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Feedforward and Ratio Control ISA Mentor Program Presentation by:

Gregory K. McMillan

Presenter

• Gregory K. McMillan is a retired Senior Fellow from Solutia/Monsanto and an ISA Fellow. Greg was an adjunct professor in the Washington University Saint Louis Chemical Engineering Department 2001-2004. Greg received the ISA “Kermit Fischer Environmental” Award for pH control in 1991, the Control Magazine “Engineer of the Year” Award for the Process Industry in 1994, was inducted into the Control “Process Automation Hall of Fame” in 2001, was honored by InTech Magazine in 2003 as one of the most influential innovators in automation, and received the ISA Life Achievement Award in 2010. Greg is the author of numerous ISA books on process control, his most recent being Advances in Reactor Measurement and Control and Good Tuning: A Pocket Guide - 4th Edition. Greg has been the monthly “Control Talk” columnist for Control magazine since 2002. Greg is the founder and co-leader with Hunter Vegas of the ISA Mentor Program for users. Greg’s expertise is available on the web sites: http://www.controlglobal.com/blogs/controltalkblog/ http://automation.isa.org/author/gregmcmillan/

2

When there is no secondary flow or speed controller, the feedforward summer in the primary controller is used to directly manipulate a valve position or power input signal. A secondary controller is too slow for pressure control.

When there is a flow or speed controller, Ratio control is predominantly used where a secondary flow or speed controller setpoint is manipulated to follow a leader flow or speed that is multiplied by a desired ratio. Ratio control is used to assist primary PIDs for composition, level, pH, temperature, & quality control.

In Ratio control the leader and follower flow first go to a Ratio block whose output is the input to a Bias/Gain block whose output is the cascade setpoint for a flow or speed controller. The setpoint (SP) of each block (ratio or bias) can be set by operator (auto mode) or automatically corrected by a primary PID (cascade mode). The manipulation of the primary PID of the Bias SP and Ratio SP is effectively a feedforward summer and feedforward multiplier, respectively. The use of the ratio and bias/gain blocks provide the operator visibility and accessibility in ratio control particularly important for understanding and procedural automation during startup, changes in products and abnormal operations.

The Bias SP is manipulated for volumes with back mixing due to agitation, turbulence or boiling (e.g., vessels and columns).

The actual and desired Ratio SP are displayed. During startup until the process is at its normal operating point, the primary controller is often in manual. In this case the operator runs with a manually set bias and ratio without correction.

Feedforward Multiplier vs Summer

Blend composition control - additive/feed (flow/flow) ratio Column temperature control - distillate/feed, reflux/distillate, reflux/feed,

steam/feed, and bottoms/feed (flow/flow) ratio Combustion temperature control - air/fuel (flow/flow) ratio Drum level control - feedwater/steam (flow/flow) ratio Extruder quality control - extruder/mixer (power/power) ratio Heat exchanger temperature control - coolant/feed (flow/flow) ratio Neutralizer pH control - reagent/feed (flow/flow) ratio Reactor reaction rate control - catalyst/reactant (speed/flow) ratio Reactor composition control - reactant/reactant (flow/flow) ratio Sheet, web, and film line machine direction (MD) gage control -

roller/pump (speed/speed) ratio Slaker conductivity control - lime/liquor (speed/flow) ratio Spin line fiber diameter gage control - winder/pump (speed/speed) ratio Header pressure control – letdown/user (flow/flow) ratio

For level and pressure, the mass flow theoretical ratio is simply 1

Ratios Here, There and Everywhere

Cascade Ratio or Cascade Bias Correction by Primary PID output

Follower Flow or Speed

Leader Flow or Speed

Cascade Ratio Correction

Cascade Bias Correction

Original Relationship per Process Flow Diagram (PFD)

Automatic correction of cascade Ratio Setpoint (feedforward multiplier) creates a gain factor in the open loop gain that is proportional to flow. For plug flow processes this multiplier gain factor cancels out a process gain that is inversely proportional to flow.

For back mixed processes, the process time constant being inversely proportional to flow cancels out process gain nonlinearity in the PID tuning where the PID gain is proportional to the process time constant divided by the process gain.

