#### Read Microsoft PowerPoint - Lecture11_IMC.ppt text version

`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 14EE392m - Spring 2005 GorinevskyControl Engineering11-1Processes with Deadtime· Examples: transport deadtime in paper, mining, oil · Deadtime = transportation timeEE392m - Spring 2005 GorinevskyControl Engineering11-2Processes with Deadtime· Example: transport deadtime in food processingEE392m - Spring 2005 GorinevskyControl Engineering11-3Processes with Deadtime· Example: resource allocation in computingComputing TasksDifference EquationModeling Resource Queues ResourceDesired PerformanceFeedback ControlEE392m - Spring 2005 GorinevskyControl Engineering11-4Control of process with deadtime· PI control of a deadtime process ydPLANT: P = z-5-CPyP = e - sTD P=z-d; PI CONTROLLER: k P = 0.3, k I = 0.2continuous time discrete time1 0.8 0.6 0.4 0.2 0· Can we do better? PC ­ Make = z -d 1 + PC­ Deadbeat controller-d0510 15 20 DEADBEAT CONTROL25301 0.8 0.6 0.4 0.2 0 0 5 10 15 20 25 30z PC = 1 - z -dEE392m - Spring 2005 Gorinevsky1 C= 1 - z -du ( t ) = u ( t - d ) + e( t )11-5Control Engineering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 desiredP( 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 yd· 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 11-6Causal Transfer FunctionB ( 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 31 -1 N -N 0 M -N 1 M - N -1 B(z) N -N A( z )EE392m - Spring 2005 GorinevskyControl Engineering11-7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 -11 - bz -1 1- C( z) =  g (1 - b) 1 - z -1 - (1 -  ) z -d· Dahlin's controllerEE392m - Spring 2005 Gorinevsky· Single tuning parameter:  - tuned controller a.k.a.  - tuned controllerControl Engineering11-8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.CLOSED-LOOP STEP RESPONSE WITH DAHLIN CONTROLLER· Industrial tuning guidelines: Closed loop time constant = 1.5-2.5 deadtime.1 0.8 0.6 0.4 0.2 0 0 10 20 30 40 Ta=2.5TD Ta=1.5TD Open-loop 50 60CONTROL STEP RESPONSE 1.5 1 0.5 00102030405060EE392m - Spring 2005 GorinevskyControl Engineering11-9Internal Model Control - IMCGeneral controller design approach; some use in process industryeP P0e = r - ( y - P0u ) u = Qe· continuous time s · discrete time zEE392m - Spring 2005 GorinevskyQ C= 1 - QP0Reference model: T = QP0 Filter QControl EngineeringInternal model: P011-10IMC and Youla parametrizationreference yd disturbance dQ C= 1 - QP0 Q=CP-y output e error u control dy yd  y d u· SensitivitiesS = 1 - QP0 T = QP0 Su = QC · 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 wellEE392m - Spring 2005 Gorinevsky Control Engineering 11-11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:Loopshaping-1S = 1 - QP0S &lt;&lt; 1  Q  (P0 )· in band· Recall system inversionEE392m - Spring 2005 GorinevskyInversion11-12Control EngineeringQ-loopshaping· LoopshapingS = 1 - QP0 T = QP0Q = P0 = F (P0 ) ,-1S &lt;&lt; 1  Q  (P0 )-1· in band · out of bandT &lt;&lt; 1  QP0 &lt;&lt; 1· For a minimum phase plantT = QP0 = FF=1(1 + s )nS = 1 - QP0 = 1 - F· F is called IMC filter, F T, reference model for the output · Lambda-tuned IMCEE392m - Spring 2005 Gorinevsky Control Engineering 11-13IMC extensions· Multivariable processes · Nonlinear process IMC · Multivariable predictive control - Lecture 14EE392m - Spring 2005 GorinevskyControl Engineering11-14Nonlinear process IMC· Can be used for nonlinear processes­ linear Q ­ nonlinear model N ­ linearized model LeEE392m - Spring 2005 GorinevskyControl Engineering11-15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 equipmentEE392m - Spring 2005 GorinevskyControl Engineering11-16Dynamic inversion in flight control&amp; v = F ( x , v ) + G ( x , v )u &amp; u = G -1 ( v des - F )· Honeywell MACH · Dale Enns X-38 - Space Station Lifeboat Reference model: 1 &amp; v = v des s LCV  v =  MCV     NCV   EE392m - Spring 2005 GorinevskyControl Engineering11-17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 2005 GorinevskyControl Engineering11-18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 practiceEE392m - Spring 2005 Gorinevsky Control Engineering 11-19`

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