1

Enhanced Single-Loop Control Strategies

1. Cascade control2. Time-delay compensation3. Inferential control4. Selective and override control5. Nonlinear control6. Adaptive control

Cha

pter

16

2

Example: Cascade ControlC

hapt

er 1

6

3

Cha

pter

16

4

Cha

pter

16

5

Cascade Control

• Distinguishing features:1. Two FB controllers but only a single control

valve (or other final control element).2. Output signal of the "master" controller is the

set-point for “slave" controller.3. Two FB control loops are "nested" with the

"slave" (or "secondary") control loop inside the "master" (or "primary") control loop.

• Terminology:slave vs. master

secondary vs. primaryinner vs. outer

Cha

pter

16

6

Cha

pter

16

7

1

2

1

2

1

2

= hot oil temperature= fuel gas pressure= cold oil temperature (or cold oil flow rate)= supply pressure of gas fuel= measured value of hot oil temperature= measured value of fuel gas tem

m

m

YYDDYY

1 1

2 2

perature= set point for

= set point for sp

sp

Y Y

Y Y%

Cha

pter

16

1 21

2 2 2 2 1 2 2 1 1(16 5)

1P d

c v p m c c v p p m

G GD G G G G G G G G G GY

= −+ +

8

Cha

pter

16

Example 16.1Consider the block diagram in Fig. 16.4 with the following transfer functions:

( )( )1 2

1 22 1

5 4 11 4 1 2 1

11 0.05 0.23 1

v p p

m md d

G G Gs s s

G G G Gs

= = =+ + +

= = = =+

9

Cha

pter

16

10

Cha

pter

16

Example 16.2Compare the set-point responses for a second-order process with a time delay (min) and without the delay. The transfer function is

Assume and time constants in minutes. Use the following PI controllers. For min, while for min the controller gain must be reduced to meet stability requirements

( ) ( )( )16 18( )

5 1 3 1

s

peG s

s s

θ−−=

+ +

1m vG G= =0,θ= 13.02 6.5cK andτ= = 2θ=

( )11.23, 7.0min .cK τ= =

11

Cha

pter

16

( ) ( )1 1 2 16 19spE E Y Y Y Y Y −= − = − − −% % %'

If the process model is perfect and the disturbance is zero, then 2Y Y=% and

( )1 16 20spE' Y Y −= − %

For this ideal case the controller responds to the error signal that would occur if not timewere present. Assuming there is no model error the inner loop has the effective transfer function

( ),G G=%

( ) ( )16 211 * 1

cs

c

GPGE G G e θ−

−= =+ −

'

Time Delay Compensation

12

For no model error:

By contrast, for conventional feedback control

θ= * - sG = G G e%

( )1 1

1 1

θ

θ

θ

−

−

−

′ =+ −

′= =

′+ +

cc * s

c

* sc c

* s *sp c c

GG

G G e

G G e G GYY G G e G G

Cha

pter

16

( )* 16 231 *

sc

ssp c

G G eYY G G e

θ

θ

−

−= −+

13

Cha

pter

16

14

Cha

pter

16

15

Cha

pter

16

Inferential Control

• Problem: Controlled variable cannot be measured or has large sampling period.

• Possible solutions:1. Control a related variable (e.g., temperature instead

of composition).2. Inferential control: Control is based on an estimate

of the controlled variable.• The estimate is based on available measurements.

– Examples: empirical relation, Kalman filter • Modern term: soft sensor

16

Inferential Control with Fast and Slow Measured Variables

Cha

pter

16

17

Selective Control Systems & Overrides

• For every controlled variable, it is very desirable that there be at least one manipulated variable.

• But for some applications,

NC > NMwhere:

NC = number of controlled variables

NM = number of manipulated variables

Cha

pter

16

• Solution: Use a selective control system or an override.Selective control is also referred as “Auctioneering”.