In this case the correction of the cascade ratio creates a residual nonlinearity that adversely affects PID tuning The primary PID output scaling is more critical and prone to error when correcting a ratio

The PID output scaling can be as simple as -50% to +50% of secondary PID scale when correcting a Bias Finally, many corrections in Ratio Control are simply associated with offsets from bias errors in the flow measurements or unmeasured loads

When in doubt which is best, automatically correct the Bias Setpoint You can slowly adapt the uncorrected Ratio or Bias by use of a generic integral only controller to reduce the correction by primary PID

Loop and Load Disturbance Dynamics Block Diagram

Y fraction of small lag that is equivalent dead time is a logarithmic function of the ratio of the small to largest lag (Y = 0.28, 0.88 for ratios = 1.0 and 0.01, respectively)

Feedforward correction should arrive at this point at same time as the Load Upset

Steam Header Feedforward and Decoupler (Linear Valves)

Definition of Loop Lag and Leader Lag: Loop Lag is Primary Loop’s time constant in path of follower flow or speed to primary process output

(primary time constant in self-regulating process and secondary time constant in an integrating process) Leader Lag is Leader’s time constant in path of leader flow or speed to the primary process output

(load is positive for user pulling steam from header and negative for user pushing steam into the header)

ADD

DEADTIME

FF1 Lead = Loop Lag (block diagram Secondary Lag

Letdown Flow To Lower Header (kpph)

LEAD/LAG

Disturbance 1 Flow Load1 (kpph)

FF2 Delay => Load2 Delay – Loop Delay

FF1 Lag = Load1 Lag

DEADTIME

LEAD/LAG

Disturbance 2 Flow Load2 (kpph)

FF2 Lead = Loop Lag

FF2 Lag = Load2 Lag

FF1 FF0 FF2

FF1 Delay => Load1 Delay – Loop Delay

If letdown valves are not linear, a signal characterizer (SG) would be needed on PID OUT

SG would use installed flow characteristic of letdown valve. SG Y outputs would be 0-100% signal

SG X inputs would be 0-100% max letdown valve flow

If Load1 nonlinear valve must be used as an inference of flow a signal characterizer (SG) would be needed on FF1

SG would use installed flow characteristic of load valve. SG Y outputs would be 0 – F1max (kpph) SG X inputs would be 0-100% position where F1max is max Load1 valve flow

PID

Header PID PV (psig)

Header PID SP (psig)

Header FF FF Scale

0 – FFmax (kpph) where FFmax is max letdown

valve flow

FF Gain 0.8 to 1.0

ANALOG OUTPUT

Header PID OUT 0 -100%

(% of Fmax) Valve Signal 0 -100%

(% of Fmax)

If Load Delay is less than Loop Delay, often a delay can be inserted in the PID

SP that is triggering the disturbance. The SP before the delay is used as

the feedforward signal so that Loop Delay is now less than Load Delay. This is an important

often overlooked technique!

Ratio Control Dynamic Compensation & Adaptive Feedback Correction of Ratio

Examples of Follower to Leader flow ratio corrected by Primary Controller output: Reboiler Steam Flow to Column Feed ratio corrected by Temperature Controller

Receiver Distillate Flow to Column Feed ratio corrected by Temperature Controller Reagent Flow to Neutralizer Feed ratio corrected by pH Controller

Follower Reactant Flow to Leader Reactant Flow ratio corrected by Composition Controller

Leader Flow or Speed (e.u.)

DEADTIME

Follower Lag = Leader Lag

LEAD/LAG

Follower PV

Follower Delay => Leader Delay – Loop Delay

RATIO

Follower Lead = Loop Lag

Leader PV

AUTO Ratio SP

CAS Ratio SP

Actual Ratio PV after correction

Uncompensated Follower Flow or Speed SP

(Leader PV x Ratio)

Follower Flow or Speed (e.u.)

PID

Primary PID PV (e.u.)

Primary PID SP (e.u.)

ANALOG OUTPUT

BIAS/GAIN

CAS Bias SP

Dynamic Compensated Follower SP

AUTO Bias SP

Gain PID

Secondary PID PV (e.u.)

(Follower PV)

Secondary CAS SP (e.u.)

Secondary AUTO SP (e.u.)

(Corrected Follower Flow or Speed SP)

Secondary PID OUT 0 -100%

-0.5xFmaxto 0.5xFmax Bias Correction (e.u.)

Primary PID OUT

Valve Signal 0 -100%

(% of Fmax)

PID

Zero Correction SP

0.5xRnorm to 2.0xRnorm Ratio Correction

Adaptive PID OUT

Gradual Adaptation by PID Integral Only Controller

Ratio Control Dynamic Compensation & Adaptive Feedback Correction of Bias

Definition of Loop Lag and Leader Lag: Loop Lag is Primary Loop’s time constant in path of follower flow to primary process output

(primary time constant in self-regulating and secondary time constant in an integrating process) Leader Lag is Leader’s time constant in path of leader flow to the primary process output

Examples of Follower to Leader flow ratio corrected by Primary Controller output: Reboiler Steam Flow to Column Feed ratio corrected by Temperature Controller

Receiver Distillate Flow to Column Feed ratio corrected by Temperature Controller Reagent Flow to Neutralizer Feed ratio corrected by pH Controller

Follower Reactant Flow to Leader Reactant Flow ratio corrected by Composition Controller

Leader Flow or Speed (e.u.)

