Dr. Xavier KESTELYN L2EP, Arts et Métiers ParisTech Lille, Prof. Pierre SICARD GRÉI, Université du Québec à Trois-Rivières

Transcription

1 EMR 13 Lille Sept Summer School EMR 13 Energetic Macroscopic Representation «INVERSION BASED CONTROL» Dr. Xavier KESTELYN L2EP, Arts et Métiers ParisTech Lille, Prof. Pierre SICARD GRÉI, Université du Québec à Trois-Rivières

2 - Outline Principle of model-based control Open-loop and closed-loop controls Inversion-based control of complex systems 2. Inversion of EMR elements Inversion 1: single-input time-independent relationship Inversion 2: multiple-input time-independent relationship Inversion 3: single-input causal relationship 3. Inversion-based control structures Inversion-based methodology Maximum and practical control schemes 4. Conclusion: towards energy management

3 EMR 13 Lille Sept Summer School EMR 13 Energetic Macroscopic Representation 1. «Principle of model-based control»

4 - Open loop and closed-loop controls - 4 Controlling a system for output tracking can be interpreted as inverting the system u(t) input Σ(.) y(t) output System u ref (t) input reference Σ -1 (.) y ref (t) desired output Control if we can implement a good approximation of the system s inverse

5 - Open loop and closed-loop controls - Let s take a simple example (a car in translation): 5 F(t) m v(t) F(t) Σ (.) : 1 f + ms v(t) System f F ref (t) Σ -1 (.) v ref (t) Control ~ ~ Σ 1 t (.) : Fref ( t) f vref ( ) ~ Fref ( s) ~ Σ 1 (.) : = f m ~ s vref ( s) + Approximation ~ Σ ~ 1 (.) : Fref ( t) = f vref ( t) + m ~ aref No derivative in real-time Trajectory planning Direct inversion or Open-loop control or FeedForward control is not always the best solution!

6 - Open loop and closed-loop controls - Closed-loop control is then required when: - the model is not directly invertible - the model is ill known or too complex 6 F(t) input Σ(.) v(t) output System F ref (t) input reference Controller v ref (t) desired output Control Closed-loop controllers can be used to: -Improve reference tracking performances, stabilize unstable processes -Reject disturbances -Cope with model uncertainties, reduce sensitivity to parameter variations

7 Let s take a simple example (a car in translation): F(t) m v(t) - Open loop and closed-loop controls - F(t) Σ(.) v(t) 7 Σ (.) : f v( s) F( s) = f 1 + ms F ref (t) Controller v ref (t) For example, and depending on expected performances: PI controller C + 1 ( s) = K p 1 τ i s Closed-loop control offers many advantages!

8 - Open loop and closed-loop controls - Open loop and closed-loop controls can be conjointly used to take advantages of both strategies: - FF for good dynamics with respect to intrinsic systems properties - FB for the rest 8 F(t) input Σ(.) v(t) output System F FBref (t) Controller v ref (t) Control F FFref (t) ~ Σ -1 (.) input references desired output

9 Let s take a simple example (a car in translation): v(t) F(t) m F(t) f F FBref (t) K - Open loop and closed-loop controls - p 1 v(t) f + ms τ i s v ref (t) 9 F FFref (t) ~ f Solutions to control simple systems can be easily obtained thanks to existing model-based methods (FB and FF)

10 Parallel HEV BAT «Inversion Based Control» - Open loop and closed-loop controls - VSI Fuel EM ICE Trans. 10 fast subsystem controls EM control ICE control Trans control Is there a way to find a slow system supervision control structure for a Energy management (supervision/strategy) complex system??? driver request

11 Parallel HEV BAT «Inversion Based Control» - Open loop and closed-loop controls - VSI1 Fuel EM1 ICE EMR Trans. 11 fast subsystem controls EM1 control ICE control Trans control Inversion-based control slow system supervision Energy management (supervision/strategy) driver request