18

• Low selector:

• High selector:

Cha

pter

16

• Median selector:

• The output, Z, is the median of an odd number of inputs

19

• multiple measurements• one controller• one final control element

Cha

pter

16

Example: High Selector Control System

20

2 measurements, 2 controllers, 1 final control element

Cha

pter

16

21

Overrides• An override is a special case of a selective control

system• One of the inputs is a numerical value, a limit.• Used when it is desirable to limit the value of a

signal (e.g., a controller output).• Softer than ESD or SIS• Example:

- anti-reset wind-up- lower and upper heat input rate for distillation

column for ensuring liquid inventory or preventing flooding of the column

• Split-range control

Cha

pter

16

22

Cha

pter

16

23

Nonlinear Control Strategies• Most physical processes are nonlinear to some degree. Some are very

nonlinear.Examples: pH, high purity distillation columns, chemical reactions

with large heats of reaction. • However, linear control strategies (e.g., PID) can be effective if:

1. The nonlinearities are rather mild.or,

2. A highly nonlinear process usually operates over a narrow range of conditions.

• For very nonlinear strategies, a nonlinear control strategy can provide significantly better control.

• Two general classes of nonlinear control:1. Enhancements of conventional, linear, feedback control 2. Model-based control strategies

Reference: Henson & Seborg (Ed.), 1997 book.

Cha

pter

16

24

Enhancements of Conventional Feedback Control

We will consider three enhancements of conventional feedback control:1. Nonlinear modifications of PID control2. Nonlinear transformations of input or output variables3. Controller parameter scheduling such as gain scheduling.

Nonlinear Modifications of PID Control:

0(1 ( ) ) (16-26)c cK K a|e t |= +Cha

pter

16

• Kc0 and a are constants, and e(t) is the error signal (e = ysp - y).

• Also called, error squared controller because controller output is proportional to |e(t)||e(t)|

• Example: level control in surge vessels.

• One Example: nonlinear controller gain

25

Nonlinear Transformations of Variables

• Objective: Make the closed-loop system as linear as possible. (Why?)• Typical approach: transform an input or an output.

Example: logarithmic transformation of a product composition in a high purity distillation column. (cf. McCabe-Thiele diagram)

Cha

pter

16

where x*D denotes the transformed distillate composition.

• Related approach: Define u or y to be combinations of several variables, based on physical considerations.

Example: Continuous pH neutralizationCVs: pH and liquid level, hMVs: acid and base flow rates, qA and qB

• Conventional approach: single-loop controllers for pH and h.• Better approach: control pH by adjusting the ratio, qA / qB , and

control h by adjusting their sum. Thus,u1 = qA / qB and u2 = qA / qB

1 (16-27)1

* DD

Dsp

xx logx−

=−

26

Gain Scheduling• Objective: Make the closed-loop system as linear as possible.• Basic Idea: Adjust the controller gain based on current measurements of

a “scheduling variable”, e.g., u, y, or some other variable.

Cha

pter

16

• Note: Requires knowledge about how the process gain changes with this measured variable.

27

Cha

pter

16

Examples of Gain Scheduling• Example 1. Titration curve for a strong acid-strong base neutralization.• Example 2. Once through boiler

The open-loop step response are shown in Fig. 16.18 for two different feedwater flow rates.

Fig. 16.18 Open-loop responses.

• Proposed control strategy: Vary controller setting with w, the fraction of full-scale (100%) flow.

(16-30)c c I I D DK wK , / w, / w,τ τ τ τ= = =

• Compare with the IMC controller settings for Model H in Table 12.1:

1 2( ) , , ,1 2 2

2

s

c I D

c

KeG s Ks K

θθτ θ τθτ τ τθτ τ θτ

− += = = + =

+ ++Model H :

28

Cha

pter

16

Adaptive Control

• A general control strategy for control problems where the process or operating conditions can change significantly and unpredictably.

Example: Catalyst decay, equipment fouling

• Many different types of adaptive control strategies have been proposed.

• Self-Tuning Control (STC):– A very well-known strategy and probably the most widely used adaptive

control strategy.

– Basic idea: STC is a model-based approach. As process conditions change, update the model parameters by using least squares estimation and recent u & y data.

• Note: For predictable or measurable changes, use gain scheduling instead of adaptive controlReason: Gain scheduling is much easier to implement and less trouble

prone.

29

Cha

pter

16

Block Diagram for Self-Tuning Control

30

Bumpless Transfer

• When a control loop is turned on without bumpless transfer, the process can become unduly upset.