DEADTIME

Follower Lag = Leader Lag

LEAD/LAG

Follower PV

Follower Delay => Leader Delay – Loop Delay

PID

Primary PID PV (e.u.)

Primary PID SP (e.u.)

ANALOG OUTPUT

RATIO

Follower Lead = Loop Lag

Leader PV

AUTO Ratio SP

CAS Ratio SP

Actual Ratio PV after correction

BIAS/GAIN

CAS Bias SP

Dynamic Compensated Follower SP

AUTO Bias SP

Gain

Uncompensated Follower Flow or Speed SP

(Leader PV x Ratio)

PID

Secondary PID PV (e.u.)

(Follower PV)

Secondary CAS SP (e.u.)

Secondary AUTO SP (e.u.)

(Corrected Follower Flow or Speed SP) Secondary

PID OUT 0 -100%

Primary PID OUT

Follower Flow or Speed (e.u.)

Valve Signal 0 -100%

(% of Fmax)

PID

Zero Correction SP

0.5xRnorm to 2.0xRnorm Ratio Correction

Adaptive PID OUT

-0.5xFmaxto 0.5xFmax Bias Correction (e.u.)

Gradual Adaptation by PID Integral Only Controller

Steam Header System Feedforward Control

FT 3-3

FT 3-2

PT 2-1

PC 2-1c

PY 2-1

Cogen

FT 3-1

Boiler

FT 2-2

PC 2-1a

PC 2-1b

PX 3-2

PX 3-3

PX 2-3

FT 2-3

FT 2-2

PX 2-2

RY 2-1

FC 3-1

PY 3-1

PT 1-1

PY 1-1

PC 1-1a

PC 1-1b

PX 1-3

FT 1-3

FT 1-2

PX 1-2

Hi Pressure Header

Med Pressure Header

Lo Pressure Header

Hi SP

Hi SP

Lo SP

Hi SP

Norm SP

Norm SP

Hi Signal Selection

Vent

Vent

FF

Steam Generators

Steam Generators

Steam Generators

Steam Users

Steam Users

Steam Users

+

−

+

−

+

−

FF

(kpph)

(kpph)

(kpph)

PX 1-3, PX 1-2, PX 2-3, PX 2-2, PX 3-3, PX 3-2 are Deadtime and Lead/Lag blocks in series for dynamic compensation of feedforward signals PY 1-1, PY 2-1, PX 3-1 are Add blocks where generator flows are negative and user flows and decoupling flows are positive signals Decoupling flows from lower header letdown valves typically do not need dynamic compensation if valves are in same proximity of header Feedforward signals are in same engineering flow units (kpph) with Feedforward scale in PID set to be max flow of manipulated letdown valve All letdown valves must be precise (0.1% resolution 0.2% deadband) fast valves (4 sec T86 86% response time) with linear flow characteristics

+

+

Liquid Reactor Ratio Control of Reactants with Feed Maximization

TT 1-4

TC 1-3

TC 1-4

AT 1-6

LY 1-8

FT 1-2

FC 1-2

Reactant A

Reactant B

SP

Level SP for Optimum

Residence Time SP

AC 1-6

Makeup

Return

LY 1-8 LT

1-8 TT 1-3

LC 1-8

Reactant Ratio Control

Product

Vent FT 1-1

FC 1-1

FC 1-7

FT 1-7

SP

PT 1-5

PC 1-5

FT 1-5

CTW

CTW

FC 1-1 SP

ZC1-4 OUT

ZC 1-4

ZC1-4 is an enhanced PID VPC

RC 1-2

Leader

Follower

SP

jacket recirculation

process recirculation

Dynamic compensation of reactant ratio control is not needed because reactants arrive at the same point

at the same time in reactor if equal reactant flow setpoint filters are used.

Valve Position Controller ZC1-4 pushes coolant

valve to max position to maximize reactant feed rate. The ZC1-4 setpoint is the maximum position.

The ZC1-4 should have smart integral action to prevent interaction and limit cycles. The correction for a valve position less than setpoint should be slow to

provide a slow approach to optimum. The correction for a valve position greater than setpoint must be fast to

provide a fast getaway from the point of loss of control. Directional setpoint rate limits with dynamic reset limit in

an enhanced PID that tempers integral action can achieve these optimization objectives.

