cascade and ratio control

Report
CHE 185 – PROCESS
CONTROL AND DYNAMICS
CASCADE AND RATIO
CONTROL
METHODS TO IMPROVE BASIC
PID CONTROL
• APPLIED WHEN THE STANDARD PID DESIGN
IS NOT DOES NOT PROVIDE ADEQUATE
CONTROL
• METHODOLOGY
– ADDITIONAL MEASURES OF PROCESS OUTPUTS
– ADDITIONAL MEASURES OF PROCESS INPUTS
– EXPLICIT MODELS IN THE CONTROL
CALCULATION
– MODIFY THE PID ALGORITHM AND TUNING TO
MEET CONTROL CRITERIA
CASCADE, RATIO, AND
FEEDFORWARD CONTROL
• EACH OF THESE TECHNIQUES OFFERS
ADVANTAGES WITH RESPECT TO
DISTURBANCE REJECTION:
• CASCADE REDUCES THE EFFECT OF
SPECIFIC TYPES OF DISTURBANCES.
• RATIO REDUCES THE EFFECT OF FEED
FLOW RATES CHANGES
• FEEDFORWARD CONTROL IS A GENERAL
METHODOLOGY FOR COMPENSATING FOR
MEASURED DISTURBANCES.
METHODS TO IMPROVE BASIC
PID CONTROL
• CATEGORIES OF ENHANCEMENT
– CASCADE CONTROL
– FEEDFORWARD CONTROL
– NONLINEAR FUNCTIONS - ADJUST CONTROL
FOR VARYING PROCESS DYNAMICS
– INFERENTIAL CONTROL - CHANGE THE
MEASURED VARIABLES
– LEVEL CONTROL - TO ADJUST INVENTORIES TO
STABLE LEVELS
– MODEL PREDICTIVE CONTROL - FOR COMPLEX
PROCESS DYNAMICS
COMPENSATING FOR DISTURBANCES
REDUCES DEVIATIONS FROM SETPOINT
AND SETTLING TIME
CASCADE CONTROL
• CONDITIONS THAT SUPPORT APPLICATION
– SINGLE LOOP CONTROL IS NOT SATISFACTORY
– A MEASURED SECONDARY VARIABLE IS AVAILABLE
• PROPERTIES OF THE SECONDARY
VARIABLE
– MUST BE AFFECTED BY SIGNIFICANT
DISTURBANCES
– MUST BE RELATED TO THE PRIMARY MANIPULATED
VARIABLE
– SECONDARY VARIABLE DYNAMICS MUST BE FASTER
THAN THE PRIMARY VARIABLE DYNAMICS.
CASCADE CONTROL
• CASCADE CONTROL GENERIC BLOCK FLOW
DIAGRAM.
CASCADE CONTROL
• THE CASCADE LOOP COMBINES TWO
FEEDBACK CONTROLLERS WITH THE
PRIMARY CONTROLLER OUTPUT SERVING
AS THE SECONDARY CONTROLLER
SETPOINT.
• THE DISTURBANCE REJECTION CLOSED
LOOP TRANSFER FUNCTION FOR THIS
SYSTEM
Gd ( s )G pp ( s )
Y ( s)

D( s ) Gcs ( s )G ps ( s )  Gcp ( s )G pp ( s )Gcs ( s )G ps ( s ) 1
CASCADE CONTROL
• THE EFFECTIVE PROCESS TIME CONSTANT,
τ`p, CAN BE SHORTER THAN THAT FOR THE
PRIMARY PROCESS TIME CONSTANT
– THE SECONDARY LOOP TIME CONSTANT IS
SHORTER THAN THE PRIMARY LOOP
– THE SECONDARY LOOP AND PRIMARY LOOP TIME
CONSTANTS ARE COMBINED TO OBTAIN THE
EFFECTIVE TIME CONSTANT (FOR FIRST ORDER
Gpp(s) AND Gps(s) AND P-ONLY CONTROLLERS - A
SECOND ORDER RESPONSE RESULTS)
 
'
p
 pp ps
1  Kcs K ps (1  Kcp K pp )
CASCADE CONTROL
• THE DISTURBANCE ENTERS THE
SECONDARY CONTROL LOOP AND
MAY BE EFFECTIVELY
COUNTERACTED BY THE PRIMARY
LOOP - SOMEWHAT LIKE A FILTER.
• THE SECONDARY ERROR IS ADDED
TO THE PRIMARY ERROR FOR EACH
CYCLE.
