DEDUCED FROM EMR» Prof. B. Lemaire-S , Prof. A. Bouscayrol (Université Lille1, L2EP, France)

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1 Polytech Paris Sud June 2014 «INVERSION-BASED CONTROL DEDUCED FROM EMR» Prof. B. Lemaire-S , Prof. A. Bouscayrol (Université Lille1, L2EP, France) based on the course of Master Electrical Engineering for Sustainable Development Université Lille1

2 Parallel HEV «Inversion-Based Control from EMR» - Objective: example of HEV control - BAT VSI Fuel EM ICE Trans. 2 fast subsystem controls EM control ICE control Trans control slow system supervision Energy management (supervision/strategy) driver request

3 Parallel HEV «Inversion-Based Control from EMR» - Objective: example of HEV control - BAT VSI1 Fuel EM1 ICE EMR Trans. 3 fast subsystem controls How to define control scheme of complex ICE systems? Trans control control (Structure? sensors?) EM1 control slow system supervision Energy management (supervision/strategy) driver request

4 - Outline - 1. Principle of model-based control Open-loop and closed-loop controls Inversion-based control methodology 2. Inversion of EMR elements Inversion of accumulation elements Inversion of conversion elements 3. Inversion-based control structures Maximum control schemes Practical control schemes 4. Example of a paper processing system 4

5 Polytech Paris Sud June «Principle of model-based control» Prof. P. Sicard (Université du Québec à Trois-Rivières, Canada) Prof. A. Bouscayrol (Université Lille1, L2EP, France)

6 - Cybernetic systemic approach - or Black box approach: no internal knowledge 6 in out identification test: observation of out(t) from selected in(t) Behavior model: out(t) = f(t) in(t) control out ref closed-loop control of out(t): for uncertainty compensations Limitations: limited validity range of the model risk of physical mistake non-optimal management of internal energy multi-physical complex energetic systems?

7 - Cognitive systemic approach - or White box approach: prior internal knowledge 7 Physical laws of system components Knowledge model: out(t) = f(t) in(t) in out in out control out ref control = inversion of model: (closed loop = an inversion way) Limitations: physical knowledge of each subsystem functions are not all reversible multi-physical complex energetic systems?

8 - Causality principle and control - 8 Principle of causality physical causality is integral input output CONTROL = real-time process management x? cause t effect xdt OK in real-time area knowledge of past evolution t 1 impossible in real-time slope knowledge of future evolution dx dt

9 - Open-loop control and inversion - 9 Controlling a system for output tracking can be interpreted as inverting the system control y ref (t) wished output System -1 (.) u(t) input System y(t) output if we can implement a good approximation of the system s inverse. [Sicard 09]

10 - Principle of closed-loop control - 10 control A closed-loop control is required when: the model is not invertible, the model is ill known or too complex, and for robustness purpose. y ref (t) wished output controller u(t) input System y(t) output [Sicard 09] Controller objectives: tracking of reference changes rejection of disturbances and uncertainties

11 - Principle of Inversion-based methodology - 11 cause input System effect output [Hautier 96] measurements? right cause Control desired effect control = inversion of the causal path 1. Which algorithm? (how many controllers) 2. Which variables to measure? 3. How to tune controllers? 4. How to implement the control? Inversion-based methodology automatic control industrial electronics

12 - EMR and Inversion-based methodology - 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) Remember, divide and conquer! Inversion-based control: systematic inversion of each subsystems using open-loop or closed-loop control

13 - Mirror effect - 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 - Mirror effect: example of cascaded control loops - 14 Well-known cascaded control loops can be described in the same may y ref (t) C 2 C 1 u(t) SS 1 SS 2 y(t) u(t) SS 1 SS 2 y(t) Submodels C 1 C 2 y ref (t) Functional inverses

15 Polytech Paris Sud June «Inversion of EMR elements»

16 - Inversion of I/O relationships - 16 in(t) System out(t) measurements? Control in(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]

17 - Inversion 1: single-input time-independant relationship - output depends on a single input without delay 17 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-known and constant R i(t) i ref (t) 1 i( t) v( t) R direct inversion v( t) R i ( t) ref

18 - Inversion 2: multiple-input time-independant relationship - Output depends on several inputs without delay 18 Example: u 1 (t) + + u 2 (t) y(t) y ( 2 t) u1( t) u ( 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 well-known and can be measured

