1. UNIVERSITÀ DEGLI STUDI DI SALERNO
Bachelor Degree in Chemical Engineering
Course: Process Instrumentation and Control
(Strumentazione e Controllo dei Processi Chimici)
AUTOMATIC FEEDBACK CONTROL
AUTOMATIC CONTROLLERS
Rev. 2.3 – May 22, 2019

2. Process Instrumentation and Control - Prof. M. Miccio
CONTROL LAW
the mathematical (or graphical or tabular) relationship between input and output of the controller
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Process Instrumentation and Control - Prof. M. Miccio

3. CONTROLLER STRATEGIES
DISCONTINUOUS CONTROL (ON/OFF CONTROL)
absence of a one-to-one correspondence between input and output
"Discreet" control law
Ex.: RELAY controller
CONTINUOUS CONTROL (INTERMEDIATE VALUE CONTROL)
There is a one-to-one correspondence between input and output
"Continuous" control law
Ex.: PID controller
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Process Instrumentation and Control - Prof. M. Miccio

4. CONTROL LAW of the RELAY CONTROLLER
Actual RELAY with hysteresis
Ideal RELAY
see:
par. 7.1 in Magnani, Ferretti e Rocco (2007)
 The term hysteresis is used to indicate that the behavior is different depending on the direction that the input or independent variable is moved.
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Process Instrumentation and Control - Prof. M. Miccio

5. Process Instrumentation and Control - Prof. M. Miccio
ON/OFF CONTROL
A dead band (upper and lower set point values) is introduced for the controlled variable
The final control element is either completely open/on/maximum or closed/off/minimum
As long as the measured variable remains between these limits, no changes in control action are made
The aim is that of protecting the actuator/final control element from wear
adapted from:
Ch. 1 “Fundamental Principles of Process Control” in Cooper D. (2008), "Practical Process Control ", PDF textbook
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Process Instrumentation and Control - Prof. M. Miccio

6. AUTOMATIC FEEDBACK CONTROL WITH RELAY CONTROLLER
see:
par. 7.1 in Magnani, Ferretti e Rocco (2007)
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Process Instrumentation and Control - Prof. M. Miccio

7. RELAY CONTROLLERS COMMON APPLICATIONS
Temperature control in household appliances
House temperature control
Temperature control in big rooms (slow dynamic behaviour allowed limit cycle)
Averaging control of the level
with 2 or also 3 and 5 outputs
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Process Instrumentation and Control - Prof. M. Miccio

8. RELAY CONTROLLERS COMMON APPLICATIONS
Thermostat for ambient air
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Process Instrumentation and Control - Prof. M. Miccio

9. PID “CONTINUOUS” CONTROLLERS
Control law
in the time domain in the Laplace domain
PROPORTIONAL
(P)
Control action proportional to the error
Kc = CONTROLLER GAIN
cs = CONTROLLER BIAS
PROPORTIONAL DERIVATIVE
(PD)
Control action proportional to the rate of error variation D
DERIVATIVE TIME
PROPORTIONAL INTEGRAL
(PI)
Control action proportional to the integral of the error with the time I
INTEGRAL TIME
or RESET TIME
PROPORTIONAL INTEGRAL DERIVATIVE
(PID)
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Process Instrumentation and Control - Prof. M. Miccio

10. FEEDBACK CONTROL (CLOSED LOOP)
PID CONTROLLER
FINAL CONTROL ELEMENT
PROCESS
MEASURING DEVICE
ε(t)
o(t)
m(t)
d(t)
ym(t)
y(t) + -
ySP(t) or SP
CLOSED
LOOP
see:
Ch.14 - Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall, 1984
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Process Instrumentation and Control - Prof. M. Miccio

11. Function of the Proportional Term
The proportional term, Kc  e(t), immediately impacts CObias based on the size of e(t) at a particular time t
The past history and current trajectory of the controller error have no influence on the proportional term computation

12. Control Calculation is Based on Error, e(t)
Here is identical data plotted two ways
To the right is a plot of error, where: e(t) = SP – PV
Error e(t) continually changes size and sign with time
ERR

13. Function of the Integral Term
The integral term continually sums up error, e(t)
Through constant summing, integral action accumulates influence based on how long and how far the measured PV has been from SP over time.
Even a small error, if it persists, will have a sum total that grows over time and the amount added to CObias will similarly grow.
The continual summing of integration starts from the moment the controller is put in automatic

14. Integral Term Continually Sums the Value: SP – PV
The integral is the sum of the area between SP and PV
At t = 32 min, when the PV first reaches the SP, the integral is:

15. Integral of Error is the Same as Integral of: SP – PV
At t = 60 min, the total integral is: 135 – 34 = 101
When the dynamics have ended, e(t) is constant at zero and the total integral has a final residual value: 135 – = 108

16. PID “CONTINOUS” CONTROLLER
The first published theoretical analysis of a PID controller was by the Russian American engineer Nicolas Minorsky in Minorsky was designing automatic steering systems for the US Navy, and based his analysis observing that the helmsman controlled the ship not only based on the current error, but also on past error and current rate of change.
TYPE
ADVANTAGES
DISADVANTAGES
Proportional
It is the simplest controller without the limit ot the ON/OFF controller
It does not introduce delay of the dynamic response (Dynamics of order 0)
It provides a single value of the controller output for each value of the error
For a step forcing function, it provides a dynamic response having an offset both in servo problem and regulator problem
Integral
It eliminates the offset of the dynamic response
The process control can be more accurate
It introduces a delay in the dynamic response (integral time)
If extends the time of oscillation of the dynamic response
Derivative
It amplifies the control action because “feels” the rate of variation of the error. Therefore, it acts for each error variation, even if it is small
It shortens the time of oscillation of the dynamic response
It is suitable for processes with a “slow” dynamic behavior.
It is too sensitive to the noise
It does not eliminate the offset from the dynamic response
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Process Instrumentation and Control - Prof. M. Miccio