CASCADE CONTROL
• THE SECONDARY LOOP RESPONDS
TO SHORT TERM DISTURBANCES
• THE PRIMARY LOOP RESPONDS TO
LONGER TERM TRENDS
• THERE CAN BE MULTIPLE LEVELS OF
CASCADE CONTROL
• HAVING ADDITIONAL CONTROL
COMPONENTS CAN REDUCE THE
OVERALL CONTROL SYSTEM
RELIABILITY
CASCADE CONTROL
• CSTR COOLING EXAMPLE
CASCADE CONTROL
• CRITERIA FOR ADDING CASCADE
CONTROL
• SINGLE LOOP DOES NOT EXHIBIT
SATISFACTORY RESPONSES
– TO FEED CHANGES
– TO COOLING WATER TEMPERATURE CHANGES
– LAG TIME IS EXCESSIVE
CASCADE CONTROL
• CSTR COOLING EXAMPLE
• MODIFIED CONTROL SYSTEM
CASCADE CONTROL
• CSTR COOLING EXAMPLE
• SECONDARY LOOP VARIABLE CAN BE
MEASURED = DISCHARGE COOLING
WATER TEMPERATURE
• SECONDARY LOOP VARIABLE IS
RELATED TO PRIMARY CONTROL
VARIABLE - HEAT TRANSFER TO
REACTOR IS REFLECTED IN
DISCHARGE COOLING WATER
TEMPERATURE
CASCADE CONTROL
• CSTR COOLING EXAMPLE
– SECONDARY LOOP CAN BE INFLUENCED BY THE
MEASURED VARIABLE - CHANGE IN PRODUCT
EXIT TEMPERATURE WILL CHANGE SETPOINT
TO SECONDARY CONTROLLER
– SECONDARY LOOP HAS SHORTER TIME
CONSTANT - TEMPERATURE CHANGE IN
COOLING WATER SHOULD BE QUICKER IN
RESPONSE TO A DISTURBANCE BECAUSE
THERE IS LESS CAPACITANCE ON THE COOLING
WATER SIDE.
CASCADE CONTROL
• CSTR COOLING EXAMPLE
• WHY NOT USE COOLING WATER
FLOW AS THE SECONDARY
VARIABLE?
• CAN IT HANDLE CHANGES IN FEED
RATES?
• HOW WILL IT RESPOND TO CHANGES
IN EITHER FEED OR COOLING WATER
TEMPERATURE?
LEVEL CONTROLLER ON A TANK WITH
AND WITHOUT CASCADE CONTROL
ANALYSIS OF CASCADE
EXAMPLE
• WITHOUT A CASCADE LEVEL CONTROLLER,
CHANGES IN DOWNSTREAM PRESSURE WILL
DISTURB THE TANK LEVEL.
• WITH CASCADE LEVEL CONTROLLER, CHANGES IN
DOWNSTREAM PRESSURE WILL BE ABSORBED BY
THE FLOW CONTROLLER BEFORE THEY CAN
SIGNIFICANTLY AFFECT TANK LEVEL BECAUSE
THE FLOW CONTROLLER RESPONDS FASTER TO
THIS DISTURBANCE THAN THE TANK LEVEL
PROCESS.
FEATURES FOR CASCADE
CONTROL TO BE SUCCESSFUL
• SECONDARY LOOP SHOULD REDUCE THE
EFFECT OF ONE OR MORE DISTURBANCES.
• SECONDARY LOOP MUST BE AT LEAST 3
TIMES FASTER THAN MASTER LOOP.
• THE CV FOR THE SECONDARY LOOP
SHOULD HAVE A DIRECT EFFECT ON THE
CV FOR THE PRIMARY LOOP.
• THE SECONDARY LOOP SHOULD BE TUNED
TIGHTLY
MULTIPLE CASCADE EXAMPLE
• THIS APPROACH WORKS BECAUSE THE FLOW
CONTROL LOOP IS MUCH FASTER THAN THE
TEMPERATURE CONTROL LOOP WHICH IS MUCH
FASTER THAN THE COMPOSITION CONTROL LOOP.
QUICK CHECK
• DRAW SCHEMATIC: A TEMPERATURE
CONTROLLER ON THE OUTLET STREAM IS
CASCADED TO A PRESSURE CONTROLLER ON THE
STEAM WHICH IS CASCADED TO A CONTROL
VALVE ON THE CONDENSATE.
