designs of single neuron control systems: survey ~陳奇中教授演講投影片

1

Direct Adaptive Process Control Based on Using a Single Neuron Controller:

Survey and Some New Results

陳奇中

Chyi-Tsong [email protected]

Department of Chemical Engineering Feng Chia UniversityTaichung 407, Taiwan

逢甲大學化工系FCU PSE Lab., C.T. Chen

2

OutlineIntroduction

The single neuron controller (SNC) and its parameter tuning algorithm

Direct adaptive control schemes for chemical processes using SNCs

Some alternative SNC controllers and their parameter tuning algorithms

Model-based design of SNC control systems

Conclusions

FCU PSE Lab., C.T. Chen

3

Conventional control strategies and limitationsStructure and design methodologies─ Open-loop control

─ Manual control─ Suitable for process whose mathematical model is hard to

characterize precisely

Introduction


4

Closed-loop control system

─ Use system output error to generate control signal ─ Automatic control─ Widely used algorithm: PID type controller


5

⎥⎦

⎤⎢⎣

⎡++= ∫

tD

Ic dt

tdedttetektu 0)()(1)()( τ

τ

⎥⎦

⎤⎢⎣

⎡−−++= ∑

=))1()(()()()(

0keke

TieTkekku

s

Dk

iI

sc

ττ

: proportional gain: integral time constant: derivative time constant: sampling time

ckIτDτST

PID controller for continuous system

PID controller for discrete system


6

New challenges─ Extremely nonlinearities─ Immeasurable disturbances and uncertainties ─ Unknown or imprecisely known dynamics─ Time-varying parameters─ Multi-objectives

Modeling problem

─ Controller parameter's tuning problem ─ Control performance degradation

Artificial Intelligence (AI)

Motivation: Searching for new approaches for complex process control


7

Research fields of AI


8

Structure of neurons

An artificial neuron

Introduction to artificial neural networks


9

Multilayer feedforward neural network


receive signals from external environment

Signal transmission

transmit output signals to environment

10

Operations of an artificial neural network

1. Training or learning phase─ use input-output data to update the network parameters

(interconnection weights and thresholds)

2. Recall phase─ given an input to the trained network and then generate an

output

3. Generalization (prediction) phase─ given a new (unknown) input to the trained network and then

gives a prediction


11

Properties (advantages) of MNN1. It has the ability of approximating any extremely

nonlinear functions.

2. It can adapt and learn the dynamic behavior under uncertainties and disturbances.

3. It has the ability of fault tolerance since the quantity and quality information are distributively stored in the weights and thresholds between neurons.

4. It is suitable to operate in a massive parallel framework.


12

+

What happen when some neurons of the neural network werebroken down?

Direct adaptive control using a shape-tunable neural network controller (Chen and Chang, 1996)

single neuron controller


13

The single neuron controller (SNC) and its parameter tuning algorithm

Single neuron controller

)(te )()()( tytyte d −=p Tba ],,[ θ≡pabθ

process output error, given bycontroller parameter vector, defined ascontrol output levelslope (sensitivity factor) bias

( ) ( ) [ ]{ }[ ])(exp1

)(exp1,θθ

−−+−−−

==ebebaeNLtu p


θ−ee u

14

The characteristic plots for parameter a


15

The characteristic plots for parameter b


16

The characteristic plots for parameter θ


17

A SNC-based direct adaptive control scheme

kee ku uydy +


18

SNC parameters tuning algorithm

─ System performance

─ Parameter tuning algorithm (Chen, 2001)

where

and( ) ( ))(,)()()()()()( kkukukykkyk ppz Φ∂∂=∂∂≡

2))((21)( kyykE d −=

)()(1)()()()1(

kkkkekk T zz

zpp+

+=+ η

( )

( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛ −−⎟

⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛ −−=

∂∂≡Φ

au

auab

au

auea

au

uu

1121,11

21,

,

θ

pp


19

Stability of the SNC parameter learning algorithm

Assume is bounded

Let ;

the controller parameter vector converges to its local optimal asymptotically, where (the desired control input) and .

