Cascade Control

1. Introduction

2. Process examples

3. Closed-loop analysis

4. Controller design

5. Simulink example

Introduction

Feedback control » Corrective action taken regardless

of disturbance source

» Corrective action not taken until after the output has deviated from the setpoint

» Problematic for processes with large time constants and/or long time delays

Feedforward control » Corrective action can be taken

before the output has deviated from the setpoint

» Disturbance must be explicitly measured

» Typically requires a process model

Cascade Control

Cascade control can provide improved performance for unmeasured disturbances

Basic characteristics

» A second measurement and a second controller are used in an inner feedback loop

» The setpoint for the inner control loop is provided by an outer control loop designed to regulate the controlled output

» The disturbance can be more rapidly identified with the secondary measurement than with the primary measurement

Particularly useful when the disturbance is associated with the manipulated input

Flow Control Example

Control problem

» Regulate flow rate through control value despite changes in upstream and/or downstream pressures

Control alternatives

» Specify the value position to indirectly achieve the desired flow rate

» Utilize a measurement of the flow rate to design a feedback controller that explicitly regulates the flow rate

Applications

» Any control problem in

which a flow rate is used as a

manipulated variable

» Outer controller provides the

setpoint for the inner flow

controller in a cascade

arrangement

Furnace Example

Conventional control

» Directly regulate hot oil

temperature with fuel gas

value position

» Poor performance for

changes in fuel gas

supply pressure

» Disturbance is related to

the manipulated input

Cascade control

» Add an inner controller that regulates fuel gas pressure by manipulating the value position

» Hot oil temperature controller provides setpoint for inner controller

» Improved performance for changes in fuel gas supply pressure

Chemical Reactor Example

Secondary (inner) controller » Manipulated variable – cooling water makeup value position

» Controlled output – cooling jacket temperature

» Disturbance – cooling water inlet temperature

Primary (outer) controller » Manipulated variable – cooling jacket temperature setpoint

» Controlled output – reactor temperature

» Disturbance – reactant feed flow rate

Cascade Control Block Diagram

Closed-Loop Transfer Function

General formula for closed-loop transfer functions

» Z = any variable in feedback system

» Zi = any input variable in feedback system

» Pf = product of all transfer functions between Z and Zi

» Pe = product of all transfer functions in feedback loop

Closed-loop transfer function for inner disturbance (D2)

e

f

iZ

Z

P

P

1

12211222

12

1111

12

2

1

2

222

2

2

21

222

22

2

2

11

11~

ppvccmpvcm

pd

pcm

p

pvcm

d

pvcm

pvc

sp

GGGGGGGGGG

GG

GGGG

GG

D

Y

GGGGG

G

D

YG

GGGG

GGG

Y

Y

Closed-Loop Stability

Characteristics equation for cascade control

Characteristic equation for conventional

control (Gm2 = 0, Gc2 = 1)

If inner loop has faster dynamics then the

outer loop, then cascade control usually has

improved stability characteristics

01 12211222 ppvccmpvcm GGGGGGGGGG

01 1211 ppvcm GGGGG

Closed-Loop Stability Example

Transfer functions

Inner loop for cascade control (Kc2 = 4)

Inner loop for conventional control

2.005.0113

1

1)12)(14(

4

1

5

2121

21

mmdd

ppv

GGGs

G

Gss

Gs

G

12.0

4

)1(1

5)4)(2.0(1

)1(1

5)4(

1~

222

22

2

2

s

s

s

GGGG

GGG

Y

Y

pvcm

pvc

sp

1

5

)1)(0(1

)1()1(

1~

2222

22

2

2

sG

GG

G

GGGG

GGG

Y

Yv

pv

v

pvcm

pvc

sp

Closed-Loop Stability Example cont.

Characteristic equation for cascade control

Characteristic equation for conventional control

Can use larger gains in outer control loop with cascade control than with conventional control

3.43

04531468

01

,1

1

23

12211222

uc

c

ppvccmpvcm

K

Ksss

GGGGGGGGGG

3.11

017148

01

,1

1

23

1211

uc

c

ppvcm

K

Ksss

GGGGG

Cascade Controller Design

Inner loop

» Typically a P or PI controller

» Tuned first with outer controller in manual

» Tuned to provide fast response to setpoint changes

Outer loop

» Typically a PI or PID controller

» Tuned second with inner controller in automatic

» Tuned to provide acceptable responses to setpoint changes and/or disturbances

» Must be retuned if inner loop is retuned

Direct Synthesis Design

Inner loop

Outer loop

2

2

processInner

2

22

22

2

2

22

222

22

2

2

1

11 If

1

1

1~

d

d

vp

cm

dm

d

vp

cd

pvcm

pvc

sp

G

G

GGGG

GG

G

GGGG

GGGG

GGG

Y

Y

1

1

processOuter

211

111

111

1

21

1

1

1211

1211

1111

1111

1

1

1

1 If

1

11

d

d

dpm

cmm

dmm

d

dp

c

d

pdcm

pdcm

pcm

pcm

sp

G

G

GGKGKG

GGK

G

GGG

GGGGG

GGGK

GGGG

GGGK

Y

Y

Cascade Controller Design Example

Transfer functions

Inner controller design

Outer controller design

1111

1110

4

1

5

2121

21

mmdd

ppv

GGGG

Gs

Gs

G

s

sK

s

s

s

s

G

G

GGG

sG

I

Ic

d

d

vp

cd

11

2.0

1

5

1

1

1

12.0

1

2

2

2

22

s

sK

s

s

s

s

G

G

GGKG

sG

I

Ic

d

d

dpm

cd

1

10

110

2

1

5

1

4

110

1

1

15

1

1

1

211

11

Conventional Controller Design

Process transfer function

IMC tuning (c = 5)

Simulink PID controller parameters

)110)(1(

20)()()()()( 121

sssGsGsGsGsG mppv

91.01111.01

21

2121

21

DI

c

cK

K

10.001.011.0 Dc

I

cc KD

KIKP

Simulink Implementation

Valve

5

s+1 To Workspace 1

output

To Workspace

setpoint

Setpoint

Process

4

10s+1Outer Controller

PID

Inner Controller

PID

Disturbance 2Disturbance

Add3 Add2Add 1

Add

0 5 10 15 20 25 30 35 40 45 50-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time

Outp

ut

Inner Disturbance

Cascade

Conventional

Setpoint

Closed-Loop Performance

0 5 10 15 20 25 30 35 40 45 50-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Outp

ut

Time

Outer Disturbance

Cascade

Conventional

Setpoint

0 5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

1.2

1.4Setpoint

Outp

ut

Time

Cascade

Conventional

Setpoint