• With bumpless transfer, an internal setpoint is used for the controller and the internal setpoint is ramped at a slow rate from the initial conditions to the actual desired setpoint to order to provide a smooth startup of a control loop.

31

Comparison of True and Internal Setpoints

Time

Internal Setpoint

True Setpoint

32

Control Performance With and Without Bumpless Transfer

Time

w/o bumpless transfer

w/ bumpless transfer

33

Split Range Flow Control• In certain applications, a single flow control

loop cannot provide accurate flow metering over the full range of operation.

• Split range flow control uses two flow controllers (one with a small control valve and one with a large control valve) in parallel.

• At low flow rates, the large valve is closed and the small valve provides accurate flow control.

• At large flow rates, both valve are open.

34

Split Range Flow Controller

FT

FT

FC

FC

35

Coordination of Control Valves for Split Range Flow Control

Total Flow Rate

Sign

al to

Con

trol

Val

ve

(%)

Larger ControlValve

Smaller ControlValve

36

Example for Split Range Flow Control

AcidWastewater

NaOHSolution

Effluent

FTFT

FC

pHTpHC

RSP×

37

Titration Curve for a Strong Acid-Strong Base System

02468

101214

0 0.002 0.004 0.006 0.008 0.01Base to Acid Ratio

pH

• Therefore, for accurate pH control for a wide range of flow rates for acid wastewater, a split range flow controller for the NaOH is required.

38

Other Split-Range Flow Control Examples

• When the controlled flow rate has a turn down ratio greater than 9

• See value sizing examples in Chapter 2

39

Split Range Temperature Control

TT

CoolingWater

Steam

Split-RangeTemperature

Controller

TT TC

RSP

40

Split Range Temperature Control

0

20

40

60

80

100

Error from Setpoint for Jacket Temperature

Sign

al to

Con

trol

Val

ve

(%)

SteamCooling Water

41

Overview

• All controllers that employ integral action should have anti-reset windup applied.

• Bumpless transfer provides a means for smooth startup of a control loop.

• When accurate metering of a flow over a very wide flow rate range is called for, use split range flow control.

42

Bumpless Transfer

• When a control loop is turned on without bumpless transfer, the process can become unduly upset.

• With bumpless transfer, an internal setpoint is used for the controller and the internal setpoint is ramped at a slow rate from the initial conditions to the actual desired setpoint to order to provide a smooth startup of a control loop.

43

Comparison of True and Internal Setpoints

Time

Internal Setpoint

True Setpoint

44

Control Performance With and Without Bumpless Transfer

Time

w/o bumpless transfer

w/ bumpless transfer

45

Split Range Flow Control• In certain applications, a single flow control

loop cannot provide accurate flow metering over the full range of operation.

• Split range flow control uses two flow controllers (one with a small control valve and one with a large control valve) in parallel.

• At low flow rates, the large valve is closed and the small valve provides accurate flow control.

• At large flow rates, both valve are open.

46

Split Range Flow Controller

FT

FT

FC

FC

47

Coordination of Control Valves for Split Range Flow Control

Total Flow Rate

Sign

al to

Con

trol

Val

ve

(%)

Larger ControlValve

Smaller ControlValve

48

Example for Split Range Flow Control

AcidWastewater

NaOHSolution

Effluent

FTFT

FC

pHTpHC

RSP×

49

Titration Curve for a Strong Acid-Strong Base System

02468

101214

0 0.002 0.004 0.006 0.008 0.01Base to Acid Ratio

pH

• Therefore, for accurate pH control for a wide range of flow rates for acid wastewater, a split range flow controller for the NaOH is required.

50

Other Split-Range Flow Control Examples

• When the controlled flow rate has a turn down ratio greater than 9

• See value sizing examples in Chapter 2

51

Split Range Temperature Control

TT

CoolingWater

Steam

Split-RangeTemperature

Controller

TT TC

RSP

52

Split Range Temperature Control

0

20

40

60

80

100

Error from Setpoint for Jacket Temperature

Sign

al to

Con

trol

Val

ve

(%)

SteamCooling Water

53

Overview

• All controllers that employ integral action should have anti-reset windup applied.

• Bumpless transfer provides a means for smooth startup of a control loop.

• When accurate metering of a flow over a very wide flow rate range is called for, use split range flow control.