19 - Inversion 3: single-input causal relationship - output depends on a single input and time (delay) causality principle 19 Example: y( t) u( t)dt u(t) dt y(t) - direct inversion indirect inversion + C(t)? not possible u(t) y ref (t) in real-time d u( t) yref ( t) dt 1. measurement of output u( t) C( t) yref ( t) ymeas ( t) 2. a controller is required (closed-loop control) closed loop controller

20 - Example: PM-DC machine - 20 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+ s I(s) L m di dt u r m i U(s) + + U ref (s) C(s) - + I ref (s) direct inversion closed-loop

21 - Inversion of a conversion element (1) - 21 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 u21 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: at first, compensate all disturbances assuming measurement is available. u Hb_ref

22 - Inversion of a conversion element (2) - 22 Objective: to control y 2 Ex : speed gearbox u 1 y 2 y 2 = f(u 1, u 21 ) gear = k gear 1 T gear = k gear T load y 1 u 21 u 2 1_ref = gear_ref / k gear_meas u 1-reg y 2-ref k gear_meas 2. Manipulate u 1 u 21 is a disturbance 1_ref gear_ref

23 - Inversion of a conversion element (3) - 23 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 1 T trans = r tpull F load 1_ref = trans_ref / r tpull u 1-reg y 2-ref 3. Manipulate u 1 1_ref 1 r tpull V trans_ref

24 - Inversion of an accumulation element - 24 Objective: to control y 2 u 1 y 2 =f(u 1, u 2 ) y 2 Ex : rotating shaft y 1 u 2 f is in integral form d J dt f T T em load u 1-reg u 2-meas y 2-ref Manipulate u 1 y 2-meas Direct inversion is in derivative form Approximate inversion by closed loop control u 2 is a disturbance Basic rule: compensate disturbances or linearize dynamics, then design a controller to obtain the desired dynamics. T em_ref T C( t)( em ref ref meas) _ T load _ meas + T load_meas + C(t) meas - + ref

25 - Example: PM-DC machine - 25 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+ s I(s) u i e meas i e U(s) + + U ref (s) C(s) - + I ref (s) u i ref i meas

26 u 11 y 11 u 1m y 1m u 11 u 1m k D1 k D(m-1) y 2 u 2 - Inversion of coupling elements - y 2-ref next lecture! no measurement no controller (m - 1) distribution variables u11 kd1 y2ref... u1( m 1) kd( m 1) y2 u 1m (1 kdi ) y ref 2ref F bog2 F bog3 F bog4 v train v train v train v train Example: chassis of a train F bog1 F bog1 F bog2 F bog3 F bog4 k D1 k D3 k D2 F tot v train F tot-ref 26

27 Legend - Inversion of EMR elements - conversion element direct inversion + disturbance rejection 27 Control = light blue Parallelograms with dark blue contour direct inversion accumulation element controller + disturbance rejection indirect inversion sensor mandatory link facultative link coupling element distribution criteria

28 Polytech Paris Sud June «Inversion-based methodology for control structures»

29 1. EMR of the system - Maximum control scheme - 29 S1 x 1 x 2 x 3 x 4 x 5 x 6 x 7 y 1 y 2 y 3 y 4 y 5 y 6 y 7 z 23 z 67 S2 EMR depends on: - the study objective (limits between system and sources) - the physical laws of subsystems (physical causality) - the association of subsystems (systemic approach)

30 1. EMR of the system - Maximum control scheme Tuning path S1 x 1 x 2 x 3 x 4 x 5 x 6 x 7 y 1 y 2 y 3 y 4 y 5 y 6 y 7 z 23 z 67 S2 delay delay The tuning path is: - dependant on the technical requirements (chosen tuning input / output to control) - independent of the power flow direction

31 - Maximum control scheme - 1. EMR of the system 2. Tuning path 3. Inversion step-by-step Strong assumption: all variables can be measured! 31 S1 x 1 x 2 x 3 x 4 x 5 x 6 x 7 y 1 y 2 y 3 y 4 y 5 y 6 y 7 z 23 z 67 S2 x 3-ref x 4-ref x 5-ref x 6-ref x 7-ref Maximal Control Structure (or scheme): - maximum of sensors - maximum of operations Example: - 6 sensors - 2 closed-loop controls

