment No. 1

Experiment No. 02

Aim: Experimental study of time response characteristics of R-L-C

second order system: Validation using simulation.

Apparatus: DC supply, Resistor, Inductor, Capacitor, voltmeters and ammeters.

Theory:

For the series RLC circuit below, application of Kirchhoff s voltage law gives following equations in terms of current

d2 id t 2 +

RL

d idt

+ iLC

=0

second order ordinary differential equations whose general solution can be found from the roots of the characteristic equation:

s2+2αs+ω02=0

Where the roots are given by

Where α= 12 RC

and ω0=1

√LCThe values of α and ω0determine the form of the natural (or step) response of a second order series RLC circuit. The form of the response can be categorized as:

Overdamped. The response is overdamped when α 2>ω02. In this case the natural (or step)

response approaches its final value without oscillation.

Overdamped. In this case α 2<ω02 and the response oscillates about its final value.

Critically damped. In this case α 2=ω02, and the response is on the verge of oscillating about

its final value.

Depending on the damping, the solution to the differential equation describing the response of the circuit can be found by applying the appropriate set of equations.

Circuit for getting step response.

Observation Table:

Time V R V L V C

Procedure: Connect the circuit taking components of appropriate values. Apply source and measure different voltages across different elements wrt time. Plot the graphs

Results and conclusions:

Experiment No. 3

Experiment No. 4

PID control of level/Pressure/Temperature control system.

WATER LEVEL CONTROLLER

(ON/OFF MODE)

**INTRODUCTION:

This water level controller is demonstration type set

up with the following accessories.

1. Main control unit.

2. Sensing systems mounted on a M.S. water tank.

3. Fractional Horsepower motor system coupled to a pump (monoblock

Pump).

Demonstration is based on one type of sensor.

Aluminum electrode system.

Electrode System.

This system has two alluminium electrodes. The basic idea on the

Which the circuit operates is that the tap water or bulk water used for

general consumption has always sufficient conductivity. This

Conductivity of water forms the basis of the level sensing .The electrode

‘A’ is used for upper limit while sensor ‘B’ is used for lower limit. The

body of the tank provides return path through the water itself.

Now refer to the circuit diagram for water level controller. Note that

the electrode ‘B’ is connected through the N/C contact on the relay

‘RL1’.

When the water level is below the electrode ‘B’, the transistor gets

properly biased and the relay ‘RL1’ is turned ON. This in turn switches

ON the motor pump set. When the water level touches electrode ‘B’, no

change takes place as the sensor is connected through N/C contact. This

contact is now open.

When the water level rises and touches electrode ‘A’, the base current

of the transistor is diverted to the ground through the electrode and the

transistor gets turned OFF and the motor stops. The pump is switched

ON again only when the water level goes below sensor ‘B’ again.

The main advantage of the two electrode system is that the electrode ‘A’ prevents overflowing and the electrode ‘B’ does not allow the water level to go below certain level. The electrodes A and B might be located very close to each other (Height wise) and a close level control within 2 cm can be readily obtained.

Operating Instructions :

1>Ensure that the suction pipe is completely full of water (i.e. perform

the priming operation of the pump.) Ensure good earthing of the

Motor.

2>Pump outlet might be connected to the tank inlet.

3> Establish connection between the controller unit and the water tank

by supplied cables.

4>Now ensure that the electrode ‘A’ and ‘B’ are suitably located.

5>Switch ON the supply and observe the operation of the system.

6>You may check the operation at various positions of the electrodes,

but the electrode ‘B’ should be always at the lower level than that of

Electrode ‘A’.

PRECAUTION:

1> If there is lot of scaling on the electrode system, the electrodes are required to be cleaned before re-use.

2> Ensure that the water from the tank does not split out on the electronic unit.

Experiment No. 5

Experimental analysis of D.C. Position Control System

Experiment No. 06

Aim: Stability analysis using a) Bode plot b) Root locus c) Nyquist plot.

Apparatus: Matlab softaware

Theory:

Explain stability and its types.

Consider the following transfer function.

1. G(s)= 10(s+1 ) (s+2 )(s+3)

2. G(s)=5 ( s+2 )

(s−3 ) ( s+4 )(s+5)

Create m-file and following code.clcclear allclose all G=zpk(system)bode (G)figurerlocus(G)figurenyquist(G)

Obtain the plots.

Comment

Conclusion

Experiment No. 07

Aim: Time response of second order system effect of P, PI, PID on it.

Apparatus: Matlab softaware

Theory:

What is PID controller Draw simple mass, spring, damper system and write down is 2nd order TF.