QUICK CHECK SOLUTION
RATIO CONTROL
• THIS IS A VARIATION OF CASCADE
CONTROL
• THE RATIO CONTROLLER RESPONDS
A DISTURBANCE IN A MASTER
VARIABLE, BY SENDING A RATIO
SETPOINT TO THE CONTROLLER FOR
A SLAVE VARIABLE.
• THE PRIMARY CONTROLLER SENDS A
RATIO SETPOINT TO THE RATIO
CONTROLLER
RATIO CONTROL
• TYPICAL APPLICATIONS
– MIXING STREAMS
– MAINTAINING STOCHIOMETRIC FLOWS TO A
REACTION SYSTEM
– MAINTAINING REFLUX RATES ON DISTILLATION
COLUMNS
– MAINTAINING FUEL/AIR RATIOS TO
COMBUSTION SYSTEMS
RATIO CONTROL
• CONSIDER THE TOP OF A
DISTILLATION COLUMN
TEMP. S/P
LEVEL S/P
TC
AN
S/P
LC
AC
FFRC
RATIO S/P
RATIO CONTROL
• THE TARGET IS TO MAINTAIN THE
COMPOSITION AT A CERTAIN VALUE
– THE PRIMARY METHOD IS TO ADJUST THE
REFLUX RATIO
– A SECOND OBJECTIVE IS TO HAVE THE SYSTEM
RESPOND TO CHANGES IN BOILUP RATES
• NOTE THIS SKETCH DOES NOT SHOW
THE PRESSURE CONTROL, WHICH IS
ASSUMED TO HAVE A VERY SHORT
LAG TIME AND BE LINEAR
RATIO CONTROL
• THE PRIMARY MEASURE OF ANALYSIS
IS EITHER AN ON-LINE SAMPLER OR
AN OFF-LINE ANALYSIS - EITHER ONE
WITH A RELATIVELY LONG LAG TIME
• THE SIGNAL FROM THIS LOOP
BECOMES THE SETPOINT FOR THE
TRAY TEMPERATURE CONTROLLER
• THE OUTPUT FROM THE TRAY
TEMPERATURE CONTROLLER IS THE
RATIO SIGNAL TO THE FFRC.
RATIO CONTROL
• THE MASTER SIGNAL FOR THE FFRC
IS THE PRODUCT FLOW RATE AND
THE SLAVE IS THE REFLUX FLOW
RATE
• THE PRODUCT FLOW RATE IS BASED
ON THE OUTPUT FROM THE LEVEL
CONTROL IN THE DISTILLATE
ACCUMULATOR
RATIO CONTROL
• FOR THIS SYSTEM TO WORK AS
SHOWN:
• THE TRAY TEMPERATURE NEEDS TO
BE LINEAR WITH COMPOSITION
• THE LEVEL CONTROL SHOULD HAVE A
SHORTER LAG TIME THAN CHANGES
IN BOIL-UP RATES
RATIO CONTROL EXAMPLE
• RATIO CONTROL FOR WASTEWATER
NEUTRALIZATION
RATIO CONTROL EXAMPLE
ANALYSIS
• THE FLOW RATE OF BASE SCALES
DIRECTLY WITH THE FLOW RATE OF THE
ACIDIC WASTEWATER.
• THE OUTPUT OF THE pH CONTROLLER IS
THE RATIO OF NaOH FLOW RATE TO ACID
WASTEWATER FLOW RATE; THEREFORE,
THE PRODUCT OF THE CONTROLLER
OUTPUT AND THE MEASURED ACID
WASTEWATER FLOW RATE BECOME THE
SETPOINT FOR THE FLOW CONTROLLER
ON THE NaOH ADDITION.
