Upload
dinhdieu
View
217
Download
1
Embed Size (px)
Citation preview
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Multi-loop PI based control strategies on the
Activated Sludge Process
Dr. Ramon Vilanova
Dept. Telecomunications and Systems EngineeringUniversitat Autonoma de Barcelona
(with Prof. Reza Katebi from ICC, University of Strathclyde, Glasgow, Soctland)
March 31, 2009
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
1 The Activated Sludge ProcessActivated Sludge ProcessNon-linear four state modelLinearized model
2 Multivariable PI control approachesMultivariable PI/PID methods
Application to the ASP
3 Decentralized PI control approachControl of TITO ProcessesApplication to the ASP
4 MIMO Decoupling control plus Decentralized PIThe control configurationApplication to the ASP
5 Decentralised PI control with Feedforward decoupling actionFeedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Activated Sludge ProcessNon-linear four state modelLinearized model
1 The Activated Sludge ProcessActivated Sludge ProcessNon-linear four state modelLinearized model
2 Multivariable PI control approachesMultivariable PI/PID methods
Application to the ASP
3 Decentralized PI control approachControl of TITO ProcessesApplication to the ASP
4 MIMO Decoupling control plus Decentralized PIThe control configurationApplication to the ASP
5 Decentralised PI control with Feedforward decoupling actionFeedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Activated Sludge ProcessNon-linear four state modelLinearized model
Activated Sludge Process
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Activated Sludge ProcessNon-linear four state modelLinearized model
Activated Sludge Process Non-linear four state model
dX
dt= µ(t)X − D(1 + r)X − rDXr
dS
dt= −
µ(t)
YX − D(1 + r)S + DSin
dDO
dt= −
Koµ(t)
YX − D(1 + r)DO + KLa(DOs − DO) + DOinDO
dXr
dt= D(1 + r)X − D(β + r)Xr
µ(t) = µmax
S
kS + S
DO
kDO + DO
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Activated Sludge ProcessNon-linear four state modelLinearized model
Biomass X (0)=215 mg/lSubstrate S(0)=55 mg/lDissolved Oxygen DO(0)=6 mg/lRecycled Biomass Xr (0) = 400 mg/l
Table: Initial Contitions
β = 0.2 Kc=2 mg/lr = 0.6 Ks=100 mg/lα = 0.018 KDO=0.5Y = 0.65 DOs = 0.5 mg/lµmax = 0.15 h−1
Table: Kinetic parameters
G (s) =
(
G11(s) G12(s)G21(s) G22(s)
)
⇒
(
S(t)DO(t)
)
= G (s)
(
D(t)W (t)
)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Activated Sludge ProcessNon-linear four state modelLinearized model
The Gij(s) transfer function components are given as:
Linear Model Transfer functions
G11(s) =n11(s)
d(s)=
134.0243s3 + 295.3529s2 + 53.5176s + .5855
s4 + 2.4617s3 + 0.9859s2 + 0.1107s + 0.0008
G12 =n12(s)
d(s)=
−0.0312s2 − 0.0062s − 0.0001
s4 + 2.4617s3 + 0.9859s2 + 0.1107s + 0.0008
G21 =n21(s)
d(s)=
−9.2834s3 − 15.0312s2 − 2.6325s − 0.0123
s4 + 2.4617s3 + 0.9859s2 + 0.1107s + 0.0008
G22 =n22(s)
d(s)=
0.0699s3 + 0.0340s2 + 0.0042s + 2.9e−5
s4 + 2.4617s3 + 0.9859s2 + 0.1107s + 0.0008
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Activated Sludge ProcessNon-linear four state modelLinearized model
Output responses for a 2.5% input change
0 500 1000 1500 200041
41.5
42
42.5
43 Linear System (dashed) Non−Linear (solid)
Time (h)
Sub
stra
te
0 500 1000 1500 20000.0825
0.083
0.0835
0.084
0.0845
0.085
0.0855 Linear System (dashed) Non−Linear (solid)
Time (h)
Dilu
tion
rate
0 500 1000 1500 20006.06
6.08
6.1
6.12
6.14
6.16
6.18
6.2 Linear System (dashed) Non−Linear (solid)
Time (h)
Dis
solv
ed O
xiyg
en
0 500 1000 1500 200090
90.5
91
91.5
92
92.5 Linear System (dashed) Non−Linear (solid)
Time (h)
Aer
atio
n ra
te
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Multivariable PI/PID methodsApplication to the ASP
1 The Activated Sludge ProcessActivated Sludge ProcessNon-linear four state modelLinearized model
2 Multivariable PI control approachesMultivariable PI/PID methods
Application to the ASP
3 Decentralized PI control approachControl of TITO ProcessesApplication to the ASP
4 MIMO Decoupling control plus Decentralized PIThe control configurationApplication to the ASP
5 Decentralised PI control with Feedforward decoupling actionFeedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Multivariable PI/PID methodsApplication to the ASP
Multivariable Control of a TITO process
G11(s)r1 u1
y1
G22(s)u2 y2r2
G12(s)
G21(s)
K(s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Multivariable PI/PID methodsApplication to the ASP
Four design methods for multivariable PI/PID tuning are compared
Davidson Method
Penttinen -Koivo Method
Maciejowski Method
Combined Method
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Multivariable PI/PID methodsApplication to the ASP
Davidson Method
The objective of this method reduces to finding steady state gain matrixof the plant for a step input. The expression for this controller is:
u(s) =1
sKie(s) Ki = ǫG (0)−1
The multiplier ǫ can be tuned and adjusted simultaneously so the closedloop plant has a maximum speed of response for a step input.
