CHE 185 – PROCESS
CONTROL AND DYNAMICS
OPTIMIZATION AND PRIMARY
LOOP ELEMENTS
TYPES OF CONTROL
• OPTIMIZATION
– INTENTION IS TO GET THE “BEST”
ECONOMIC/QUALITY CONDITIONS
– CONTROL IS THE MORE GENERAL FORM
OF RESPONDING TO CHANGE
CONTROL & OPTIMIZATION
• FOR A BIOREACTOR
http://www.automation.siemens.com/wcmsnewscenter/details.aspx?xml=/conte
nt/10001666/en/as/Pages/PN-200201-06Alles_unter_Kontrolle.xml?NoRedirect=true&xsl=publication-en-www4.xsl
EXAMPLE OF OPTIMIZATION
• OPTIMIZATION AND CONTROL OF A
CSTR
EXAMPLE OF OPTIMIZATION
• ECONOMIC OBJECTIVE FUNCTION
  Q CA VA  Q CB VB  Q CC VC  Q CA0 VAF
•
•
•
•
Φ = $/𝑡𝑖𝑚𝑒
ECONOMIC VALUES , VB > VC, VA, OR VAF
AT LOW T, LITTLE FORMATION OF B
AT HIGH T, TOO MUCH OF B REACTS TO
FORM C
• SO THERE EXISTS AN OPTIMUM REACTOR
TEMPERATURE, T*
OPTIMZATION EXAMPLE
• METHOD OF SOLUTION
• 1. SELECT INITIAL GUESS FOR
REACTOR TEMPERATURE, T*
• 2. EVALUATE CA, CB, AND CC
• 3. EVALUATE 
• 4. CHOOSE NEW REACTOR
TEMPERATURE AND RECYCLE
THROUGH STEP 2 UNTIL T* IS
IDENTIFIED.
EXAMPLE OF OPTIMIZATION
ABC
Mole balance on A :
Q C A0  Q C A  k1 exp[ E1 / RT ] C A Vr
Solving for C A
C A0
CA 
k1 exp[ E1 / RT ]Vr
1
Q
Likewise, C B and CC are calculated from mole
balances.
EXAMPLE OF OPTIMIZATION
• GRAPHICAL SOLUTION OF OPTIMUM
REACTOR TEMPERATURE, T*
OTHER TYPES OF CONTROL
• SUPERVISORY
– RESPONDS TO THE SIGNAL FROM THE
OPTIMIZATION CONTROLLER
– SENDS A SIGNAL TO THE REGULATORY
CONTROL LOOP
TYPES OF CONTROL
• REGULATORY
– RECEIVES A SIGNAL FROM THE
SUPERVISORY CONTROLLER
– ACTUALLY ADJUSTS A PROCESS
VARIABLE TO MAKE NECESSARY
CHANGES FOR OPERATION.
