Selvoptimaliserende hierarkiske systemer Prosessregulering, nasjonaløkonomi, hjerne og maratonløping - PDF

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Selvoptimaliserende hierarkiske systemer Prosessregulering, nasjonaløkonomi, hjerne og maratonløping Sigurd Skogestad Institutt for kjemisk prosessteknologi NTNU Trondheim 1 DNVA, 19 Jan Oversikt

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Selvoptimaliserende hierarkiske systemer Prosessregulering, nasjonaløkonomi, hjerne og maratonløping Sigurd Skogestad Institutt for kjemisk prosessteknologi NTNU Trondheim 1 DNVA, 19 Jan. 2017 Oversikt 1. Mitt utgangspunkt 2. Styring av virkelige systemer 3. Sentralisert beslutningssystem 4. Hvordan fungerer virkelige styringssystemer? 5. Hvordan designe et hierarkisk system på en systematisk måte? 6. Hva skal vi regulere? 1. Aktive begrensninger 2. Selvoptimaliserende variable 7. Eksempler: Biologi, prosessregulering, økonomi, maraton 3 Fokus: Ikke optimal beslutning Men: Hvordan implementere beslutning på en enkel måte i en usikker verden Mitt utgangspunkt: Hvordan skal man regulere et helt prosessanlegg? Mer generelt: Hvordan designer man komplekse beslutningssystemer? 4 Why control (regulering)? Operation Actual value(dynamic) Steady-state (average) time 5 In practice never steady-state: Feed changes Startup Operator changes Disturbances (d s) Failures.. - Control is needed to reduce the effect of disturbances - 30% of investment costs are typically for instrumentation and control Main objectives control system 1. Stabilization 2. Implementation of acceptable (near-optimal) operation ARE THESE OBJECTIVES CONFLICTING? Usually NOT Different time scales 6 7 Alle virkelige beslutningssystemer: Hierarkisk pyramide Practice: Engineering systems Most (all?) large-scale engineering systems are controlled using hierarchies of quite simple controllers Large-scale chemical plant (refinery) Commercial aircraft 1000 s of loops Simple elements Same in biological systems Why are real decision systems hierchical and decentralized? How should such systems be designed? 8 Hierarchical decomposition Example: Bicycle riding Note: design starts from the bottom Stabilizing (regulatory) control: First need to learn to stabilize the bicycle CV = y 2 = tilt of bike MV = body position Economic (supervisory) control: Then need to follow the road. CV = y 1 = distance from right hand side MV=y 2s Usually constant setpoint, e.g. y 1s =0.5 m Optimization: Which road should we follow? 9 MV = manipulated variable CV = controlled variable Process control: Hierarchical structure (pyramid) Our Paradigm setpoints 10 setpoints u = valves 1. Tidsskalaseparasjon 2. Selvoptimaliserende variable 3. Lokal feedback Self-optimizing Control Self-optimizing control is when acceptable operation can be achieved using constant set points (c s ) for the controlled variables c (without re-optimizing when disturbances occur). c=c s 11 Håndtere usikkerhet: Lokal feedback y 1 Setpoints (distance from curb) y 2 Setpoints (bike tilt) u = body position 12 Prosess Measurements y 13 In theory: Optimal control and operation In theory: Optimal control and operation Objectives Present state Model of system CENTRALIZED OPTIMIZER Approach: Model of overall system Estimate present state Optimize all degrees of freedom Process control: Excellent candidate for centralized control Problems: Model not available Objectives =? Optimization complex Not robust (difficult to handle uncertainty) Slow response time 14 (Physical) Degrees of freedom In theory: Optimal control and operation Objectives Present state Model of system CENTRALIZED OPTIMIZER Approach: Model of overall system Estimate present state Optimize all degrees of freedom Process control: Excellent candidate for centralized control Problems: Model not available Objectives =? Optimization complex Not robust (difficult to handle uncertainty) Slow response time 15 (Physical) Degrees of freedom Academic process control community fish pond Optimal centralized Solution (EMPC) Sigurd 16 Menneskets beslutningssystem Tenke Bevissthet Neurale nettverk i hjernen Intuisjon Instinkt Kjemisk signal (hormoner) Ryggmarg Reflekser Organer