Experiment – Control 3

By,

Group A4 (b) :

Piyush Lakhmani (11D020027)

Abhinay Korukonda (110020076)

Vaibhav Gupta

Rahul Parmata

Aim of the Experiment

The experiments aims at studying the input-output relation of an

interacting tank system by analyzing the system’s open loop

behavior on given positive and negative step inputs.

The relation obtained would be used to get the controller

parameters. We will use those parameters to set the controller such

that it gives minimum offset and stable output

Schematic

• Manipulated variable – Fi (m3/s)• Disturbance Variable – Fd (m3/s)• Controlled variable – h2 (m)

Introduction

System – Interacting Tank system – both h1 and h2 affect each other

We have 2 tanks and there are interconnected. The water flow into

tank 1 is Fi and tank 2 is Fd. Height of water in tank1 is h1 and in tank

2 is h2.

Controller is a PI controller. Set point and Fd are kept fixed to a

certain value and the controller controls Fi to reach the set point

value of h2

Theory

Open Loop systems – Systems in which there is no controller. Any

change in input affect the output according to the process

dynamics. The process has an inertia, or opposing force which tries

to oppose the changes brought in by the manipulated variable and tends to achieve a steady state. We analyze this behavior of the

system to get its dynamics

Closed loop systems - Here, output is affected by not only input but by controllers which tend to sense the variation between set value

and current value, work out their dynamics and send a signal to end

element which may be a valve. This helps us to achieve stable

output if the controller settings are proper

Theory

Servo Response

• When the step change is made in the set point and then the response of the system in presence of the controller is said to be servo response

∆𝑦 = (𝐺𝑝𝐺𝑐

𝐺𝑝𝐺𝑐 + 1)∆𝑦𝑑

Regulatory Response

• When the change is made in the disturbance variable, then the response of the system in presence of controller is termed as regulatory response

∆𝑦 = (1

𝐺𝑝𝐺𝑐 + 1)∆𝐹𝑑

Gp= Plant dynamics, Gc = controller dynamics, ∆𝑦 = output response, ∆𝑦d = change in set point, ∆𝐹𝑑 = Change in disturbance variable

Procedure

We get the Controller gain and time constant from the previous

experiment.

The set point is initially fixed to 9 mA and Fd is set to 10 mA

Fi is regulated by the controller

Once we start the experiment, we see that h2 increases from 0 to 9 mA

Then, we change the value of set point and see the output response

Same is done for negative step change in set point.

Again, we repeat the same steps for step changes in Fd and record the

results

Results

1. Initial Configuration:

Set point = 9 mA

Fd = 10 mA

h2 (s.s)= 9 mA

Positive Step change in set point (+3 mA)

Set Point = 12 mA

Fd = 10 mA

H2(s.s) = 12 mA

Positive Step change in Fd (+2 mA)

Set Point = 12 mA

Fd = 12 mA

H2(s.s) = 12 mA

Negative Step change in Fd (-2 mA)

Set Point = 12 mA

Fd = 10 mA

H2(s.s) = 12 mA

Overall variation in H2, set point and Fd

0

2

4

6

8

10

12

14

16

1

123

245

367

489

611

733

855

977

1099

1221

1343

1465

1587

1709

1831

1953

2075

2197

2319

2441

2563

2685

2807

2929

3051

3173

3295

3417

va

lue

in m

A

H2 vs set point and Fd

H2

Set Value

Fd

Conclusion

PI controller was able to remove offset for both servo and regulatory

cases

P controller is unable to remove offset unless there is an integrator in

the process itself