EE392m - Spring 2005Gorinevsky
Control Engineering 11-1
Lecture 11 - Processes with Deadtime, Internal Model Control
• Processes with deadtime • Model-reference control • Deadtime compensation: Dahlin controller• IMC• Youla parametrization of all stabilizing controllers• Nonlinear IMC
– Receding Horizon - MPC - Lecture 14
EE392m - Spring 2005Gorinevsky
Control Engineering 11-2
Processes with Deadtime• Examples: transport deadtime in paper, mining, oil• Deadtime = transportation time
EE392m - Spring 2005Gorinevsky
Control Engineering 11-3
Processes with Deadtime
• Example: transport deadtime in food processing
EE392m - Spring 2005Gorinevsky
Control Engineering 11-4
Processes with Deadtime
• Example: resource allocation in computing
ComputingTasks
Resource
ResourceQueues
Modeling
DifferenceEquation
Feedback Control
DesiredPerformance
EE392m - Spring 2005Gorinevsky
Control Engineering 11-5
Control of process with deadtime
• PI control of a deadtime process
0 5 10 15 20 25 300
0.2
0.4
0.6
0.8
1
PLANT: P = z -5 ; PI CONTROLLER: kP = 0.3, k I= 0.2
• Can we do better? – Make
– Deadbeat controller
d
sT
zPeP D
−
−
== continuous time
discrete time
dzPC
PC −=+1
d
d
zzPC −
−
−=
1 dzC −−
=1
1 0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
DEADBEAT CONTROL
)()()( tedtutu +−=
C P- yyd
EE392m - Spring 2005Gorinevsky
Control Engineering 11-6
Model-reference Control
• Deadbeat control has bad robustness, especially w.r.t. deadtime
• More general model-reference control approach – make the closed-loop transfer function as desired
)()()(1
)()( zQzCzP
zCzP =+
)(1)(
)(1)(
zQzQ
zPzC
−⋅=
• Works if Q(z) includes a deadtime, at least as large as in P(z). Then C(z) comes out causal.
)(zQ is the reference modelfor the closed loop
C P- yyd
EE392m - Spring 2005Gorinevsky
Control Engineering 11-7
Causal Transfer Function
• Causal implementation requires that N ≥ M
( ) ( ) )(...)(...1)(
110
)(
11 tezbzbzbtuzaza
zB
NN
NMNM
zA
NN 444444 3444444 214444 34444 21
−−−−−− +++=+++
NN
NN
NMNMN
NNN
MM
zazazbzbzb
azazbzbzb
zAzBzC
−−
−−−−
−
−
++++++=
++++++==
...1...
......
)()()(
11
110
11
110
EE392m - Spring 2005Gorinevsky
Control Engineering 11-8
Dahlin’s Controller
• Eric Dahlin worked for IBM in San Jose (?) then for Measurexin Cupertino.
• Dahlin’s controller, 1967
d
d
zz
zQ
zbz
bgzP
−−
−−
−−=
−−=
1
1
11)(
1)1()(
αα
dzzbgbzzC −−
−
−−−−⋅
−−=
)1(11
)1(1)( 1
1
ααα
• plant, generic first order response with deadtime • reference model: 1st order+deadtime
• Dahlin’s controller
• Single tuning parameter: α - tuned controller a.k.a. λ - tuned controller
)(1)(
)(1)(
zQzQ
zPzC
−⋅=
EE392m - Spring 2005Gorinevsky
Control Engineering 11-9
Dahlin’s Controller• Dahlin’s controller is broadly used through paper industry
in supervisory control loops - Honeywell-Measurex, 60%. • Direct use of the identified model parameters.
0 10 20 30 40 50 600
0.2
0.4
0.6
0.8
1
CLOSED-LOOP STEP RESPONSE WITH DAHLIN CONTROLLER
Ta=2.5TDTa=1.5TDOpen-loop
0 10 20 30 40 50 600
0.5
1
1.5
CONTROL STEP RESPONSE
• Industrial tuning guidelines: Closed loop time constant = 1.5-2.5 deadtime.