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Multivariable PI/PID methodsApplication to the ASP
Penttinen -Koivo Method
In this method, the plant is diagonalised at very high frequencies. Theexpression for the controller is slightly altered from previous method toform:
u(s) = (Kp +1
sKi )e(s)
where
Kp = (CB)−1ρ Ki = ǫG (0)−1
Matrices C and B are taken from the corresponding state-spacerealisation of G (s):
G (s) :
{
x = Ax + Bu
y = Cx + Du
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Multivariable PI/PID methodsApplication to the ASP
Maciejowski method
The technique proposed is to diagonalise the system near bandwith, ωb.In keeping with the earlier proportional - integral controller design, thiscontributes three terms that of proportional, integral and derivative:
K (s) = Kp + Ki
1
s+ Kd s
where
Kp = ρG (jωb)−1 Ki = ǫG (jωb)
−1 Kd = δG (jωb)−1
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Multivariable PI/PID methodsApplication to the ASP
Combined method
This method has been proposed in [Wahab & Katebi UKCC, 2006] andproposes the extension of the three studied controller methods tocombine all together to form:
Kp = ρG (jωb)−1 Ki = ǫG (0)−1 Kd = δ(CB)−1
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Multivariable PI/PID methodsApplication to the ASP
Comparison of Multivariable PID approaches applied to the ASP
0 20 40 60 80 10040
45
50
55 Substrate
Time (h)
0 20 40 60 80 1000.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
0.16 Dilution rate
Time (h)
0 20 40 60 80 1003.5
4
4.5
5
5.5
6
6.5 DO
Time (h)
0 20 40 60 80 10040
50
60
70
80
90
100
110 Aeration rate
Combined
Davidson
Maciejowski
Penttinen−Koivo
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Control of TITO ProcessesApplication to the ASP
1 The Activated Sludge ProcessActivated Sludge ProcessNon-linear four state modelLinearized model
2 Multivariable PI control approachesMultivariable PI/PID methods
Application to the ASP
3 Decentralized PI control approachControl of TITO ProcessesApplication to the ASP
4 MIMO Decoupling control plus Decentralized PIThe control configurationApplication to the ASP
5 Decentralised PI control with Feedforward decoupling actionFeedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Control of TITO ProcessesApplication to the ASP
Decentraliced control block diagram for a TITO System
G11(s)K1(s)r1
u1y1
G22(s)K2(s)u2 y2r2
G12(s)
G21(s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Control of TITO ProcessesApplication to the ASP
The transfer functions seen by each local controller:
G1(s) = G11(s)
(
1 −G12(s)G21(s)
G11(s)G22(s)T2(s)
)
= G11(s) (1 − I (s)T2(s))
G2(s) = G22(s)
(
1 −G12(s)G21(s)
G11(s)G22(s)T1(s)
)
= G22(s) (1 − I (s)T1(s))
where
I (s) =G12(s)G21(s)
G11(s)G22(s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Control of TITO ProcessesApplication to the ASP
T1(s) =K1(s)G11(s)
1 + K1(s)G11(s)≈ T d
1 (s)
T2(s) =K2(s)G22(s)
1 + K2(s)G22(s)≈ T d
2 (s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Control of TITO ProcessesApplication to the ASP
The desired input-output transfers will obey to (Tc1 = 2, Tc2 = 0.5):
T d1 (s) =
1
Tc1s + 1T d
2 (s) =1
Tc2s + 1
FO approximation of the effective transfer functions
0 5 10 15 20 25 300
100
200
300
400
500
600
Step response of G11
(s)
Time (h)0 1 2 3 4 5
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Step response of G22
(s)
Time (h)
0 5 10 15 20 25 300
100
200
300
400
500
600
Step resp. of G1(s) (dash−dot) FO (solid) G
11(s) (dasehd)
Time (h)0 1 2 3 4 5
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Step resp. of G2(s) (dsah−dot) FO (solid) G
22(s) (dasehd)
Time (h)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Control of TITO ProcessesApplication to the ASP