For the theoretical and rigorous proof, please refer to Chen (2001).

)(kz

20 <<η

p*p ( ) duNL =∗p,0

0*)( =pe


20

A simplified version of the learning algorithm--- Using system response direction

)()(1)()()()1(

kkkkekk T zz

zpp+

+=+ η

parameter tuning algorithm (Chen, 2001)

where

( ) ( ))(,)()()()()()( kkukukykkyk ppz Φ∂∂=∂∂≡

( ) ( ))(,)()()()( kkukukysignk pz Φ∂∂=

system response direction

( )

( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛ −−⎟

⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛ −−=

∂∂≡Φ

au

auab

au

auea

au

uu

1121,11

21,

,

θ

pp


21

[ ] [ ]TTba 011)0()0()0()0( == θp

Example :

I.C.

Setpoint : 5=dy


Learning rate : 15.0=η

System response direction: ( ) 1)()( =∂∂ kukysign

22


Simulation results

23


SNC shape tuning progress

u

e

24

Direct adaptive control schemes for chemical processes using SNCs

A SNC-based control scheme for large time-delay processes(Chen, 2001)


25

A SNC-based control scheme for non-minimum phase processes(Chen, 2001)

)()()( sGsGsG ppp+−=


26

A decentralized SNC control scheme for multi-input/multi-output processes (Chen and Yen, 1998)

• Consider an multivariable process described by

• In loop , the produces its controller output through the following nonlinear mapping (Assume loop paring results are: )

nn×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

)(

)()(

)()()(

)()()()()()(

)(

)()(

2

1

21

22221

11211

2

1

su

susu

sGsGsG

sGsGsGsGsGsG

sy

sysy

nnnnn

n

n

n

M

L

MOMM

L

L

M

i iSNC

( ) [ ][ ]{ }[ ][ ]ii

iiiii teb

tebatu

θθ

−−+−−−

=)(exp1)(exp1~


ii uy ↔

27

A static decoupler for the decentralized SNC control system: the decoupling gain can be given simply by

Parameter tuning algorithm (in continuous form) for

where and

nieti

Ti

iiii ,,2,1,1

)( K& =+

=zz

zp η

( ) ( )iiiii uuysign pz ,~~ Φ∂∂≡

( )

( )T

i

i

i

iii

i

i

i

iiii

i

i

iiii

au

auba

au

auea

au

uu

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−−⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−−=

∂∂≡Φ

~1

~1

21,

~1

~1

21,

~

~,~

θ

pp

)( jiDij ≠

ii

ij

ii

ij

sij

KK

sGsG

D

−=

−=→ )(

)(lim

0

iSNC


28

A decentralized SNC scheme for 2x2 processes


29

Some alternative SNC controllers and their parameter tuning algorithms

A bounded SNC (Chen and Peng, 1999) For handling with the input constraint of ,a bounded nonlinear controller of the form

where

the parameter tuning algorithm for the bias parameter

maxmin )( utuu ≤≤

( ) ( )( ) ( )( )[ ]minmax~1~1

21 utuututu −++=

( ) ( )( )[ ]( )( )[ ]θ

θ−−+−−−

=tebteb

tuexp1exp1~

( ) ( ) ( )( ) ( )( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+−−=uy

signtututebt ~1~1ηθ&


30

A SNC for the temperature trajectory control of a batch process (Chen and Peng, 1998)

0)( =tu

( ) ( )( )[ ]θ−−+=

tebtu

exp11

)())(1()()( tetutubt −−= ηθ&

• To achieve tight temperature tracking controlBoth heating and cooling of the processunit are necessary

A parametric variable is used to express the twomanipulated variables simultaneously

1)( =tu

maximum cooling and minimum heating

The simplified SNC

:

: maximum heating and minimum cooling

• Parameter tuning algorithm


31

Unsolved Problem ?

Fact:System performance depends on the initial SNC controller parameters.

Question: How to start up SNC systematically?