REGULATORY CONTROL EXAMPLE
• TEMPERATURE CONTROL FOR A
HEAT EXCHANGER
Steam
Setpoint
TC
Product
Stream
TT
Feed
Condensate
CATEGORIES OF LOOP
COMPONENTS
• FEEDBACK LOOP THE PRIMARY COMPONENTS
ARE SHOWN SCHEMATICALLY
LOOP COMPONENTS - SENSORS
• MEASURE THE VALUE OF THE
TARGET AND MANIPULATED
VARIABLES
– TYPICALLY P, T, L, D, ρ,Μ, COMPOSITION,
MASS
– LOCATED “IN-LINE”, EVEN IF THEY DO
NOT CONTACT PROCESS FLUIDS
LOOP COMPONENTS - SENSORS
• TYPICALLY ANALOG DEVICES WITH
FULL SCALE RANGES:
– 20 MA CURRENT SIGNAL
– mV VOLTAGE SIGNAL
– 3 - 15 PSIG PNEUMATIC SIGNAL
LOOP COMPONENTS TRANSMITTERS
• ANALOG DEVICES
– CONVERT SIGNAL INTO A VALUE THAT
CAN BE TRANSMITTED WITHOUT
SIGNIFICANT LOSS IN VALUE
– TYPICAL OUTPUT IS 4 - 20 MA CURRENT
FULL SCALE RANGE
LOOP COMPONENTS TRANSDUCERS
• CONVERT THE ANALOG SIGNAL FROM
THE TRANSMITTER INTO A DIGITAL
SIGNAL
– LABELED A/D FOR ANALOG TO DIGITAL
– LABELED D/A FOR DIGITAL TO ANALOG
• CAN TRANSFER ELECTRONIC TO
PNEUMATIC
LOOP COMPONENTS CONTROLLERS
• RECEIVES DIGITAL SET/POINT AND
MEASURED SIGNALS FOR A VARIABLE
• MAKES A COMPARISON BETWEEN
THE SIGNALS USING A BRIDGE
• PRODUCES A DIGITAL OUTPUT
SIGNAL TO ADJUST THE MEASURED
VALUE TO THE SET/POINT VALUE
LOOP COMPONENTS - ACTUATORS
• RECEIVES THE OUTPUT SIGNAL FROM
THE CONTROLLER, VIA THE
TRANSDUCER
• ADJUSTS THE POSITION OF A DEVICE
(FINAL CONTROL ELEMENT) TO
CHANGE A PROCESS VARIABLE
LOOP COMPONENTS - FINAL
CONTROL ELEMENT
• CHANGES A PROCESS VARIABLE TO
OBTAIN A CORRECTION TO THE
MEASURED VARIABLE
• FOR CHEMICAL PLANTS, MOST OF
THE TIME THESE DEVICES ARE
VALVES
SOURCE OF SET/POINTS
• FOR A SIMPLE PROCESS, THESE MAY
BE ENTERED MANUALLY
• FOR CONTEMPORARY SYSTEMS,
THESE SIGNALS COME FROM A
COMPUTER
– PLC - PROGRAMMABLE LOGIC
CONTROLLER
– DCS COMPUTER - DISTRIBUTED
CONTROL SYSTEM COMPUTER
DCS FUNDAMENTALS
• DCS HAS THE FOLLOWING GENERAL
COMPONENTS
– LOCAL CONTROLLERS
– INPUT/OUTPUT PANELS (I/O PANELS) TO
RECEIVE PROCESS VARIABLE VALUES
FROM THE CONTROLLER AND SEND
SET/POINT VALUES
– DATA HIGHWAY/MULTIPLEXER TO
SAMPLE THE VALUES ON A REGULAR
FREQUENCY
DATA HIGHWAY/MULTIPLEXER
DCS FUNDAMENTAL COMPONENTS
• HOST COMPUTER TO ENTER
SET/POINTS
• ALARM COMPUTER - PLC’S TO
INITIATE ALARMS AND/OR
INTERLOCKS
• DATA STORAGE COMPUTER
– KEEPS TREND DATA
– LOGS ALARMS
– OTHER COMPUTERS THAT HAVE ACCESS
FINAL CONTROL ELEMENT
CHARACTERIZATION - VALVES
• VALVES ARE USED FOR EITHER
ON/OFF OR THROTTLING OPERATION
- SEE PERRY’S 7TH PAGE 8-64
• ON/OFF VALVE CHARACTERISTICS
– HAVE A COMPLETELY OPEN AND
COMPLETELY CLOSED POSITION
– HAVE A TIGHT SHUT-OFF CAPABILITY
– HAVE LIMITED VALUE FOR THROTTLING
PLUG VALVES AND BALL VALVES