12 - Inversion-based control of complex systems - 12 cause effect input SS 1 SS 2 SS n output measure? measure? measure? right cause C 1 C 2 C n desired effect EMR = system decomposition in basic energetic subsystems (SSs) Inversion-based control: systematic inversion of each subsystems using open-loop or/and closed-loop controls divide and conquer

13 - Inversion-based control of complex systems - 13 cause SS 1 SS 2 SS n effect right cause C 1 C 2 C n desired effect The control scheme is developed as a mirror of the model [Hautier 96] [Bouscayrol 03]

14 EMR 13 Lille Sept Summer School EMR 13 Energetic Macroscopic Representation 2. «Inversion of EMR elements»

15 - Basic inversion of EMR elements - 15 in(t) System out(t) measurements? Control in ref (t) Algorithm? out ref (t) There are 3 basic inversion categories: 1. Single-input time independent relationships (incl. conversion elements) 2. Multiple-input time independent relationships (incl. coupled conversion elements) 3. Single-input causal relationships (accumulation elements) Other inversion schemes can be deduced from these basic inversions. [Barre 06]

16 - Inversion 1: single-input time-independent relationship - Output depends on a single input without delay 16 Example: u(t) u (t) K? 1/K y(t) y ref (t) 1. no measurement 2. no controller (open-loop control) y ( t) = K u( t) direct inversion 1 u( t) = yref ( t) K Example: Resistance vt) v(t) 1/R Assumption: K well-know and constant R i(t) i ref (t) 1 i ( t) = v( t) R direct inversion v( t) = R i ( t) ref

17 - Inversion 1: single-input time-independent relationship - Inversion of a conversion element 17 Objective: to control y 2 Ex : pulley or roller u 1 y 1 y 2 u 2 y 2 = f(u 1 ) V trans = r pull Ω 1 T trans = r pull F load Ω 1_ref = v trans_ref / r pull u 1-reg y 2-ref Manipulate u 1 Ω1_ref 1 r pull V trans_ref

18 - Inversion 2: multiple-input time-independent relationship - Output depends on several inputs without delay 18 Example: u 1 (t) + + u 2 (t) y(t) y ( t) = u1( t) + u2( t) u 1 is chosen to act on the output y u 2 becomes a disturbance input u 1 (t) -? + y ref (t) direct inversion u1( t) = yref ( t) u2meas ( t) 1. measurement of the disturbance input 2. no controller (open-loop control) Assumption: u 2 can be measured

19 - Inversion 2: multiple-input time-independent relationship - Inversion of a conversion element 19 Objective: to control y 2 Ex : H-bridge chopper u 1 y 2 y 2 = f(u 1, u 21 ) u Hb = m Hb V DC i Hb = m Hb i dcm y 1 u 21 u 2 m Hb = u Hb_ref / V DC_meas u 1-meas y 2-ref V DC_meas m Hb Manipulate u 21 u 1 is a disturbance Basic rule: as a first step, compensate all disturbances assuming measurement is available. u Hb_ref

20 - Inversion 2: multiple-input time-independent relationship - Inversion of a conversion element 20 Objective: to control y 2 Ex : speed transmission u 1 y 2 y 2 = f(u 1, u 21 ) Ω trans = k trans Ω 1 T trans = k trans T load y 1 u 21 u 2 Ω 1_ref = Ω trans_ref / k trans_meas u 1-reg y 2-ref k trans_meas Manipulate u 1 u 21 is a disturbance Ω 1_ref Ω trans_ref

21 u 11 y 11 - Inversion 2: multiple-input time-independent relationship - Inversion of a neutral coupling elements u 21 y 21 Example: Park s transformation θ d/s 21 u 13 i s1 u 23 v sd i sd v sq u 1m y 1m u 2m y 2m i s2 i sq θ d/s u 11 y 21-ref u 13-ref v sd-ref u 1m y 2m-ref u 23-ref v sq-ref no measurement no controller / direct inversion use of the inverse matrix