Model-based SNC control systems

32

θ *e

*e−

du

The typical function

characteristics of the SNC

Model-based design of SNC control systemsSNC control of first-order processes

─ upper/lower limit part

─ linear part


33

Analysis of the SNC closed-loop control system

Case 1: upper/lower part

Closed-loop dynamics ⎩⎨⎧

−<<−>>

= *

*

,,

)(eea

eeatu

⎪⎩

⎪⎨⎧

−<<−>>

=+ *

*

,,

eeaKeeaK

yyp

p&τ


θ *e

*e−

du

34

Case 2: linear partsince

,0=e )exp(1)]exp(1[

θθ

bbauu d +

−==

,θ=e 0=u

⎟⎠⎞

⎜⎝⎛ −=

θ)(1)( teutu d

⎟⎟⎠

⎞⎜⎜⎝

⎛+−

=)exp(1))exp(1θθ

bbaud


θ *e

*e−

du

Approximated linear function

35

The closed-loop system dynamics in this case can be represented by

Let , we arrive at

or

where is the time constant of the closed-loop system and is an index regarding the system performance

The value of can be given by

⎟⎠⎞

⎜⎝⎛ −−=+

θτ yyuKyy d

dp 1&

ddP yuK =

ddd yuKyuKy ⎟⎠⎞

⎜⎝⎛ −=⎟

⎠⎞

⎜⎝⎛ −+

θθτ 11&

dyyy =+&'τ

ταθττ ≡−= )/1/(' dy)/( dy−= θθα

θ

dy1−

=ααθ


36

Also, from we have

we obtain from the solution of that

Let , then the above equation leads to

ddP yuK = 0)exp(1)exp(1>

−+

=θθ

bb

Kya

p

d

⎪⎩

⎪⎨⎧

−<<−>>

=+ *

*

,,

eeaKeeaK

yyp

p&τ

⎟⎠⎞⎜

⎝⎛ −

−+

=

−=

−

−

τ

τ

θθ t

P

d

t

P

ebb

Ky

eaK

ty

1)exp(1)exp(1

)1()(

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=P

d

Kysign

eb

121ln1

4αθ

dt yty == '4)( τ


37

The SNC parameter value setting procedure is summarized as follows:

• Given a performance factor , , and the desired process’s output value

α 10 <<αdy

one can calculate sequentially the values of , and from θ b a

)exp(1)exp(1

121ln1

1

4

θθ

θ

ααθ

α

bb

Kya

Kysign

eb

y

p

d

P

d

d

−+

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

−=


38

Hard input constraintset

Thus from

we have and then

Together with and under the condition of ,

we obtain

uu ≤

ua =0

)exp(1)exp(1>

−+

=θθ

bb

Kya

p

d

)exp(1)exp(1

θθ

bb

Kyua

P

d

−+

==

dt yty =′= τ4)(

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−

+−

=

P

d

P

d

Kyu

Kyu

b ln1θ

⎟⎠⎞⎜

⎝⎛ −

−+

=−τ

θθ t

P

d

P

ebb

Ky

Kty 1

)exp(1)exp(1)(

dP

d yuK

y1

and1ln41

−=⎟

⎟⎠

⎞⎜⎜⎝

⎛−−=

ααθα


39

Table 1a. SNC parameter settings for


0≠dy

40

Table 1b. SNC parameter settings for the case of 0=dy


41

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

syst

em o

utpu

t

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

1

1.5

2

2.5

3

time

cont

rol i

nput

α=0.3

α=0.5α=0.7

Example 1: First-order system Assume CASE 1: Effects of on system performance ( , )

( )1+

=sK

sG pP τ

1=pK 1=τ1=dy

α


42

0 10 20 30 400

0.2

0.4

0.6

0.8

1

syst

em o

utpu

t

0 10 20 30 400.8

1

1.2

1.4

1.6

1.8

time

cont

rol i

nput

τp=1

τp=5

τp=10

different time constants ( fixed)1=pK


)/'(5.0 ττα =CASE 2:

different process gain ( fixed)