• 90° RANGE FROM OPEN TO CLOSED
• USE PNEUMATIC OR MOTOR
ACTUATORS
GATE VALVES
• TYPICALLY USED
FOR ISOLATION
VALVES - FOR
MAINTENANCE AND
AS BACK-UP FOR
CLOSED
THROTTLING VALVES
GATE VALVES
• MAY HAVE SEVERAL TURNS
BETWEEN OPEN AND CLOSED
• MAY HAVE MOTOR OPERATORS –
BUT MORE FREQUENTLY USE
MANUAL OPERATION
THROTTLING (CONTROL) VALVES
• VARIOUS FLOW CHARACTERISTICS BASED ON THE
SHAPE OF THE PLUG AND THE SEAT
• FLOW THROUGH THE VALVE DEPENDS ON THE
FRACTION OPEN AND THE NET PRESSURE DROP
• HAVE COMPLETELY OPEN AND COMPLETELY
CLOSED POSITION, BUT DESIGNED FOR
INTERMEDIATE POSITION FOR CONTINUOUS
OPERATION - NOT TIGHT SHUT OFF
• GENERAL REFERENCE HTTP://WWW.DOCUMENTATION.EMERSONPROCES
S.COM/GROUPS/PUBLIC/DOCUMENTS/BOOK/CVH99
.PDF
GLOBE (THROTTLING) CONTROL
VALVE
CROSS-SECTION OF A GLOBE
VALVE
THROTTLING (CONTROL) VALVES
• BASIC FLOW EQUATION IS THE SAME AS
FOR AN ORIFICE:
𝑄𝑓𝑙𝑜𝑤
𝑃1 − 𝑃2
= 𝐾𝐶𝑣 (𝑥)
𝜌
• CV IS SIMILAR TO AN ORIFICE COEFFICIENT,
HOWEVER IT VARIES WITH VALVE POSITION
• K IS EQUAL TO UNITY WHEN  IS
EXPRESSED AS SPECIFIC GRAVITY,
FLOWRATES ARE IN gpm AND PRESSURE
DROP IS IN psi
GLOBE VALVE TYPES
• QUICK OPENING- FOR SAFETY BY-PASS
APPLICATIONS WHERE QUICK OPENING IS
DESIRED
• EQUAL PERCENTAGE- FOR ABOUT 90% OF
CONTROL VALVE APPLICATIONS SINCE IT
RESULTS IN THE MOST LINEAR INSTALLED
CHARACTERISTICS
• LINEAR- WHEN A RELATIVELY CONSTANT
PRESSURE DROP IS MAINTAINED ACROSS
THE VALVE
GLOBE VALVE FLOW
CHARACTERISTICS
GLOBE VALVES - LINEAR
• PLUGS/SEATS DESIGNED TO HAVE
THE FRACTION OF FLOW BE LINEAR
WITH THE VALVE STEM POSITION FOR
A CONSTANT Δp
• f(x) = x WHERE x IS VALVE POSITION
• DESIGN POSITION IS ABOUT 50%
OPEN
GLOBE VALVES - EQUAL
PERCENTAGE
• EQUAL PERCENTAGE CHANGE IN
VALVE POSITION RESULT IN EQUAL
PERCENTAGE CHANGE IN FLOW
• 𝑓 𝑥 = 𝑅 𝑥−1 WHERE 20 < R < 50 AND x
IS VALVE OPENING
• DESIGN POSITION IS ABOUT 70%
OPEN
GLOBE VALVES - QUICK OPENING
• TRIM IS DESIGNED TO HAVE LARGE
INCREASE IN FLOW WITH SMALL CHANGE
IN VALVE OPENING
• 𝑓 𝑥 = 𝑥
• DESIGN POSITION IS OPEN OR CLOSED
GLOBE VALVES - OTHER TYPES
• ECCENTRIC PLUG VALVES
– COMBINATION OF PLUG AND GLOBE IN THEIR
CHARACTERISTICS
– CLAIM TO BE TIGHT SHUT OFF
– REFERENCE:
http://www.millikenvalve.com/pdf/plug2011
.pdf
CHARACTERIZATION OF CONTROL
ELEMENTS
• TIME CONSTANTS
– TIME IT TAKES FOR A UNIT TO RESPOND
TO A SIGNAL AND COMPLETE A CHANGE
– FOR VALVES THIS IS THE TIME TO
STROKE TO A NEW POSITION
• DEADBAND
– RANGE OF SIGNAL THAT REQUIRED TO
INDICATE AN ACTUAL CHANGE
CHARACTERIZATION OF CONTROL
ELEMENTS
• POSITION
– DEADBAND
– RANGE OF SIGNAL THAT REQUIRED TO
INDICATE AN ACTUAL CHANGE
– FOR THERMOCOUPLES THIS MIGHT BE
+1 C.