32 - Practical control schemes - 1. EMR of the system 2. Tuning path 3. Inversion step-by-step Strong assumption: all variables can be measured! 32 S1 x 1 x 2 x 3 x 4 x 5 x 6 x 7 y 1 y 2 y 3 y 4 y 5 y 6 y 7 z 23 z 67 S2 4. Simplification of control x 3-ref Simplifications: - non-consideration of disturbances - merging control blocks x 4-ref x 7-ref impact on the tuning and/on the performances

33 - Practical control schemes - 1. EMR of the system 2. Tuning path 3. Inversion step-by-step Strong assumption: all variables can be measured! 33 S1 x 1 x 2 x 3 x 4 x 5 x 6 x 7 y 1 y 2 y 3 y 4 y 5 y 6 y 7 S2 z 23 z 67 x 7-est y 4-est 4. Simplification of control x 3-ref x 4-ref x 7-ref 5. Estimation of non-measured variables from measured variables

34 - Practical control schemes - 1. EMR of the system 2. Tuning path 3. Inversion step-by-step Strong assumption: all variables can be measured! 34 S1 x 1 x 2 x 3 x 4 x 5 x 6 x 7 y 1 y 2 y 3 y 4 y 5 y 6 y 7 S2 z 23 z 67 x 7-est y 4-est 4. Simplification of control x 3-ref x 4-ref x 7-ref 5. Estimation of non-measured variables 6. Tuning of controllers PI / PID / fuzzy controller? Calculation of parameters?

35 - Inversion-based control of a system EMR of the system 2. Tuning path 3. Inversion step-by-step Maximal Control Scheme mirror of the EMR (systematic) unique and theoretical solution 4. Simplification of control 5. Estimation of variables 6. Tuning of controllers Practical Control Schemes several solutions (expertise) reduced performances

36 Polytech Paris Sud June «Example of a paper processing system» Prof. A. Bouscayrol, Prof. B. Lemaire-S (Université Lille1, L2EP, France) Prof. P. Sicard (Université du Québec à Trois-Rivières, Canada) based on common paper at IEEE-IECON 2006

37 - Paper processing system as an example - 37 Paper processing using 2 induction machines IM1 IM2 IM1 IM2 [Leclerc 04] [Barre 06] Technical requirements: - paper tension control for high quality of paper roll - winding velocity control for high quality of processing

38 - Maximum control structure - 38 VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 V dc u vsi1 i im1 T im1 im1 v roll1 T band T roll2 im2 e im2 i im2 i vsi2 DC Bus DC Bus i vsi1 i im1 svsi1 e im1 im1 T roll1 T band v roll2 im2 T im2 i im2 u vsi2 s vsi2 V dc Step 1: develop the EMR of the system Step 2a: identify all variables to be controlled (outputs) and control inputs Step 2b: identify tuning paths from inputs to outputs, avoiding crossing the paths

39 - Maximum control structure - 39 VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 V dc u vsi1 i im1 T im1 im1 v roll1 T band T roll2 im2 e im2 i im2 i vsi2 DC Bus DC Bus i vsi1 i im1 svsi1 e im1 im1 im1-ref T roll1 T band v roll2 im2 T im2 i im2 u vsi2 s vsi2 V dc 2 1 u vsi1-ref im1-ref T band-ref i im1-ref T im1-ref v roll1-ref 1. FOC: Field Oriented Control 2. PWM: Pulse Width Modulation im2-ref v roll2-ref 1 2 im2-ref T im2-ref i im2-ref u vsi2-ref Step 3: invert each element of the tuning paths by applying inversion rules assume that all the signals are measurable; compensate for all disturbances.