Take its Laplae transform. Get the TF between displace x and the output f (t) Let

M = 1kg b = 10 N.s/m k = 20 N/m F(s) = 1 Plug these values into the above transfer function

Get the Open-loop step response.

Create a new m-file. Add in the following code:

num=1; den=[1 10 20]; step (num,den)

Obtain and save the plot. The closed-loop transfer function of the above system with a proportional controller:

X (s)F (s )

=k p

M s2+bs+(k+k p) Obtain step resp.

Kp=300; num=[Kp]; den=[1 10 20+Kp]; t=0:0.01:2;

step (num,den,t)

Now consider PD controlX (s)F (s )

=kd s+k p

M s2+(b+k d)s+(k+k p) Obtain step resp.

Kp=300; Kd=10; num=[Kd Kp];

den=[1 10+Kd 20+Kp]; t=0:0.01:2; step (num,den,t)

Now consider PI controlX (s)F (s )

=k p s+k i

s3+b s2+(k+k p)s+k i

Obtain step resp.Kp=30; Ki=70; num=[Kp Ki]; den=[1 10 20+Kp Ki]; t=0:0.01:2; step (num,den,t)

Now consider PID controllerX (s)F (s )

=kd s2+k p s+k i

s3+¿¿ Obtain step resp

Kp=350; Ki=300; Kd=50; num=[Kd Kp Ki]; den=[1 10+Kd 20+Kp Ki]; t=0:0.01:2; step (num,den,t)

Conclusion

Experiment No. 08

Aim: Study of addition of pole-zero on root locus of second order system.

Apparatus: Matlab software

Theory:

Root locus is a technique which gives pictorial representation of variation of closed loop poles on variation of different system parameters.

Procedure

Obtain a root locus of a given transfer function.

Add pole close to origin and observer the root locus of modified system

Add a pole far away from origin and observe the root locus of the modified system

Add zero close to the origin and observe the root locus of the modified system

Add zero far away from the origin and observe the root locus of the modified system

Add pole and zero simultaneously to the original transfer function and observed the root locus of modified system.

Result and conclusion: From the various root locus sketches effect of addition of pole-zero on the root locus is studied.

Experiment No. 5

AIM:- To study performance of PID controller with model as temperature control system.

APPARATUS:- PID control kit and stop watch. process as temperature control system.

THEORY: - The set up has built in signal source as reference, DVM as temperature indicator; PID controller and DC supply to operate the system. The set has three controls, P for proportional gain, I for integrated gain, and D for derivative gain. A separate oven with fan is provided to raise the temperature.

PROCEDURE:-

The experiment is completed in four parts.

1. TO OBSERVE PROCESS CHARACTERISTICS: - Connect the oven and switch on the power. Select temperature switch to oven and note the temperature. Now select the temperature switch to S.P. adjust temperature to 20*C. again select temperature switch to oven, switch on the heater and start the stop watch. Note the temperature at intervals of 5, 10,20,30,40 seconds till the temperature is stable. Plot the curve between temperature and time.

2. TO OBSERVE SIGNAL CONDITIONAL CHARACTERISTICS:- Connect the Circuit as before and set the temp. about 10* C. Connect the DVM across ground 0And signal conditional socket. Select temp. switch to oven and note the temp. and voltage at error detector point. Switch on heater and note error detector negative side input voltage.

3 P. CONTROL:-Connect the set as before and set temp. to 60*C and P control Kp To 10. switch on the heater and note temp. at 10 sec. interval. Switch off the heater and allow it to cool with the help of fan. Now adjust Kp to 16. Switch on the heater and repeat the experiment. Plot graph between temp. and time.

4 PI CONTROL:- Set temp. to 60* C . Select oven temp. at display reading. Switch On the heater and stop watch. Note the temp. at 10 sec. interval. Plot graph between time and temp.

5 PID CONTROL:- Set temp. at 60* C select ovan temp. at display reading. Switch on heater and stop watch. Note temp. at 10 sec. interval . plot response curve from results obtained from the experiment. Find out set temp. percentage from graph as: T( set) – T(ovan) / T(set) * 100.

OBSERVATION TABLE:-

Sr. No. Time Temperature

PRECAUTIONS:-

1 Do not switch on the heater for long time.2 Allow the heater to cool before next experiment.3 Take the reading carefully.4 Switch off the kit when not in use

GRAPH:-

DISCUSSION:-The graph is plotted between time and temperature. The temperature increases with time upto a certain limit and then becomes steady . this time temperature graph is used to find out steady state error (Ess) the rise in temperature depends Upon feedback gain . More the feedback gain less the steady state error but it does not become zero .