22 u 1 y 1 - Inversion 2: multiple-input time-independent relationship - Inversion of upstream coupling elements y 21 u 21 y 2p u 2p Implement a compromise or prioritize outputs. V DC i coup Example: current node 22 v 1 =V DC i 1 v 2 =V DC i 2 y 21-ref u 1 k W1 k Wp u1... y 2p-ref ' ' = kw 1y21 ref + + kwp y2 p ref no measurement no controller p weighting variables V DC k W v 1ref [ k v + ( 1 k v ] VDC = W 1 ref W ) 2ref 0 k W 1 v 2ref

23 - Inversion 2: multiple-input time-independent relationship - Inversion of downstream coupling elements 23 u 11 y 11 u 1m y 1m y 2 u 2 There are extra degrees of freedom!!! an opportunity for energy management, efficiency optimization, load sharing Inversion principle Distribute the reference signal Examples: - Equal torque criteria; - Equal power criteria; - Field weakening strategy.

24 u 11 y 11 «Inversion Based Control» - Inversion 2: multiple-input time-independent relationship - Inversion of downstream coupling elements Example: chassis of a train F bog1 24 y 2 F bog2 v train F tot u 1m y 1m u 2 F bog3 v train v train v train u 11 no measurement no controller m distribution variables F bog4 F bog1 F bog2 v train u 1m k D1 k Dm y 2-ref u u1 11 m = = k k ' D1... ' Dm y 2ref y 2ref F bog3 F bog4 k D1 k D2 k D3 F tot-ref

25 - Inversion 3: single-input causal relationship - 25 Output depends on a single input and time (delay) causality principle Example: y( t) = u( t)dt u(t) u (t) dt? C(t) y(t) - + y ref (t) 1. measurement of output 2. a controller is required (closed-loop control) direct inversion not possible in real-time d u( t) = yref ( t) dt indirect inversion [ y ( t) y ( )] u( t) = C( t) t ref closed loop controller meas

26 - Inversion 3: single-input causal relationship - 26 Output depends on a single input and time (delay) causality principle u 1 di dt i L = u 1 u2 u 2 u 1 i i u 2 u 2meas U 1 (s) + - U 2 (s) U(s) 1 Ls I(s) u 1ref i ref i meas U 1 (s) + + U ref (s) C(s) - + I ref (s)

27 - Example: PM-DC machine - 27 i L m r m multi-input causal relationship u u i e L m di dt = u e r m i decomposition u = u e U(s) + - E(s) U(s) K 1+τp I(s) L m di dt = u r m i U (s) + + U ref (s) C(s) - + I ref (s) direct inversion closed-loop controller

28 - Example: PM-DC machine - 28 i L m r m u u i e L m di dt = u e r m i U(s) + - E(s) U(s) K 1+τp I(s) u i 1 e meas i e U (s) + + U ref (s) C(s) - + I ref (s) u i ref i meas

29 Legend - Inversion of EMR elements - conversion element direct inversion + disturbance rejection 29 Control = light blue parallelogram with dark blue contour direct inversion accumulation element controller + disturbance rejection indirect inversion sensor mandatory link optional link coupling element distribution criteria

30 EMR 13 Lille Sept Summer School EMR 13 Energetic Macroscopic Representation 3. «Inversion-based control structures»

31 - Paper processing system as an example - 31 Paper processing using 2 induction machines IM1 IM2 IM1 IM2 [Djani 06] Technical requirements: - paper tension control for high quality of paper roll - winding velocity control for high quality of processing

32 - Maximum control structure - 32 dc bus VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 dc bus V dc u vsi1 i im1 T im1 Ω im1 v roll1 T band T roll2 Ω im2 e im2 i im2 i vsi2 ES ES i vsi1 i im1 svsi1 e im1 Ω im1 T roll1 T band v roll2 Ω im2 T im2 i im2 u vsi2 s vsi2 V dc Step 1: Develop the EMR of the system Step 2a: Identify all control variables (outputs) and control inputs Step 2b: Identify tuning paths from inputs to outputs, avoiding crossing the paths