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

syst

em o

utpu

t

0 2 4 6 8 100

0.5

1

1.5

2

time

cont

rol i

nput

kp=1

kp=5

kp=10

1=τ

43

If the hard input constraint is

one can calculate the performance

index as

for the case of and

SNC controller parameters

2≤u

1733.0=α

1=PK 1=dy

2=a2412.5=b

2096.0−=θ


CASE 3: Hard input constraint

44

Model-based SNC control of a first-order plus dead-time processes

• First-order plus dead-time (FOPDT) process with transfer function of

where

The feedforward compensator

is designed as

)exp()()( stsGsG dp −=

)1()( += sKsG p

τ

)()(

)(sGsG

sGp

dff −=


45

Example 2 Process: ,

The feedforward controller :

Setpoint:

Let , the SNC controller parameter vector is set as

The IMC-PID controller is given by (Brosilow and Joseph, 2001 )

( ) sP e

ssG −

+=

11 ( ) s

d es

sG 5.0

141 −

+=

141)(++

−=sssG ff

1=dy5.0=α

[ ] [ ]TTbap 16231.21565.1 −== θ

=)(sGPID ( )]1090.0179.024.111[610.0 +++ sss


46

0 10 20 30 40 50 60 700

0.5

1

1.5

syst

em o

utpu

t

0 10 20 30 40 50 60 700.5

1

1.5

2

time

cont

rol i

nput

SNCIMC-PID

The performance comparison of SNC with the IMC-PID controller


47

A direct adaptive model-based SNC control system• The presence of process uncertainties and nonlinearities

plant/model mismatch

In this situation, the associated SNC parameter tuning algorithm should be implemented to update the parameters.

direct adaptive SNC control system


48

Example 3: SNC control of a nonlinear process

A bioreactor

XXDX μ+−=&

( ) XY

SSDSSX

f μ1−−=&

( )XPDP βμγ ++−=&

im

mm

KSSK

SPP

2

1

++

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=μ

μ

μ is the specific growth rate


49

From open loop test, we have the process model

and the disturbance model

The feedforward controller

The control objective is to regulate the concentration of cell mass at its desired value by manipulating the dilution rate

( ) sP e

ssG −

+−

=14.2

576.20

( ) sd e

ssG −

+=

1325.51092.0

( )576.2056.109

1092.0262.0++

=s

ssGff


50

Based on the identified model and let

We have the initial controller parameter as

Learning rate:

The PI controller set as and

(Henson and Seborg, 1991 )

,1.0=α

hgLKc ⋅−= 07.0 hI 5.4=τ

1.0=η

[ ] [ ]TTba 111.01644.61474.0)0()0()0()0( −−== θp


51

0 50 100 150 200 250 300 350 400 4506

6.5

7

7.5

8

X

0 50 100 150 200 250 300 350 400 4500

0.05

0.1

0.15

0.2

0.25

time (hr)

D

SNCPI


Substrate concentration: +25% variation (150 hr)-25% variation (300 hr)

52

The parameter tuning progress


53

─ Model : ( ) ( )∑=

−+=+N

iim ikuhky

111

─ Predictive model : ( ) ( ) ( ) ( )[ ]kykykyky mm −++=+ 11ˆ

( ) ( ) ( ) ( )kuhkqkyky Δ++=+ 11ˆ

where ( ) ( )∑=

−+= ΔN

ii ikuhkq

21

Since

( ) ( ) ( )kekku eΔΔ += φpφpΔ and ( ) ( ) ( )kykrke −=

Model-based SNC predictive control system


Impulse response model

( ) ( ) [ ]{ }[ ])(exp1

)(exp1,θθ

−−+−−−

==ebebaeNLtu p

54

Then

( ) ( ) ( ) ( ) ( )[ 11

11ˆ 111

+++++

=+ Δ krhkhkqkrh

ky ee

φφ

pφp

( ) ( )]keh eφ11+−Objective function

( ) ( )[ ] ( ) ( )kkkykrwJ T pWp ΔΔ++−+= 22

1 211ˆ1

21

( ) 0=∂∂Δ k

Jp ( )