17. FEEDBACK CONTROL (CLOSED LOOP)
The external inputs are the disturbance and set point
CONTROLLER
FINAL CONTROL ELEMENT
PROCESS
MEASURING DEVICE
ySP(t)
ε(t)
o(t)
m(t)
d(t)
ym(t)
y(t) + -
CLOSED
LOOP
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Process Instrumentation and Control - Prof. M. Miccio

18. OFFSET (CLOSED LOOP RESPONSE)
Referring to the controlled variable y(t) and the dynamic response of the unit step u(t):
“SERVO” PROBLEM
OFFSET = (NEW SET-POINT) - (FINAL VALUE OF THE RESPONSE)
UNIT STEP CHANGE IN SET POINT
Hp:
FOR A FIRST-ORDER LAG
PROPORTIONAL CONTROLLER
Any other block of the loop PURELY ALGEBRIC
see:
Ch.14 - Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall
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Process Instrumentation and Control - Prof. M. Miccio

19. OFFSET (CLOSED LOOP RESPONSE)
“REGULATOR” PROBLEM
OFFSET = (SET-POINT) - (FINAL VALUE OF THE RESPONSE)
Hp:
FOR A FIRST-ORDER LAG
PROPORTIONAL CONTROLLER
Any other block of the loop PURELY ALGEBRIC
OPEN LOOP
CLOSED LOOP
UNIT STEP CHANGE IN LOAD
see:
Ch.14 - Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall
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Process Instrumentation and Control - Prof. M. Miccio

20. Advantage of PI Control – No Offset
The PI controller stops computing changes in CO when e(t) equals zero for a sustained period
At that point, the proportional term equals zero, and the integral term may have a residual value
This residual value, when added to CObias, essentially creates an overall “moving bias” that tracks changes in operating level
This moving bias eliminates offset, making PI control the most widely used industry algorithm
Integral acts as
“moving bias” term
CO(t)

21. "CONTINUOUS" CONTROLLERS of the PID class
The first published theoretical analysis of a PID controller was by the Russian American engineer Nicolas Minorsky in Minorsky was designing automatic steering systems for the US Navy, and based his analysis observing that the helmsman controlled the ship not only based on the current error, but also on past error and current rate of change.
TYPE
ADVANTAGES
DISADVANTAGES
Proportional
It is the simplest type of controller without the limitations of ON / OFF
Does not introduce delays in the response (Dynamics of order 0)
For each error value, it provides a unique controller output value
For step forcing function, it provides an answer both to the servomechanism problem and to the regulator with offset and to the servomechanism and regulator problem
Integral
Delete the offset from the dynamic response
Process control can be more accurate
Introduces a dynamic delay in the response (integration time)
Lengthen the oscillation time in the response
Derivative
Amplifies the control action because it "feels" the speed of change of the error. Therefore it acts for every variation of the error, even if the error is very small
Shortens the oscillation time in the dynamic response
Suitable for processes with "slow" dynamics
It is too sensitive to noise
Does not delete the offset from the dynamic response

22. PID CONTROLLERS – IMPLEMENTATION ASPECTS
Common production with microprocessor
taken from Magnani, Ferretti e Rocco (2007)
standard front dimensions (ex., 1/8 DIN 4896)
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Process Instrumentation and Control - Prof. M. Miccio

23. PID CONTROLLERS – IMPLEMENTATION ASPECTS
taken from Magnani, Ferretti e Rocco (2007)
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Process Instrumentation and Control - Prof. M. Miccio

24. PID CONTROLLERS – IMPLEMENTATION ASPECTS
taken from Magnani, Ferretti e Rocco (2007)
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Process Instrumentation and Control - Prof. M. Miccio

25. CONTROLLERS: FURTHER CLASSIFICATION
DIRECT ACTING
The controller provides a decreasing output signal o(t) as the error ε(t) increases (controller gain Kc < 0 for PID controllers)
REVERSE ACTING
The controller provides an increasing output signal o(t) as the error ε(t) increases (controller gain Kc > 0 for PID controllers)
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Process Instrumentation and Control - Prof. M. Miccio

26. Proportional Band PB = (COmax — COmin)/Kc PB = 100%/Kc
Manufacturers make controller tuning confusing by using different names and units for the same parameters
A popular alternative to Kc is proportional band, PB.
If CO and PV are in % and the CO signal ranges from a minimum (COmin) to maximum (COmax) value, then:
PB = (COmax — COmin)/Kc
When CO and PV range from 0% to 100%, the common conversion between Kc and PB is:
PB = 100%/Kc
So if Kc is large, then PB will be small

27. PROPORTIONAL BAND Kc=(u/ufs) / (e/efs)
If Kc is reported as the ration of the normalized signal to respective fullscale:
Kc=(u/ufs) / (e/efs)
then PB represents the magnitude ot the error for which the output reachs the fullscale.
Ad es., PB=50%  Kc=2
quindi, con e=50% si ottiene u=100%=ufs (fullscale)
Usually: 1% ≤ PB ≤ 500%
see:
Ch. 7 in Magnani, Ferretti e Rocco (2007)
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Process Instrumentation and Control - Prof. M. Miccio