Elektrisk signal (nerver) 17 Celler Eksempler: Temperatur-regulering Puls-regulering Puste-regulering To hovedprinsipper for oppdeling av beslutningssystemer (pyramide) 1. Tidsskala-separasjon (vertikal oppdeling) Hierarkisk (Master-slave) Setpunkt sendes nedover Rapport om problemer sendes oppover Intet tap dersom: tidsskalaene er separert og man har selvoptimaliserende regulering mellom oppdateringer Romlig separasjon (horisontal) Desentralisert Intet tap dersom oppgaver kan utføres uavhengig av andre på samme nivå Systematic approach: Control structure design I Top Down Step 1: Define optimal operation Cost function J (to be minimized) Operational constraints Step 2: Identify degrees of freedom and optimize for expected disturbances Identify Active constraints Step 3: Select primary controlled variables y 1 Active constraints + Self-optimizing variables Step 4: Locate throughput manipulator (process control only) II Bottom Up (dynamics, y 2 ) Step 5: Regulatory / stabilizing control (PID layer) What more to control (y 2 )? Pairing of inputs and outputs Step 6: Supervisory control Step 7: Real-time optimization (Do we need it?) y 1 y 2 Process 19 S. Skogestad, ``Control structure design for complete chemical plants'', Computers and Chemical Engineering, 28 (1-2), (2004). Step 1. Define optimal operation (economics) What are we going to use our degrees of freedom u for? Define cost function J and constraints J = cost feed + cost energy value products 20 Step S2. Optimize (a) Identify degrees of freedom (b) Optimize for expected disturbances Need good model, Optimization is time consuming! But it is offline Main goal: Identify ACTIVE CONSTRAINTS A good engineer can often guess the active constraints 21 Step S3: Implementation of optimal operation Have found the optimal way of operation. How should it be implemented? What to control? 1. Active constraints 2. Self-optimizing variables (for unconstrained degrees of freedom) 22 Optimal operation - Runner Optimal operation of runner Cost to be minimized, J=T One degree of freedom. Input u (MV)=power What should we control? 23 MV = manipulated variable Optimal operation - Runner 1. Optimal operation of Sprinter 100m. J=T Active constraint control: Maximum speed ( no thinking required ) CV = power (at max) 24 CV = controlled variable Optimal operation - Runner 2. Optimal operation of Marathon runner 40 km. J=T What should we control? Unconstrained optimum J=T u opt u=power 25 Optimal operation - Runner Self-optimizing control: Marathon (40 km) Any self-optimizing variable (to control at constant setpoint)? c 1 = distance to leader of race c 2 = speed c 3 = heart rate c 4 = level of lactate in muscles 26 Optimal operation - Runner Conclusion Marathon runner J=T c opt c=heart rate select one measurement CV 1 = heart rate 27 CV = heart rate is good self-optimizing variable Simple and robust implementation Disturbances are indirectly handled by keeping a constant heart rate May have infrequent adjustment of setpoint (c s ) In practice: What variable c=hy should we control? (for self-optimizing control) 1. The optimal value of c should be insensitive to disturbances Small HF = dc opt /dd 2. c should be easy to measure and control 3. The value of c should be sensitive to the inputs ( maximum gain rule ) Large G = HG y = dc/du Equivalent: Want flat optimum Good Good BAD 28 Note: Must also find optimal setpoint for c=cv 1 Example: Cake Baking Objective: Nice tasting cake with good texture Measurements y 1 = oven temperature y 2 = cake temperature y 3 = cake color Disturbances d 1 = oven specifications d 2 = oven door opening d 3 = ambient temperature d 4 = initial temperature 29 u 1 = Heat input u 2 = Final time Degrees of Freedom Unconstrained degrees of freedom Further examples self-optimizing control Central bank. J = welfare. u = interest rate. c=inflation rate (2.5%) Cake baking. J = nice taste, u = heat input. c = Temperature (200C) Business, J = profit. c = Key performance indicator (KPI), e.g. Response time to order Energy consumption pr. kg or unit Number of employees Research spending Optimal values obtained by benchmarking Investment (portofolio management). J = profit. c = Fraction of investment in shares (50%) Biological systems: Self-optimizing controlled variables c have been found by natural selection Need to do reverse engineering : Find the controlled variables used in nature From this possibly identify what overall objective J the biological system has been attempting to optimize 30 Define optimal operation (J) and look for magic variable (c) which when kept constant gives acceptable loss (selfoptimizing control) Summary Step 3. What should we control (CV 1 )? Selection of primary controlled variables c = CV 1 1. Control active constraints! 