The desired input-output transfers will obey to:
T d1 (s) =
1
Tc1s + 1T d
2 (s) =1
Tc2s + 1
with Tc1 = 2 and Tc2 = 0.5. The resulting G1(s) and G2(s) first orderapproximations:
Gapp1 (s) =
500
(4s + 1)G
app2 (s) =
0.0355
(0.5s + 1)
TITO Decentraliced design
Local controllers will be designed on the basis of Gapp1 (s) and G
app2 (s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Control of TITO ProcessesApplication to the ASP
u(s) = Cr (s)r(s) − Cy (s)y(s)
where
Cr (s) = Kc
[
β +1
Ti s
]
Cy (s) = Kc
[
1 +1
Ti s+ Td s
]
2-DOF PI Control System
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Control of TITO ProcessesApplication to the ASP
Applied 2-DoF PI Tuning
κc = KcKp =2 − τc
τc
(1)
τi =Ti
T= τc(2 − τc) (2)
β =1
2 − τc
0 < τc ≤ 1
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Control of TITO ProcessesApplication to the ASP
Time responses for step changes on substrate and DO for two tunings ofthe Substrate controller: τc1=0.9 & τc1=0.5, whereas the DO controlleris set to τc2=1.8
0 50 100 15040
42
44
46
48
50
52
54 Substrate:
Time (h)
0 50 100 1500.08
0.09
0.1
0.11
0.12
0.13 Dilution rate
Time (h)
0 50 100 1503.5
4
4.5
5
5.5
6
6.5
Time (h)
DO
0 50 100 15040
50
60
70
80
90
100
110 Aeration rate
Time (h)
τc1=0.9 & τ
c2=1.8
τc1=0.5 & τ
c2=1.8
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Control of TITO ProcessesApplication to the ASP
Regulation performance for a periodical discharge on Sin of about 10%during one hour every 24h. Tunings are τc1=0.9 & τc1=0.5, whereas theDO controller is set to τc2=1.8
0 50 100 15040
40.5
41
41.5
42
42.5
43
43.5
44 Substrate:
Time (h)
0 50 100 150
0.075
0.08
0.085
0.09 Dilution rate
Time (h)
0 50 100 1506
6.05
6.1
6.15
6.2
Time (h)
DO
0 50 100 15089
89.5
90
90.5
91
91.5
92
92.5
93 Aeration rate
Time (h)
τc1=0.9 & τ
c2=1.8
τc1=0.5 & τ
c2=1.8
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
The control configurationApplication to the ASP
1 The Activated Sludge ProcessActivated Sludge ProcessNon-linear four state modelLinearized model
2 Multivariable PI control approachesMultivariable PI/PID methods
Application to the ASP
3 Decentralized PI control approachControl of TITO ProcessesApplication to the ASP
4 MIMO Decoupling control plus Decentralized PIThe control configurationApplication to the ASP
5 Decentralised PI control with Feedforward decoupling actionFeedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
The control configurationApplication to the ASP
Combination of a MIMO PI controller plus single-loop controllers
G11(s)r1 u1
y1
G22(s)u2 y2
r2
G12(s)
G21(s)
K(s)
K1(s)
K2(s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
The control configurationApplication to the ASP
Process outputs for the MIMO PID controlled process as well as theirapproximations as First-Order Systems (10% step ref. change
0 5 10 15 20 25 30 35 40 45 500
1
2
3
4
5 Step response on S: FO (dashed) Process output (solid)
Time (h)
0 5 10 15 20 25 30 35 40 45 500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 Step response on DO: FO (dashed) Process output (solid)
Time (h)
First-Order Systems approximation for outer PI design
G1(s) =1
(4s + 1)G2(s) =
1
(4s + 1)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
The control configurationApplication to the ASP
Process outputs for the MIMO PID plus outer PI controllers
0 50 100 15040
42
44
46
48
50
52
54 Substrate
0 50 100 1500.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12 Dilution rate
0 50 100 1504
4.5
5
5.5
6
6.5 DO
0 50 100 15020
40
60
80
100
120 Aeration rate
MIMO+Decentraliced PI
MIMO
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
The control configurationApplication to the ASP
Process outputs for the MIMO+PID controlled process for a variable Sin
0 50 100 15040
40.5
41
41.5
42
42.5