FEEDFORWARD CONTROL
• CHARACTERISTICS
• THIS TECHNIQUE DOES NOT USE
FEEDBACK CONTROL
• IT IS EFFECTIVE IN REDUCING
DISTURBANCES, THOUGH NOT AS
EFFECTIVELY AS FEEDBACK
CONTROL
• IT IS TYPICALLY USED MOST
EFFECTIVELY IN COMBINATION WITH
FEEDBACK CONTROL
FEEDFORWARD CONTROL
• CONSIDER FEEDBACK CONTROL
• POSITIVE FACTORS
– DISTURBANCE SOURCE DOES NOT PREVENT
CORRECTIVE ACTION
– PID CONTROL WORKS IN A WIDE RANGE OF PROCESSES
– CONTROL DESIGN NEEDS LIMITED PROCESS
INFORMATION
• NEGATIVE FACTORS
– DOES NOT RESPOND TO DISTURBANCE VARIABLES
– BASED ON MEASURED VALUE FOR CV
– NO CORRECTIVE ACTION UNTIL THERE IS A SETPOINT
DEVIATION
– LONG DELAYS OR LARGE TIME CONSTANTS MAY LIMIT
EFFECTIVENESS
FEEDFORWARD CONTROL
• GENERIC BLOCK FLOW DIAGRAM
FEEDFORWARD CONTROL
• COMPARE WITH FEEDBACK CONTROL
• POSITIVE FACTORS
– CHANGES CAN BE MADE BASED ON DISTURBANCE
SOURCE INSTEAD OF WAITING FOR PROCESS CHANGE
– PROVIDES POTENTIALLY BETTER
• NEGATIVE FACTORS
– BASED ON MEASURED VALUE FOR CONTROL
DISTURBANCE
– NO CORRECTIVE ACTION BASED ON OTHER
DISTURBANCES
– TYPICALLY REQUIRES A MORE DETAILED PROCESS
MODEL TO SET CONTROL PARAMETERS
FEEDFORWARD CONTROL
• GENERAL FORM FOR THE
FEEDFORWARD TRANSFER FUNCTION
 Gd ( s)
IS
G ff ( s) 
Gds ( s)Ga ( s)Gp ( s)
• COMBINING THE TERMS IN THE
DENOMINATOR INTO A SINGLE
PROCESS FUNCTION:
 Gd ( s)
G ff ( s) 
Gp ( s)
FEEDFORWARD CONTROL
• ASSUMING THE PROCESS AND
DISTURBANCE TRANSFER FUNCTIONS
HAVE FOPDT FORMS
 Kd e d s 


( p s  1)   ff s
 d s  1
( ld s  1)   ff s
G ff ( s) 
 K ff
e
 K ff
e
 ps
( d s  1)
( lg s  1)
 K pe 


  ps  1 
FEEDFORWARD CONTROL
• SUMMARY OF PARAMETERS
FEEDFORWARD CONTROL
• STATIC FEEDFORWARD CONTROL
• FEEDFORWARD LOOP THAT DOES
NOT PROVIDE DYNAMIC
COMPENSATION
• CAN BE USED WHEN THE PROCESS
HAS SIMILAR DYNAMIC RESPONSE TO
DISTURBANCE CHANGES AND THE
CHANGES IN THE MANIPULATED
VARIABLE, WHERE THE LEAD/LAG
RATIO ≈ 1
FEEDFORWARD CONTROL
• STATIC FEEDFORWARD CONTROLLER
• A STATIC FEEDFORWARD CONTROLLER MAKE A
CORRECTION THAT IS DIRECTLY PROPORTIONAL
TO THE DISTURBANCE CHANGE.
• A STATIC FEEDFORWARD CONTROLLER IS USED
WHEN THE PROCESS RESPONDS IN A SIMILAR
FASHION TO A CHANGE IN THE DISTURBANCE AND
THE MANIPULATED VARIABLE.
FEEDFORWARD CONTROL
• DYNAMIC COMPENSATION
• THIS EXAMINES HOW THE PROCESS
RESPONDS RELATIVE TO THE SIGNAL
FROM A FEEDFORWARD CONTROLLER
FEEDFORWARD CONTROL
• WHEN THE LEAD/LAG RATIO IS > 1,
THEN AN INITIAL
OVERCOMPENSATION IS NECESSARY
• WHEN THE LEAD/LAG IS < 1 THEN AN
UNDERCOMPENSATION PROVIDES A
BETTER CONTROL
FEEDFORWARD CONTROL
• TAKEN AT EXTREMES, WHEN THE LEAD ≈ 0,
THEN THE FUNCTION BECOMES AN FOPDT
 ff s
RESPONSE
K ff e
G ff ( s) 
 lg s  1
• WHEN THE VALUE OF THE LAG ≈ 0, THEN
THE FUNCTION APPROACHES A
PROPORTIONAL/DERIVATIVE FORM:
G ff ( s)  K ff ( ld s  1)e
 ff s
FEEDFORWARD CONTROL
• FEEDFORWARD WHEN τp « τd
FEEDFORWARD CONTROL
• EXAMPLE OF FEEDFORWARD CONTROL FOR
τd<τp
FEEDFORWARD CONTROL
• STATIC FEEDFORWARD RESULTS
• WHEN THE INLET TEMPERATURE DROPS BY
20ºC, Q IS IMMEDIATELY INCREASED BY 20 kW.