CHARACTERIZATION OF CONTROL
ELEMENTS
• TURNDOWN RATIO
– SPECIFIES THE RANGE OF STABLE
OPERATION FOR THE DEVICE, MINIMUM
TO MAXIMUM
– NORMAL OPERATING RANGE SHOULD
NOT BE AT EITHER EXTREME POSITION
CONTROL VALVE DESIGN
• EVALUATE CV AT THE MAXIMUM AND
𝑄𝑓
MINIMUM FLOW RATE 𝐶𝑣 𝑥 = 𝑃 𝑃
𝐾
1− 2
𝜌
• DETERMINE WHICH VALVES CAN
EFFECTIVELY PROVIDE THE MAX AND MIN
FLOW RATE
– THE VALVE POSITION SHOULD BE GREATER
THAN ABOUT 15% OPEN FOR THE MINIMUM
FLOW RATE
– AND LESS THAN 85% OPEN FOR THE MAXIMUM
FLOW RATE.
CONTROL VALVE DESIGN
• CHOOSE
– SMALLEST VALVE THAT MEETS THE RANGE CRITERION
FOR THE MINIMUM CAPITAL INVESTMENT
– THE LARGEST VALVE TO ALLOW FOR FUTURE
THROUGHPUT EXPANSION.
• CV VERSUS % OPEN FOR DIFFERENT VALVE SIZES.
• AVAILABLE PRESSURE DROP ACROSS THE VALVE
VERSUS FLOW RATE FOR EACH VALVE. NOTE
THAT THE EFFECT OF FLOW ON THE UPSTREAM
AND DOWNSTREAM PRESSURE MUST BE KNOWN.
http://www.norriseal.com/files/comm_id_47/Valve_Size_Manual.pdf
CONTROL VALVE DESIGN EXAMPLE
• SIZE A CONTROL VALVE FOR MAX 150
GPM OF WATER AND MIN OF 50 GPM.
• USE THE VALVE FLOW EQUATION TO
CALCULATE CV
• FOR DP, USE PRESSURE DROP
VERSUS FLOW RATE (E.G., TABLE ON
PAGE 82)
CONTROL VALVE DESIGN EXAMPLE
• EQUATION AT LIMITS
VALVE POSITION FOR MAX AND
MIN FLOWS BASED ON SIZE
ANALYSIS OF RESULTS
• 2-INCH VALVE APPEARS TO BE BEST
OVERALL CHOICE: LEAST EXPENSIVE
CAPITAL AND IT CAN PROVIDE UP TO A 50%
INCREASE IN THROUGHPUT.
• 3-INCH AND 4-INCH VALVE WILL WORK, BUT
NOT RECOMMENDED BECAUSE THEY WILL
COST MORE TO PURCHASE. THE 2-INCH
VALVE WILL PROVIDE MORE THAN ENOUGH
EXTRA CAPACITY (I.E., SOMETHING ELSE
WILL LIMIT CAPACITY FOR IT)
ADJUSTABLE SPEED PUMPS FOR
FLOW CONTROL
• USED EXTENSIVELY IN THE BIOPROCESSING INDUSTRIES TO MAINTAIN
STERILE CONDITIONS AND RELATIVELY
LOW FLOW RATES.
• FAST AND PRECISE.
• DO REQUIRE AN INSTRUMENT AIR SYSTEM
(I.E., 4-20 MA SIGNAL GOES DIRECTLY TO
PUMP).
• MUCH HIGHER CAPITAL COSTS THAN
CONTROL VALVES FOR LARGE FLOW RATE
APPLICATIONS.