( ) ee

T

hhw

hhw

kφφ 1

11

1

221

211

11 +⎥⎥⎦

⎤

⎢⎢⎣

⎡+

+=

−

Δppp φ

Wφφ

p

( ) ( ) ( )⎥⎦

⎤⎢⎣

⎡+

+−−+

+kekq

hkrkr

h ee φφ 11 11)()1(

11


“One-step ahead MPC learning algorithm”

55

Model-based SNC predictive control of large time-delay processes


56

• Actual process( ) s

p es

sG 9

15.11 −

+−

=

• Process model

( ) ( ) stm

desGsG −=

and ( ) sd e

ssG 30

155.0 −

+=

( )12

25.1+

−=

ssG 10=dtwhere ,

[ ] [ ]TTba 08318.09618.0)0()0()0()0( −== θp

• CASE 1: Disturbance rejection d(s)=1/s

Simulation studies (large time delay + plant/model mismatch)

• CASE 2: Setpoint change

5.0=α,

[ ] [ ]TTba 18318.00332.2)0()0()0()0( −−== θp 5.0=α,

1−=dyto


1=dy

Sampling time = 0.5

57


Disturbance rejection

58


59


Setpoint tracking

60


61

Direct Nonlinear Control Using SNC

Consider the SNC control of integrating process of order n

)exp(1)]exp(1[)(

φφ

bbay n

−+−−

= θφ −−= yyd,

and let ( generator )

∑−

=

−− =+++=

1

1

)()1(1

''2

'1

n

i

ii

nn yyyy λλλλθ L

where

dyy

ba,θ

: setpoint

: process output

: controller parameters

: designed variable

φ


θ

62

• Case 1

When is largeφ

ay n ±=)(

⎩⎨⎧

<>

00

φφ

natn

y!

1±=

0)0( =y, if

φ


63

• Case 2

When is smallφ

φ2

)( aby n ≅ ( )θ−−= yyabd2

⎟⎠

⎞⎜⎝

⎛−−= ∑

−

=

1

1

)(

2

n

i

iid yyyab λ

φTaking Laplace transformation

121

)()(

11

1 ++++=

−− sss

absYsY

nn

nd λλ L

( )ns 11+

=ε n

ab2

=ε,


64

• Implementation

)exp(1)]exp(1[

φφ

bba

−+−−

ns1

θgenerator

dy φ

y

)(ny y

Nonlinear controller called NLC


SNC control of integrating process of order n

65

⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛−−−

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛−−−

=

∑

∑

=

=

2

0

)(

2

0

)(

'''

exp1

exp1

i

iid

i

iid

yyb

yybay

λ

λ

( )⎪⎪

⎩

⎪⎪

⎨

⎧

+=

+++=

±=

3

012

23

2

11

21

)()(

!31

ssssab

sYsY

aty

d ελλλ

''2

'1 yyyyd λλφ −−−=

Example: SNC control of integrating process of order 3

,

ab

23 =ε 22 3ελ = ελ 31 =

large & positive

,,


66

• SNC control of integrating process3

1s

Stepoint change has been made at t=1

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1a=10, b=1 ( ε = 0.5848)a=100, b=1 ( ε = 0.2714)a=1000, b=1 ( ε = 0.1260)


67

01

01)(asasabsbsbsG n

n

mm

p ++++++

=L

Lmn ≥,

• Implementation to general linear processes

01

011bsbsbasasa

s mm

nn

mn ++++++

− L

L

01

01

++++++

sasabsbsb

nn

mm

L

Ldy ye )( mny − u

( ) mnd ssY

sY−+

=11

)()(

ε

Controller


68

245035106)( 234 ++++

+=

ssssssG

Example: no modeling error

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time

a=10, b=1 ( ε = 0.5848)a=10, b=2 ( ε = 0.4642)


690 5 10 15

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Tim e

a= 10, b= 1 ( ε = 0.5848)a= 10, b= 1 ( ε = 0.5848)

Example: modeling error (plant/model mismatch)

0625.59935.511212)( 234 ++++

+=

ssssssGp

modeling error

no modeling error

245035106)( 234 ++++

+=

ssssssGActual process :