EE392m - Spring 2005Gorinevsky
Control Engineering 11-10
Internal Model Control - IMC
• continuous time s• discrete time z
P
P0
e
QeuuPyre
=−−= )( 0
01 QPQC
−=
General controller design approach; some use in process industry
0QPT =Reference model:
Filter Q Internal model: 0P
EE392m - Spring 2005Gorinevsky
Control Engineering 11-11
IMC and Youla parametrization
QSQPT
QPS
u ==
−=
0
01• Sensitivities
udyy
yd
d
→→
→
• If Q is stable, then S, T, and the loop are stable• If the loop is stable, then Q is stable01 CP
CQ+
=
01 QPQC
−=
• Choosing various stable Q parameterizes all stabilizing controllers. This is called Youla parameterization
• Youla parameterization is valid for unstable systems as well
C P-
eyyd
uddisturbance
reference output
controlerror
EE392m - Spring 2005Gorinevsky
Control Engineering 11-12
Q-loopshaping
• Systematic controller design: select Q to achieve the controller design tradeoffs
• The approach used in modern advanced control design: H2/H∞, LMI, H∞ loopshaping
• Q-based loopshaping:
• Recall system inversion
01 QPS −= ( ) 101 −≈⇒<< PQS • in band
Inversion
Loopshaping
EE392m - Spring 2005Gorinevsky
Control Engineering 11-13
Q-loopshaping
• Loopshaping
• For a minimum phase plant 0
01QPT
QPS=
−= ( )11
1
0
10
<<⇒<<≈⇒<< −
QPTPQS
( )nsF
λ+=
11
• in band• out of band
• F is called IMC filter, F≈ T, reference model for the output
• Lambda-tuned IMC
( ) ,10
†0
−== PFPQ
FQPS −=−= 11 0
FQPT == 0
EE392m - Spring 2005Gorinevsky
Control Engineering 11-14
IMC extensions
• Multivariable processes• Nonlinear process IMC• Multivariable predictive control - Lecture 14
EE392m - Spring 2005Gorinevsky
Control Engineering 11-15
Nonlinear process IMC
• Can be used for nonlinear processes– linear Q– nonlinear model N– linearized model L
e
EE392m - Spring 2005Gorinevsky
Control Engineering 11-16
Industrial applications of IMC
• Multivariable processes with complex dynamics • Demonstrated and implemented in process control by
academics and research groups in very large corporations. • Not used commonly in process control (except Dahlin
controller) – detailed analytical models are difficult to obtain– field support and maintenance
• process changes, need to change the model• actuators/sensors off• add-on equipment
EE392m - Spring 2005Gorinevsky
Control Engineering 11-17
Dynamic inversion in flight control
)(),(),(
1 FvGuuvxGvxFv
des −=+=
− &
&
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
NCVMCVLCV
v
X-38 - Space Station Lifeboat
• Honeywell MACH• Dale Enns
Reference model: desv
sv &
1=
EE392m - Spring 2005Gorinevsky
Control Engineering 11-18
Dynamic inversion in flight control• NASA JSC study for X-38• Actuator allocation to get desired forces/moments• Reference model (filter): vehicle handling and pilot ‘feel’• Formal robust design/analysis (µ-analysis etc)
EE392m - Spring 2005Gorinevsky
Control Engineering 11-19
Summary• Dahlin controller is used in practice
– easy to understand and apply• IMC is not really used much
– maintenance and support issues– is used in form of MPC – Lecture 14
• Youla parameterization is used as a basis of modern advanced control design methods. – Industrial use is very limited.
• Dynamic inversion is used for high-performance control of air and space vehicles– this was presented for breadth, the basic concept is simple– need to know more of advanced control theory to apply in practice
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