UNIVERSIT DEGLI STUDI DI SALERNO Bachelor Degree in
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
CONTROL LAW Ø the mathematical (or graphical or tabular) relationship between input and output of the controller 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 2
CONTROLLER STRATEGIES • DISCONTINUOUS CONTROL (ON/OFF CONTROL) Ø absence of a one-to-one correspondence between input and output Ø "Discreet" control law Ø Ex. : RELAY controller • CONTINUOUS CONTROL (INTERMEDIATE VALUE CONTROL) Ø There is a one-to-one correspondence between input and output Ø "Continuous" control law Ø Ex. : PID controller 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 3
CONTROL LAW of the RELAY CONTROLLER Ideal RELAY see: par. 7. 1 in Magnani, Ferretti e Rocco (2007) 13/09/2021 Actual RELAY with hysteresis The term hysteresis is used to indicate that the behavior is different depending on the direction that the input or independent variable is moved. Process Instrumentation and Control - Prof. M. Miccio 4
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 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 5
AUTOMATIC FEEDBACK CONTROL WITH RELAY CONTROLLER see: par. 7. 1 in Magnani, Ferretti e Rocco (2007) 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 6
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 Ø with 2 or also 3 and 5 outputs 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 7
RELAY CONTROLLERS COMMON APPLICATIONS Thermostat for ambient air 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 8
PID “CONTINUOUS” CONTROLLERS PROPORTIONAL (P) Control action proportional to the error Kc = CONTROLLER GAIN cs = CONTROLLER BIAS PROPORTIONAL DERIVATIVE Control action proportional to the rate of error variation D Control action proportional to the integral of the error with the time I (PD) PROPORTIONAL INTEGRAL (PI) Control law in the time domain in the Laplace domain DERIVATIVE TIME INTEGRAL TIME or RESET TIME PROPORTIONAL INTEGRAL DERIVATIVE (PID) 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 9
FEEDBACK CONTROL (CLOSED LOOP) d(t) y. SP(t) or SP + ε(t) - PID CONTROLLER o(t) FINAL CONTROL ELEMENT m(t) PROCESS y(t) ym(t) MEASURING DEVICE CLOSED LOOP see: Ch. 14 - Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall, 1984 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 10
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 Copyright © 2007 Control Station, Inc. All Rights Reserved 11
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 Copyright © 2007 Control Station, Inc. All Rights Reserved 12
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 Copyright © 2007 Control Station, Inc. All Rights Reserved 13
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: Copyright © 2007 Control Station, Inc. All Rights Reserved 14
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 – 34 + 7 = 108 Copyright © 2007 Control Station, Inc. All Rights Reserved 15
PID “CONTINOUS” CONTROLLER The first published theoretical analysis of a PID controller was by the Russian American engineer Nicolas Minorsky in 1922. 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 Proportional ADVANTAGES DISADVANTAGES It is the simplest controller without the limit ot the ON/OFF controller For a step forcing function, it provides a dynamic response having an offset both in servo problem and regulator problem 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 Integral It eliminates the offset of the dynamic response The process control can be more accurate 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 introduces a delay in the dynamic response (integral time) If extends the time of oscillation of the dynamic response It is too sensitive to the noise It does not eliminate the offset from the dynamic response It is suitable for processes with a “slow” dynamic behavior. 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 16
FEEDBACK CONTROL (CLOSED LOOP) The external inputs are the disturbance and set point d(t) y. SP(t) + ε(t) - CONTROLLER o(t) FINAL CONTROL ELEMENT m(t) PROCESS y(t) CLOSED LOOP 13/09/2021 ym(t) MEASURING DEVICE Process Instrumentation and Control - Prof. M. Miccio 17
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) Hp: • FOR A FIRST-ORDER LAG • PROPORTIONAL CONTROLLER • Any other block of the loop PURELY ALGEBRIC see: UNIT STEP CHANGE IN SET POINT Ch. 14 - Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 18
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 see: UNIT STEP CHANGE IN LOAD Ch. 14 - Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 19
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 Integral acts as “moving bias” term 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 Copyright © 2007 Control Station, Inc. All Rights Reserved 20
"CONTINUOUS" CONTROLLERS of the PID class The first published theoretical analysis of a PID controller was by the Russian American engineer Nicolas Minorsky in 1922. 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 Proportional ADVANTAGES DISADVANTAGES It is the simplest type of controller without the limitations of ON / OFF 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 Does not introduce delays in the response (Dynamics of order 0) For each error value, it provides a unique controller output value Integral Delete the offset from the dynamic response Introduces a dynamic delay in the response (integration time) Process control can be more accurate 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 Copyright © 2007 Control Station, Inc. All Rights Reserved 21 It is too sensitive to noise Does not delete the offset from the dynamic response
PID CONTROLLERS – IMPLEMENTATION ASPECTS Common production with microprocessor taken from Magnani, Ferretti e Rocco (2007) standard front dimensions (ex. , 1/8 DIN 48 96) 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 22
PID CONTROLLERS – IMPLEMENTATION ASPECTS taken from Magnani, Ferretti e Rocco (2007) 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 23
PID CONTROLLERS – IMPLEMENTATION ASPECTS taken from Magnani, Ferretti e Rocco (2007) 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 24
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) 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 25
Proportional Band 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 Copyright © 2007 Control Station, Inc. All Rights Reserved 26
PROPORTIONAL BAND 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) 13/09/2021 Process Instrumentation and Control - Prof. M. Miccio 27
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