Column 1 Top Temperature Ratio Control: Small Distillate Flow

Column 1

Z

Z FT 1-2

FC 1-2

FT 1-4

FC 1-4

FT 1-5

FC 1-5

LT 1-6

LC 1-6

FT 1-3

FC 1-3

FT 1-1

FC 1-1

TT 1-8

TC 1-8

RC 1-3

RY 1-3 RC

1-2

Feed

Steam

Distillate

Bottoms

Reflux

Distillate/Feed Ratio Control

Steam/Feed Ratio Control

Bias Correction

Flow Feedforward

Receiver

Sump LT 1-7

LC 1-7

Tight Level Control

Loose Level Control

Leader Flow

Follower Flow

SP

SP

SP

SP

Leader

Follower RX 1-2 RX

1-3 Dynamic Compensation

Dyn

amic

C

ompe

nsat

ion

Relative Advantages: Internal reflux control inherently compensating for changes in reflux temperature and inherent decoupling of energy and material balances Relative Disadvantages: Slower control of bottoms composition (problematic for stripping columns)

Column 2 Top Temperature Ratio Control: Large Distillate Flow

Column 2

Z

Z FT 1-4

FC 1-4

FT 1-5

FC 1-5

LT 1-6

LC 1-6

FT 1-3

FC 1-3

FT 1-1

FC 1-1

TT 1-8

TC 1-8

RC 1-5

Feed

Distillate

Bottoms

Reflux

Reflux/Feed Ratio Control

Bias Correction

Flow Feedforward

Receiver

Sump LT 1-7

LC 1-7

Loose Level Control

Loose Level Control

FT 1-2

FC 1-2

RC 1-2

Steam

Steam/Feed Ratio Control

SP

Leader

Follower

RY 1-5

Dyn

amic

C

ompe

nsat

ion

RX 1-2

RX 1-5 D

ynam

ic

Com

pens

atio

n

SP

SP

Leader Flow

Follower Flow

SP

Relative Advantages: Faster temperature control since independent of level control Relative Disadvantages: Moderate interaction between energy and material balances

Column 3 Bottom Temperature Ratio Control: Large Bottoms Flow

Column 3

Z

Z FT 1-4

FC 1-4

FT 1-5

FC 1-5

LT 1-6

LC 1-6

FT 1-3

FC 1-3

FT 1-1

FC 1-1

TT 1-8

TC 1-8

RC 1-5

LT 1-7

LC 1-7

Feed

Distillate

Bottoms

Reflux

Reflux/Feed Ratio Control

Bias Correction

Flow Feedforward

Receiver

Sump

RY 1-2

Loose Level Control

Loose Level Control

FT 1-2

FC 1-2

RC 1-2

Steam

Steam/Feed Ratio Control

SP

Leader

Follower

Dyn

amic

C

ompe

nsat

ion

RX 1-2

RX 1-5 Dynamic

Compensation

Leader Flow Follower Flow

SP

SP

SP

Relative Advantages: Fastest temperature control Relative Disadvantages: Severe interaction between energy and material balances and possibly less process sensitivity from manipulation of separation (vapor rate)

Column 4 Bottom Temperature Ratio Control: Small Bottoms Flow

Column 4

Z

FT 1-4

FC 1-4

FT 1-5

FC 1-5

LT 1-6

LC 1-6

FT 1-3

FC 1-3

TT 1-8

TC 1-8

RC 1-5

LT 1-7

LC 1-7

Distillate

Bottoms

Reflux

Reflux/Feed Ratio Control

Bias Correction

Receiver

Sump

RC 1-4

RY 1-4

Tight Level Control

Loose Level Control

Z

FT 1-1

FC 1-1

Feed

Bias Correction

Flow Feedforward

RY 1-2

FT 1-2

FC 1-2

RC 1-2

Steam

SP

Leader

Follower

Steam/Feed Ratio Control

Dyn

amic

C

ompe

nsat

ion

RX 1-2

RX 1-4

RX 1-5 Dynamic

Compensation

Dynamic Compensation

Bottoms/Feed Ratio Control

Leader Flow Follower Flow

Leader Flow Follower Flow

SP

SP

SP

Relative Advantages: Fast temperature control if level control is tight but this may not be possible due to level inverse response (good steam/feed ratio is critical) Relative Disadvantages: Moderate interaction between energy and material balances and possibly less process sensitivity from manipulation of separation (vapor rate)

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