• DEVIATIONS FROM SETPOINT RESULT FROM
DYNAMIC MISMATCH
FEEDFORWARD CONTROL
• CONSIDER THE DISTILLATION COLUMN
PREVIOUSLY PROVIDED WITH A CASCADE
CONTROL
• WHAT FEED FORWARD ELEMENTS COULD BE
ADDED
• TO ALLOW FOR CHANGES IN COLUMN FEED
RATE?
• TO ALLOW FOR CHANGES IN FEED
COMPOSITION?
• WOULD THESE DUPLICATE OR SUPPLEMENT
THE FUNCTIONS OF EXISTING LOOPS?
FEEDFORWARD CONTROL
• TUNING FACTORS
• FEEDFORWARD CAN AMPLIFY NOISE
WHICH CAN CAUSE OVERSHOOT.
• BASED ON THE PROCESS APPROXIMATING
AN FOPDT MODEL, THEN LEAD/LAG RATIOS
< 2.0 ARE RECOMMENDED
FEEDFORWARD CONTROL
• PERFECT FEEDFORWARD CONTROL
• FF CORRECTION IS MIRROR IMAGE OF
DISTURBANCE EFFECT.
• NET EFFECT IS NO CHANGE IN
CONTROLLED VARIABLE.
FEEDFORWARD CONTROL
• INITIAL TUNING SEQUENCE – SEE FIGURES
ON NEXT SLIDE
• ESTIMATE Kff, Τld, Τlg, AND θff FOR PROCESS
• UNDER OPEN LOOP CONDITIONS, ADJUST
ONLY Kff WHILE HOLDING OTHER
PARAMETERS CONSTANT, TO ELIMINATE
OFFSET
• ADJUST θff TO ELIMINATE DYNAMIC
MISMATCH
FEEDFORWARD CONTROL
• ADJUST τld - τlg AND UNTIL THERE ARE
EQUAL AREAS ABOVE AND BELOW THE
SETPOINT
FEEDFORWARD CONTROL
• COMBINING FEEDFORWARD AND
FEEDBACK CONTROL
• FEEDBACK AND FEEDFORWARD CONTROL
HAVE COMPLEMENTARY
CHARACTERISTICS
• MOST EFFECTIVE LOOPS MIGHT COMBINE
BOTH TECHNIQUES
FEEDFORWARD AND FEEDBACK
LEVEL CONTROL
• REFERENCE FIGURE 12.4.2
FEEDFORWARD AND FEEDBACK
LEVEL CONTROL ANALYSIS
• FEEDBACK-ONLY MUST ABSORB THE
VARIATIONS IN STEAM USAGE BY
FEEDBACK ACTION ONLY.
• FEEDFORWARD-ONLY HANDLE VARIATION
IN STEAM USAGE BUT SMALL ERRORS IN
METERING WILL EVENTUALLY EMPTY OR
FILL THE TANK.
• COMBINED FEEDFORWARD AND FEEDBACK
HAS BEST FEATURES OF BOTH
CONTROLLERS
FEEDFORWARD AND FEEDBACK
• COMBINING FEEDFORWARD AND
FEEDBACK
• AN EXAMPLE OF THE COMBINATION IS
SHOWN GRAPHICALLY
FEEDFORWARD AND FEEDBACK
• COMBINED FF AND FB FOR THE CSTR
FEEDFORWARD AND FEEDBACK
• COMPARATIVE RESULTS FOR CSTR
FEEDFORWARD CONTROL
• FEEDBACK ONLY PRODUCES OVERSHOOT
BECAUSE OF THE DELAY DUE TO THE
INVENTORY OF THE SYSTEM
• FEEDFORWARD ONLY, EVEN WITH
DYNAMIC COMPENSATION, RESULTED IN
LESS OVERSHOOT BECAUSE THE HEATING
FLOW WAS INCREASED RELATIVE TO THE
FEED, BUT THE SYSTEMS HAD AN
EXTENDED SETTLING TIME
• COMBINING THE TWO METHODS
ELIMINATES EXCESSIVE OVERSHOOT AND
REDUCES SETTLING TIME

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