EXP.NO.4
PI Level Control
Objectives
1. in the following practical's ,you will
investigate PI and PID control ,comparing the two and demonstrating any
drawbacks associated with them.
2. To learn about proportional plus integral
PI control when used to control the level in the tank on the BPR.
3. To learn the limitations of PI control in particular situations
,providing the reason why another control method is required PID.
4. To learn about full three PID control for
controlling the level in the tank.
Proportional and Integral PI control
The major problem with proportional control , as explored is the
inherent offset produced by the controller .the control effort needed to
correct an error is directly proportional to that error and so the minimum
error possible is finite. The way to remove this error is to use a control
action that will produce a control effort for zero error. This is done by
introducing an extra component into the control effort that is the integral of
the error. This continuous to change until the error is zero.
Integral control
The amount of integral action is controlled by constant
Uc=UP+Ur
Where
From the previous assignments , you will already have met the expression
for the proportional term
Up=Ke
The reset term is described by :
Which shows the position of the reset time constant
The control effort can now be determined by the following expression
Uc=k[(1/Tr ) ∫e dt]
This describes the action of an automatic reset controller
The diagram above is the pervious proportional control example where
Uc=ke
The diagram below shows the new control effort arrangement to produce PI
control. Now you can see the two distinct elements of Uc:Ur
The reset time constant TR is a very important variable as it controls the contribution of the integral constant to the control effort over a given length of time
Calculations and graphics
A- Proportional control only : P-control
I = 1
|
case |
PB |
e.s.s |
Ts (sec)
|
Tr (sec) |
TP (sec)
|
Mp |
|
1 |
1 |
1.0 |
50 |
24 |
35 |
10.6 |
|
2 |
5 |
1.5 |
60 |
23 |
35 |
9.00 |
|
3 |
10 |
2.0 |
59 |
28 |
38 |
7.50 |
|
4 |
15 |
3.5 |
61 |
28 |
40 |
7.80 |
|
5 |
20 |
4.0 |
63 |
42 |
51 |
6.60 |
B-Proportional – integral control
PB = 5
|
case |
Tr |
e.s.s |
Ts (sec)
|
Tr (sec)
|
TP(sec)
|
Mp |
|
1 |
5 |
1.00 |
48 |
56 |
64 |
1 |
|
2 |
10 |
0.50 |
50 |
47 |
53 |
1 |
|
3 |
15 |
0.25 |
68 |
29 |
38 |
6 |
|
4 |
20 |
1.50 |
54 |
26 |
35 |
8 |
DISCUSSION
1. How does proportional band effect the
response time of the controller (
consider what PB is and how it influences the control effort.
Ans . when the proportional increasing the offset
increasing to suitable value
after this the increasing in PB produced decreasing in offset but the system
become unstable.
2. Recall the simple equations met in earlier
theory sections and explain how PB and
Ans. The overall TRANSFER FUNCTIOIN of PID controller is
Where
Recall this equation
|
Response |
Rise time |
overshoot |
Settling time |
s-s error |
| KP
|
Decrease |
increase |
NT |
Decrease |
| kI
|
Decrease |
increase |
increase |
Eliminate |
| KD |
NT |
Decrease |
Decrease |
NT |
3. Why must the integral action be large if PB
is large (explain each step linking these two parameters
Ans. When increasing the integral action the offset error is decrease until this error become error.