43
43.5 Substrate
0 50 100 1500.07
0.072
0.074
0.076
0.078
0.08
0.082
0.084
Dilution rate
0 50 100 1506
6.05
6.1
6.15
6.2
6.25 DO
0 50 100 15087
88
89
90
91
92
93 Aeration rate
MIMO+Decentraliced PI
MIMO
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Feedforward controlFeedforward control with Decoupling purposesApplication to the ASP
1 The Activated Sludge ProcessActivated Sludge ProcessNon-linear four state modelLinearized model
2 Multivariable PI control approachesMultivariable PI/PID methods
Application to the ASP
3 Decentralized PI control approachControl of TITO ProcessesApplication to the ASP
4 MIMO Decoupling control plus Decentralized PIThe control configurationApplication to the ASP
5 Decentralised PI control with Feedforward decoupling actionFeedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Feedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Classical Feedback + Feedforwardcontrol
P (s)K(s)r(s) u(s) y(s)
d(s)
Pd(s)−Kff (s)
uff (s)
Internal Model Control Feedback +Feedforward control
P (s)K(s)r(s) u(s) y(s)
d(s)
Pd(s)−Kff (s)
P (s)
Pd(s)
uff (s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Feedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Proposed Feedforward Control Architecture
P (s)K(s)r(s) u(s) y(s)
d(s)
Pd(s)−Kff (s)
N(s)
Pd(s)
D(s)
uff (s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Feedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Incorporation of Feedforward corrective actions on a decentralized TITOcontrol scheme.
G11(s)K1(s)
u1 y1
G22(s)K2(s)u2 y2
r2
G12(s)
G21(s)
Qff21
(s)Tff21
(s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Feedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Reference signal based feedforward corrective actions on a decentralizedTITO control scheme.
G11(s)K1(s)
u1 y1
G22(s)K2(s)u2 y2
r2
G12(s)
G21(s)Q
ff21
(s)Tff21
(s)
r1
Q1(s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Feedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Where does the Q1(s) block comes from?
IMC - Feeback controller interpretation
Ki (s) =Qi (s)
1 − Gi (s)Qi (s)
Qi (s) =Ki (s)
1 + Gi (s)Ki (s)
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Feedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Expression for the FF controllers
Qff21 =
n22(s)
n21(s)
1
(λff21s + 1)
λff21 has to be in accordance with the expected control signal
bandwidth.
λff21 is chosen five times smaller than the corresponding fastest time
constant of Q1(s) (The IMC parameter for K1(s)).
Expression for the FF controllers
λff21 = 0.4 λff
12 = 0.2
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Feedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Comparison of the reference-driven and control signal-driven feedforwardactions.
60 65 70 75 8051.2
51.4
51.6
51.8
52
52.2
52.4
Substrate:
Time (h)
60 65 70 75 800.08
0.085
0.09
0.095
0.1
Dilution rate
Time (h)
0 5 10 15 20 25 305.8
5.85
5.9
5.95
6
6.05
6.1
6.15
DO
Time (h)
0 5 10 15 20 25 3085
90
95
100
105 Aeration rate
Time (h)
Decentraliced PI
Decentraliced PI + Feedforward
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process
OutlineThe Activated Sludge Process
Multivariable PI control approachesDecentralized PI control approach
MIMO Decoupling control plus Decentralized PIDecentralised PI control with Feedforward decoupling action
Feedforward controlFeedforward control with Decoupling purposesApplication to the ASP
Multi-loop PI based control strategies on the
Activated Sludge Process
Dr. Ramon Vilanova
Dept. Telecomunications and Systems EngineeringUniversitat Autonoma de Barcelona
(with Prof. Reza Katebi from ICC, University of Strathclyde, Glasgow, Soctland)
March 31, 2009
Dr. Ramon Vilanova Multi-loop PI based control strategies on the Activated Sludge Process