3. Introduction
Motivation
Temparature control systems are used in many of the industries,
and it’s an importent example of regulator system.
Objectives
To familiarize with industrial processes.
To understand various components of control system.
To get an idea of basic control methods.
To distinguish between open loop and closed loop control actions.
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4. Block Diagram
Basic block diagram of the process control trainer is given below
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5. Basic control approaches
1. Open Loop Control
In this the control input is a function of reference, and is pre
calibrated
u = f(r) (1)
2. Closed loop Control
Here control input is a function of both reference and output, i.e.
u = f(e) = f(r
,y) (2)
One of the basic closed loop control approach is proportional
control, and in which control input is proportional to the error
(deviation), i.e.,
u =K e (3)
In two step control the control changes from one value to another
when error (deviation) changes sign.To avoid high frequency
oscillations, overlap(threshold) is provided in practice, i.e.
u =hyst
(e) (4)
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6. Transfer lag
Transfer lag is due to the dynamical elements in the
system/process.
Consider the following first order process (eg.thermal system,
hydraulic system), for which the step responce is given in figure.
G(s) =
1
1 +T s
(5)
For a pole with a time constant T, transfer lag will be T seconds.
It is the time taken by the output to reach 63.2% of it’s final value.
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7. Transport lag (distance/velocity lag)
Transport lag is charecterized by delay in system responce.
A pure delay has the input output relation
y(t) =u(t − T
) (6)
Now by taking Laplace transform we have
Y (s) =e−sT
U(s) (7)
Hence in frequency domain, delay is charecterized by it’s transfer
function - e−sT
.
|e
−jωT
| = 1 ∠e
−jωT
= −ωT
and is all pass with phase lag increasing with frequency.
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8. Questions
Derive the transfer function of a Thermal system.
What is the
time constant of this system?
Find the relation between transfer lag and system pole location?
Draw the bode plot of transport lag?.
How the transport lag affects stability?.Does it affects stability in
open loop control case?
What are the practical issues with two step control?
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