Process model :


70

• Application to Nonlinear Process Control

( ) ( )( )⎩

⎨⎧

=+=

xhyuxgxfx&

[ ]Trnrfff hLhLhLhT −−= ηηη LML 2112

System :

Let

1

32

21

),()()(

ξηξη

ξ

ξξ

ξξ

==

+=

=

=

yq

uxaxbr

&

&

M

&

&

⎪⎪⎩

⎪⎪⎨

⎧

=

=

=

+

−

irfi

rf

rfg

TLq

hLb

hLLa 1

rni −= ,,2,1 L

,

,

relative degree = r


71

Let ( )[ ]( )φ

φbbavuxaxb

−+−−

==+exp1exp1)()(

)(

)(),(

),(1 hhLL

xhLva

bvu rfg

rf−

−=

−=

ηξηξ

( )[ ]( )φ

φξbbay r

r −+−−

==exp1exp1)(&

( )rd ssYsY

11

)()(

+=

ε

( ) 111

++ rsε

Better than input-output linearization technique (A. Henson and E. Seborg, Nonlinear process control, 1997) by one order

i.e. ,

i.e. ,


72

Example: Nonlinear Bioreactor

( )

[ ]Xy

XDPP

Xy

SsDS

XDXX

sxf

=++−=

−−=

+−=

βγμ

μ

μ

&

&

&

1

im

mm

KSSK

SPP

2

01

++

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=μ

μ

System :

where


73

[ ]TPSXx = Du = sxyy =~, ,

ux

xsx

x

xy

x

xxx

f

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−

−+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+

−=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

1

1

1

3

2

1

][~1

βγμ

μ

μ

&

&

&

1xhy ==

( )( )( )φ

φbbav

−+−−

=exp1exp1

Soθφ −−= yyd

yyd −=

( since , )1=r 0=θ

1

1

xxv

hLhLv

ug

f

−−

=−

=μ

11

)()(

+=

ssYsY

d ε ab2

=ε,

,


74


0 1 2 3 4 5 6 7 8 9 104.5

5

5.5

6

6.5closed-loop response for setpoint change

time (hr)

x1 (b

iom

ass

conc

.)

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

time (hr)

dilu

tion

rate

the proposedIONIMC

75


0 10 20 30 40 50 60 70 805.9

5.95

6

6.05Closed-loop response for -20% Y disturbance

time (hr)

x1 (b

iom

ass

conc

.)

0 10 20 30 40 50 60 70 800.12

0.14

0.16

0.18

0.2

0.22

time (hr)

dilu

tion

rate

the proposedIONIMC

76

0 5 10 15 20 25 30 35 40 45 505.8

5.9

6

Closed-loop response in the presence of measurement noise

x1 (b

iom

ass

conc

.)

0 5 10 15 20 25 30 35 40 45 500.05

0.15

0.25

0.35

dilu

tion

rate

0 5 10 15 20 25 30 35 40 45 50

-0.01

0

0.01

time (hr)

nois

e si

gnal


77

ConclusionsWe have surveyed the recent direct adaptive control strategies developed based on using the SNCs.

Some alternative SNC-based control schemes as well as the associated convergence properties have been addressed for the purpose of dealing with diversified process dynamics.

New results on how to start up the SNC systematically have

been presented.

─ No input constraint: the SNC parameter values can be given by

simply assigning a performance index.

─ on the other hand, a SNC parameter settling formula is provided for the

case that there is a hard input constraint involved.


78

Extensive simulation results reveal that, with the systematic parameter setting formula, the pre-specified performance of the SNC control system can be ensured if the model is perfect.

Under the situation of plant/model mismatch, the SNC parameter

tuning algorithm can provide a more satisfactory control performance

as compared with conventional linear controllers.

Alternative model-based SNC control systems are also developed.

--- one-step ahead predictive SNC control

--- nonlinear SNC direct control


79

Based on its simple structure and effective algorithms, the proposed SNC-based control systems present to be a promising approaches to the direct adaptive control of chemical processes.


80

Thanks for your attention.


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