Automatika

1
Compensation
Using the process field GPF(s) step response
2
Analysis of step response

• The following analysis technique are also used
  using the original recorded values or the
  identified model created from these recorded
  values.
• First it must be concluded if the process field
  has or hasn't got integral effect. It possible
  from the reaction curve of the process field. It
  takes a new steady-state or uniformly changing
  the amplitude.
• It should be noted the time constants of the
  approximation model.
• It is possible editing the reaction curve.

3
Self-adjusting process fieldPI or PIDT1
compensation
European structure
4
Without integral effect
In this case the most commonly used controller
type the PI or if the reaction curve starts
relatively slowly PIDT1 The 1 can also be used if
the process field has got large dead time. The
approximation models, whose parameters can be
determined without computers the next
PTn
HPT1
5
The transfer functions
PI
PIDT1
In case of PIDT1 the transfer function has got
four variables. You must be determine the AD
differential gain to define the T time constants!
6
The principle of compensation

• Be plotted the step response of process field.
• The ratio of the steady-state amplitude of the
  input (energizing) and output (response) signals
  is the KP.
• You should look for the inflection point of the
  reaction curve.
• You need to edit the crossover points of
  beginning and final values of reaction curve with
  the line which overlaid on the inflection point.
• The intersection can be defined the apparent Tu
  dead time and the apparent Tg first order time
  constant.

7
HPT1 model from the reaction curve of process
field
8
Edited parameters
9
Determination of KP, Tu and Tg
The above figures are made MATLAB software. The
amplitude of step command of MATLAB is unit, and
so the read final value equals the process field
gain KP 0.72.
Determination with editing of Tg and Tu is quite
inaccuracy.
Recommendation of Piwinger
7.8
0
3.3
50
PI
I
PID
10
Recommendation of Chien-Hrones-Reswick
The initial conditions for optimization
parameters The process field is an ideal HPT1
The objective function is the fastest aperiodic
transient at setpoint tracking The optimization
is based on the square-integral criterion.
11
Determination of KC and TI
Defined values KP 0.72, Tg 10.6 sec., and Tu
0.9 sec. The ratio of the time constants 11.8,
and so the recommended compensation is PI. Using
the above table
The PI compensation is
12
Step response of closed loop
Important It is not an optimal parameter choice!
13
Chien-Hrones-Reswick recommendations
The initial conditions for optimization
parameters The process field is an ideal HPT1
The objective function is the fastest
periodically transient with maximum 20 overshoot
at setpoint tracking The optimization is based
on the square-integral criterion.
14
Determination of KC and TI
Defined values KP 0.72, Tg 10.6 sec., and Tu
0.9 sec. The ratio of the time constants 11.8,
and so the recommended compensation is PI. Using
the above table
A PI kompenzáló tag
15
Step response of closed loop
It can be seen that the approximation of process
field the objective function is not satisfied.
16
PTn model
17
Determination of system parameters
18
Step response of process field
19
Determination of n and T
Defined values t10 1.95sec, t30 4 sec., és
t70 10.1 sec. The process gain KP 0.72
Based on the table above the PT2 is the closest
approximation n 2.
20
Proposed parameters for PTn model The fastest
periodically transient with maximum 20 overshoot
at setpoint tracking
21
Proposed parameters for PTn model
n 2, and so you choose PI.
In the industrial area you never use a pure P
compensation to control a self-tuning process
field!
22
Step response of the closed loop
Compare the two models the PTn is the better
approximation, if the process field has not got a
real dead time.
23
Process field with integral effect P or PDT1
compensation
European structure
24
Process field with integral effect
In this case the most popular compensation is the
P or if the response signal without noise than
PDT1, but in the later case be applied the PIDT1
too.
The approximate models IT1 or HIT1
25
IT1 model from the reaction curve of process
field
26
Recommendation of Friedlich for IT1
Típus KC TI TD
P
PDT1 Tg
PIDT1 3.2Tg 0.8Tg
The initial conditions for optimization
parameters The process field is an ideal IT1
The objective function is the fastest
periodically transient with maximum 20 overshoot
at setpoint tracking The optimization is based
on the square-integral criterion.
27
Step response of the process field

• The compensation type does not depend on the
  ratio of the TI and Tg.

28
Parameters of theP, PDT1, and PIDT1

• P

It is possible other AD value too.
PDT
PIDT
29
Step response of closed loop with P compensation
The steady-state error is 0 settling time is
11.4 sec. overshoot is 6.1
30
Step response of closed loop with PDT1
compensation
The steady-state error is 0 the settling time is
10.1 sec. there is not overshoot.
31
Step response of closed loop with PIDT1
compensation
Very bad! It is convenient the open-loop transfer
function analysis.
32
The Bode plot of open-loop (G0(s)) with PIDT1
compensation
It can be seen that increasing the gain of the
compensation up to 17.4 a better phase margin
value is obtained.
33
The result of the PIDT1 compensation with the new
parameters
Better, but it is not good!
34
Tuning the PDT1 compensation
Replace the phase margin value from 95 to 90
the KC increasing by 2.8-fold.
35
The result of the PIDT1 compensation with the new
parameters
It is good enough!