2. Unconstrained variables: Control self-optimizing variables! Old idea (Morari et al., 1980): We want to find a function c of the process variables which when held constant, leads automatically to the optimal adjustments of the manipulated variables, and with it, the optimal operating conditions. 31 Unconstrained degrees of freedom The ideal self-optimizing variable is the gradient, J u c = J/ u = J u Keep gradient at zero for all disturbances (c = J u =0) Problem: Usually no measurement of gradient cost J J u 0 u opt J u 0 J u =0 u J u 0 32 Ideal: c = J u In practise, use available measurements: c = H y. Task: Determine H! H 33 With measurement noise Exact local method =0 in nullspace method (no noise) Minimize in Maximum gain rule ( maximize S 1 G J uu -1/2, G=HG y ) Scaling S 1 - No measurement error: HF=0 (nullspace method) - With measuremeng error: Minimize GF c - Maximum gain rule 34 Example. Nullspace Method for Marathon runner u = power, d = slope [degrees] y 1 = hr [beat/min], y 2 = v [m/s] F = dy opt /dd = [ ] H = [h 1 h 2 ]] HF = 0 - h 1 f 1 + h 2 f 2 = 0.25 h h 2 = 0 Choose h 1 = 1 - h 2 = 0.25/0.2 = 1.25 Conclusion: c = hr v Control c = constant - hr increases when v decreases (OK uphill!) 35 Example: CO2 refrigeration cycle J = W s (work supplied) DOF = u (valve opening, z) Main disturbances: d 1 = T H d 2 = T Cs (setpoint) d 3 = UA loss p H What should we control? 36 CO2 refrigeration cycle Step 1. One (remaining) degree of freedom (u=z) Step 2. Objective function. J = W s (compressor work) Step 3. Optimize operation for disturbances (d 1 =T C, d 2 =T H, d 3 =UA) Optimum always unconstrained Step 4. Implementation of optimal operation No good single measurements (all give large losses): p h, T h, z, Nullspace method: Need to combine n u +n d =1+3=4 measurements to have zero disturbance loss Simpler: Try combining two measurements. Exact local method: c = h 1 p h + h 2 T h = p h + k T h ; k = bar/k Nonlinear evaluation of loss: OK! 37 38 CO2 cycle: Maximum gain rule CV=Measurement combination Refrigeration cycle: Proposed control structure 39 CV1= Room temperature CV2= temperature-corrected high CO2 pressure Oversikt 1. Mitt utgangspunkt 2. Styring av virkelige systemer 3. Sentralisert beslutningssystem 4. Hvordan fungerer virkelige styringssystemer? 5. Hvordan designe et hierarkisk system på en systematisk måte? 6. Hva skal vi regulere? 1. Aktive begrensninger 2. Selvoptimaliserende variable 7. Eksempler: Biologi, prosessregulering, økonomi, maraton Konklusjon: Vær systematisk og tenk på helheten når du skal bygge opp et styringssystem Enkle løsninger vinner alltid i det lange løp 40 References The following paper summarizes the design procedure: S. Skogestad, ``Control structure design for complete chemical plants'', Computers and Chemical Engineering, 28 (1-2), (2004). The following paper updates the procedure: More: S. Skogestad, ``Economic plantwide control, Book chapter in V. Kariwala and V.P. Rangaiah (Eds), Plant-Wide Control: Recent Developments and Applications, Wiley (2012). S. Skogestad Plantwide control: the search for the self-optimizing control structure, J. Proc. Control, 10, (2000). S. Skogestad, ``Near-optimal operation by self-optimizing control: From process control to marathon running and business systems'', Computers and Chemical Engineering, 29 (1), (2004). Mathematical details: V. Alstad, S. Skogestad and E.S. Hori, ``Optimal measurement combinations as controlled variables'', Journal of Process Control, 19, (2009) More information on my home page (Skogestad): 41
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