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Lecture 11  Processes with Deadtime, Internal Model Control
· · · · · · Processes with deadtime Modelreference control Deadtime compensation: Dahlin controller IMC Youla parametrization of all stabilizing controllers Nonlinear IMC
Receding Horizon  MPC  Lecture 14
EE392m  Spring 2005 Gorinevsky
Control Engineering
111
Processes with Deadtime
· Examples: transport deadtime in paper, mining, oil · Deadtime = transportation time
EE392m  Spring 2005 Gorinevsky
Control Engineering
112
Processes with Deadtime
· Example: transport deadtime in food processing
EE392m  Spring 2005 Gorinevsky
Control Engineering
113
Processes with Deadtime
· Example: resource allocation in computing
Computing Tasks
Difference Equation
Modeling Resource Queues Resource
Desired Performance
Feedback Control
EE392m  Spring 2005 Gorinevsky
Control Engineering
114
Control of process with deadtime
· PI control of a deadtime process yd
PLANT: P = z
5

C
P
y
P = e  sTD P=z
d
; PI CONTROLLER: k P = 0.3, k I = 0.2
continuous time discrete time
1 0.8 0.6 0.4 0.2 0
· Can we do better? PC Make = z d 1 + PC
Deadbeat controller
d
0
5
10 15 20 DEADBEAT CONTROL
25
30
1 0.8 0.6 0.4 0.2 0 0 5 10 15 20 25 30
z PC = 1  z d
EE392m  Spring 2005 Gorinevsky
1 C= 1  z d
u ( t ) = u ( t  d ) + e( t )
115
Control Engineering
Modelreference Control
· Deadbeat control has bad robustness, especially w.r.t. deadtime · More general modelreference control approach
make the closedloop transfer function as desired
P( z )C ( z ) = Q( z) 1 + P( z )C ( z ) 1 Q( z) C( z) = P( z ) 1  Q ( z )
Q (z ) is the reference model for the closed loop C P y y
d
· Works if Q(z) includes a deadtime, at least as large as in P(z). Then C(z) comes out causal.
EE392m  Spring 2005 Gorinevsky Control Engineering 116
Causal Transfer Function
B ( z ) b0 z M + b1 z M 1 + ... + bN C (z) = = N A( z ) z + a1 z N 1 + ... + a N b0 z M  N + b1 z M  N 1 + ... + bN z  N = 1 + a1 z 1 + ... + a N z  N
· Causal implementation requires that N M
(1 + a44+24444 )u (t ) = (b 44444 24+ ...4444 )e(t ) z ... + a z z +bz +b z 14 4 3 1 4 4 3
1 1 N N 0 M N 1 M  N 1 B(z) N N A( z )
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Control Engineering
117
Dahlin's Controller
· Eric Dahlin worked for IBM in San Jose (?) then for Measurex in Cupertino. 1 Q( z) C( z) = · Dahlin's controller, 1967 P( z ) 1  Q ( z ) g (1  b) d · plant, generic first order response P( z ) = z 1 1  bz with deadtime 1  d Q( z) = z · reference model: 1st order+deadtime 1  z 1
1  bz 1 1 C( z) = g (1  b) 1  z 1  (1  ) z d
· Dahlin's controller
EE392m  Spring 2005 Gorinevsky
· Single tuning parameter:  tuned controller a.k.a.  tuned controller
Control Engineering
118
Dahlin's Controller
· Dahlin's controller is broadly used through paper industry in supervisory control loops  HoneywellMeasurex, 60%. · Direct use of the identified model parameters.
CLOSEDLOOP STEP RESPONSE WITH DAHLIN CONTROLLER
· Industrial tuning guidelines: Closed loop time constant = 1.52.5 deadtime.
1 0.8 0.6 0.4 0.2 0 0 10 20 30 40 Ta=2.5TD Ta=1.5TD Openloop 50 60
CONTROL STEP RESPONSE 1.5 1 0.5 0
0
10
20
30
40
50
60
EE392m  Spring 2005 Gorinevsky
Control Engineering
119
Internal Model Control  IMC
General controller design approach; some use in process industry
e
P P0
e = r  ( y  P0u ) u = Qe
· continuous time s · discrete time z
EE392m  Spring 2005 Gorinevsky
Q C= 1  QP0
Reference model: T = QP0 Filter Q
Control Engineering
Internal model: P0
1110
IMC and Youla parametrization
reference yd disturbance d
Q C= 1  QP0 Q=
C
P

y output e error u control dy yd y d u
· Sensitivities
S = 1  QP0 T = QP0 Su = Q
C · If Q is stable, then S, T, and the loop are stable 1 + CP0 · If the loop is stable, then Q is stable
· Choosing various stable Q parameterizes all stabilizing controllers. This is called Youla parameterization · Youla parameterization is valid for unstable systems as well
EE392m  Spring 2005 Gorinevsky Control Engineering 1111
Qloopshaping
· Systematic controller design: select Q to achieve the controller design tradeoffs · The approach used in modern advanced control design: H2/H, LMI, H loopshaping · Qbased loopshaping:
Loopshaping
1
S = 1  QP0
S << 1 Q (P0 )
· in band
· Recall system inversion
EE392m  Spring 2005 Gorinevsky
Inversion
1112
Control Engineering
Qloopshaping
· Loopshaping
S = 1  QP0 T = QP0
Q = P0 = F (P0 ) ,
1
S << 1 Q (P0 )
1
· in band · out of band
T << 1 QP0 << 1
· For a minimum phase plant
T = QP0 = F
F=
1
(1 + s )n
S = 1  QP0 = 1  F
· F is called IMC filter, F T, reference model for the output · Lambdatuned IMC
EE392m  Spring 2005 Gorinevsky Control Engineering 1113
IMC extensions
· Multivariable processes · Nonlinear process IMC · Multivariable predictive control  Lecture 14
EE392m  Spring 2005 Gorinevsky
Control Engineering
1114
Nonlinear process IMC
· Can be used for nonlinear processes
linear Q nonlinear model N linearized model L
e
EE392m  Spring 2005 Gorinevsky
Control Engineering
1115
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 · addon equipment
EE392m  Spring 2005 Gorinevsky
Control Engineering
1116
Dynamic inversion in flight control
& v = F ( x , v ) + G ( x , v )u & u = G 1 ( v des  F )
· Honeywell MACH · Dale Enns X38  Space Station Lifeboat Reference model: 1 & v = v des s
LCV v = MCV NCV
EE392m  Spring 2005 Gorinevsky
Control Engineering
1117
Dynamic inversion in flight control
· · · · NASA JSC study for X38 Actuator allocation to get desired forces/moments Reference model (filter): vehicle handling and pilot `feel' Formal robust design/analysis (µanalysis etc)
EE392m  Spring 2005 Gorinevsky
Control Engineering
1118
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 highperformance 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
EE392m  Spring 2005 Gorinevsky Control Engineering 1119
Information
Microsoft PowerPoint  Lecture11_IMC.ppt
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