33 - Maximum control structure - 33 dc bus VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 dc bus V dc u vsi1 i im1 T im1 Ω im1 v roll1 T band T roll2 Ω im2 e im2 i im2 i vsi2 ES ES i vsi1 i im1 svsi1 e im1 Ω im1 Φ im1-ref T roll1 T band v roll2 Ω im2 T im2 i im2 u vsi2 s vsi2 V dc PWM FOC u vsi1-ref i im1-ref T im1-ref Ω im1-ref v roll1-ref T band-ref FOC: Field Oriented Control PWM: Pulse Width Modulation Φ im2-ref FOC PWM v roll2-ref Ω im2-ref T im2-ref i im2-ref u vsi2-ref Step 3: invert each element of the control paths by applying inversion rules assume that all the signals are measurable; compensate for all disturbances.

34 - Maximum control structure - 34 dc bus VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 dc bus V dc u vsi1 i im1 T im1 Ω im1 v roll1 T band T roll2 Ω im2 e im2 i im2 i vsi2 ES ES i vsi1 i im1 svsi1 e im1 Ω im1 Φ im1-ref T roll1 T band v roll2 Ω im2 T im2 i im2 u vsi2 s vsi2 V dc PWM FOC u vsi1-ref i im1-ref T im1-ref Ω im1-ref v roll1-ref T band-ref Φ im2-ref FOC PWM v roll2-ref Ω im2-ref T im2-ref i im2-ref u vsi2-ref Maximum control structure: one elementary feedback controller per accumulator simple tuning is possible by time coordination/separation of the control loops

35 - Practical control structures - 35 dc bus VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 dc bus V dc u vsi1 i im1 T im1 Ω im1 v roll1 T band T roll2 Ω im2 e im2 i im2 i vsi2 ES ES i vsi1 i im1 svsi1 e im1 Ω im1 Φ im1-ref T roll1 T band v roll2 Ω im2 T im2 i im2 u vsi2 s vsi2 V dc PWM FOC u vsi1-ref i im1-ref T im1-ref Ω im1-ref v roll1-ref T band-ref Φ im2-ref FOC PWM v roll2-ref Ω im2-ref T im2-ref i im2-ref u vsi2-ref Step 4: Simplify the MCS: group operations, do not reject disturbances explicitly. Impact will be on cost, on processing time and on performance

36 - Practical control structures - 36 dc bus VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 dc bus V dc u vsi1 i im1 T im1 Ω im1 v roll1 T band T roll2 Ω im2 e im2 i im2 i vsi2 ES ES i vsi1 i im1 svsi1 e im1 Ω im1 Φ im1-ref T roll1 T band v roll2 Ω im2 T im2 i im2 u vsi2 s vsi2 V dc PWM FOC u vsi1-ref i im1-ref T im1-ref Ω im1-ref v roll1-ref T band-ref T roll2_est Ω im2 Φ im2-ref FOC PWM T roll2_est Ω im2_est Ω im2_est T im2_est i im2 v roll2-ref Ω im2-ref T im2-ref i im2-ref u vsi2-ref Step 5: Estimate non-measured variables, e.g. disturbances that cannot be neglected, and estimate unknown or time varying parameters

37 - Practical control structures - 37 dc bus VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 dc bus V dc u vsi1 i im1 T im1 Ω im1 v roll1 T band T roll2 Ω im2 e im2 i im2 i vsi2 ES ES i vsi1 i im1 svsi1 e im1 Ω im1 Φ im1-ref T roll1 T band v roll2 Ω im2 T im2 i im2 u vsi2 s vsi2 V dc PWM FOC u vsi1-ref i im1-ref T im1-ref Ω im1-ref v roll1-ref T band-ref T roll2_est Φ im2-ref FOC PWM v roll2-ref Ω im2-ref T im2-ref i im2-ref u vsi2-ref Step 6: choose and tune all controllers (dynamic decoupling), and estimators PI controllers OK except