40 - Maximum control structure - 40 VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 V dc u vsi1 i im1 T im1 im1 v roll1 T band T roll2 im2 e im2 i im2 i vsi2 DC Bus DC Bus i vsi1 i im1 svsi1 e im1 im1 im1-ref T roll1 T band v roll2 im2 T im2 i im2 u vsi2 s vsi2 V dc 2 1 u vsi1-ref im1-ref T band-ref i im1-ref T im1-ref v roll1-ref 1. FOC: Field Oriented Control 2. PWM: Pulse Width Modulation im2-ref v roll2-ref 1 2 im2-ref T im2-ref i im2-ref u vsi2-ref Maximal Control Structure 16 sensors (including 2 ac components for currents and voltages) 5 closed-loop controls (including 2 controllers of dimension 2 for currents)

41 - Practical control structure - 41 VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 V dc u vsi1 i im1 T im1 im1 v roll1 T band T roll2 im2 e im2 i im2 i vsi2 DC Bus DC Bus i vsi1 i im1 svsi1 e im1 im1 im1-ref T roll1 T band v roll2 im2 T im2 i im2 u vsi2 s vsi2 V dc 2 1 u vsi1-ref i im1-ref im1-ref T band-ref T im1-ref v roll1-ref im2-ref v roll2-ref 1 2 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

42 - Practical control structure - 42 VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 V dc u vsi1 i im1 T im1 im1 v roll1 T band T roll2 im2 e im2 i im2 i vsi2 DC Bus DC Bus i vsi1 i im1 svsi1 e im1 im1 im1-ref T roll1 T band v roll2 im2 T im2 i im2 u vsi2 s vsi2 V dc 2 1 u vsi1-ref i im1-ref im1-ref T band-ref T im1-ref v roll1-ref im2 T roll2_est im2_est im2_est T im2_est closed-loop observer i im2 im2-ref im2-ref v roll2-ref 1 2 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

43 - Practical control structure - 43 VSI 1 induction machine 1 roll 1 band roll 2 induction machine 2 VSI 2 V dc u vsi1 i im1 T im1 im1 v roll1 T band T roll2 im2 e im2 i im2 i vsi2 DC Bus DC Bus i vsi1 i im1 svsi1 e im1 im1 im1-ref T roll1 T band v roll2 im2 T im2 i im2 u vsi2 s vsi2 V dc 2 1 u vsi1-ref i im1-ref im1-ref T band-ref T im1-ref v roll1-ref im2-ref v roll2-ref 1 2 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

44 - Band controller - 44 band v roll1 u y T band v roll1 T band w v roll2 T band v roll2 v roll2_mes T band_mes v roll1-ref T band-ref w est v roll1_ref u ref y ref Tband-ref Details using Causal Ordering Graph (COG) [Hautier 96]

45 Velocity of roll 2 (m/s) vs time (s) «Inversion-Based Control from EMR» - Simulation results Tension of band (pu) vs time (s) 2 45 with compensation of w est reference Simulation results 1 without compensation of w est Tension of band (pu) vs time (s)

46 Polytech Paris Sud June 2014 «Conclusion» Inversion based control = inversion of EMR based on the cognitive systemic and the causality principle (energy) Inversion rule for control scheme closed-loop control to invert accumulation, direct inversion for conversion element, degree of freedom for coupling element Different steps on the control scheme From Maximum Control Scheme. to Practical Control Schemes. to the strategy level

47 BAT - Different control levels - VSI1 EM1 47 Parallel HEV Fuel ICE EMR Trans. fast subsystem controls EM1 control ICE control Trans control Inversion-based control slow system supervision Energy management (supervision/strategy) Strategy (supervision) Next Step driver request

48 - References - 48 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 A. Bouscayrol, B. Davat, B. de Fornel, B. François, J. P. Hautier, F. Meibody-Tabar, M. Pietrzak-David, Multimachine multiconverter system: application for electromechanical drives, European Physics Journal - Applied Physics, vol. 10, no. 2, May 2000, p (common paper GREEN Nancy, L2EP Lille and LEEI Toulouse, according to the SMM project of the GDR-SDSE). 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). A. Bouscayrol, J. P. Hautier, B. Lemaire-S , "Graphic Formalisms for the Control of Multi-Physical Energetic Systems", Systemic Design Methodologies for Electrical Energy, tome 1, Analysis, Synthesis and Management, Chapter 3, ISTE Willey editions, October 2012, ISBN: 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 and Jeumont SA). A. Leclercq, P. Sicard, A. Bouscayrol, B. Lemaire-S ,"Control of a triple drive paper system based on the Energetic Macroscopic Representation", IEEE-ISIE'04, Ajaccio (France), May 2004, pp P. Sicard, A. Bouscayrol, Inversion-based control of electromechanical systesm, EMR 09 summer school, Trois- Rivières, Canad,a, September 2009