38 - Practical control structures - 38 dc bus VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 dc bus V dc u vsi1 i im1 T im1 Ω im1 v roll1 T band T roll2 Ω im2 e im2 i im2 i vsi2 ES ES i vsi1 i im1 svsi1 e im1 Ω im1 Φ im1-ref T roll1 T band v roll2 Ω im2 T im2 i im2 u vsi2 s vsi2 V dc PWM FOC u vsi1-ref i im1-ref T im1-ref Ω im1-ref v roll1-ref T band-ref T roll2_est Φ im1-ref Φ im2-ref strategy Φ im2-ref v roll2-ref Ω im2-ref FOC T im2-ref i im2-ref PWM u vsi2-ref 3b: Exploit degrees of freedom to implement advanced strategies

39 EMR 13 Lille Sept Summer School EMR 13 Energetic Macroscopic Representation «Conclusion» Inversion based control = inversion of EMR based on the cognitive systemic and the causality principle (energy) Inversion rules for control scheme closed-loop control to invert accumulation elements, direct inversion for conversion elements, degrees of freedom to invert coupling elements Different steps in defining the control scheme From Maximum Control Scheme. to Practical Control Scheme. to the strategy level

40 EMR 13 Lille Sept Summer School EMR 13 Energetic Macroscopic Representation «BIOGRAPHIES AND REFERENCES»

41 - Authors - 41 Dr. Xavier KESTELYN Arts et Métiers ParisTech, L2EP, France Associate Professor HdR in Electrical Engineering PhD in Electrical Engineering at University of Lille1 (2003) Research topics: Control of multi-input electromechanical systems, EMR Prof. Pierre SICARD Université du Québec à Trois-Rivières, GRÉI, Canada Professor in electrical engineering PhD in Electrical Engineering at Rensselaer Polytechnic Institute, USA (1993) Research topics: EMR, nonlinear control, AI, tractions systems, EVs and HEVs

42 - References - [Barre 2006] P. J. Barre, A. Bouscayrol, P. Delarue, E. Dumetz, F. Giraud, J. P. Hautier, X. Kestelyn, B. Lemaire-S , E. S , "Inversion-based control of electromechanical systems using causal graphical descriptions", IEEE-IECON'06, Paris, November [Bouscayrol 2003] A. Bouscayrol, B. Davat, B. de Fornel, B. François, J. P. Hautier, F. Meibody-Tabar, E. Monmasson, M. Pietrzak-David, H. Razik, E. S , M. F. Benkhoris, "Control Structures for Multi-machine Multi-converter Systems with upstream coupling", Mathematics and Computers in Simulation, vol. 63, no. 3-5, pp , November 2003, (common paper of GE 44, GREEN, L2EP, LEEI and LESiR, according to the MMS project), [Bouscayrol 2006] A. Bouscayrol, M. Pietrzak-David, P. Delarue, R. Peña-Eguiluz, P. E. Vidal, X. Kestelyn, Weighted control of traction drives with parallel-connected AC machines, IEEE Transactions on Industrial Electronics, December 2006, vol. 53, no. 6, p (common paper of L2EP Lille and LEEI Toulouse). [Delarue 2003] P. Delarue, A. Bouscayrol, A. Tounzi, X. Guillaud, G. Lancigu, Modelling, control and simulation of an overall wind energy conversion system, Renewable Energy, July 2003, vol. 28, no. 8, p (common paper L2EP Lille and Jeumont SA). [Djani 2006] Y. Djani Wankam, P. Sicard, A. Bouscayrol, "Maximum control structure of a five-drive paper system using Energetic Macroscopic Representation", IEEE-IECON'06, Paris, November 2006, (common paper of GREI Université du Québec à Trois-Rivières and L2EP Lille). [Hautier 1996] J. P. Hautier, J. Faucher, Le graphe informationnel causal, (Text in French), Bulletin de l'union des Physiciens, vol. 90, juin 1996, pp