A Park - like transform for fluid power systems : application to pneumatic stiffness control

Transcription

1 Laboratoire Ampère Unité Mixte de Recherche CNRS Génie Électrique, Électromagnétisme, Automatique, Microbiologie Environnementale et Applications A Park - like transform for fluid power systems : application to pneumatic stiffness control Prof. Eric Bideaux, INSA Lyon, Ampère Lab, France 1

2 Context & problematics Modeling and control of Fluid Power systems is usually considered as a difficult task : o multiphysic : mechanics, fluid dynamics, thermodynamics, electrical eng., o highly non linear behavior more difficult to control than electrical drives? NO 2

3 Differences electric and fluid power drives (1/3) Electric drives Electric Power desired command angular position User friendly Load High bandwidth o lot of sensors (current, voltage) o complex control algorithm embedded (large computation capacity) o but everything is included!!! Low bandwidth o high reflected inertia o complex friction phenomena o can be considered part of the load (disturbance) The whole package is on-the-shelves!!! 3

4 Differences electric and fluid power drives (2/3) Hydraulic drives command Hydraulic Power Load Low bandwidth High bandwidth o ~ no sensor (mech/elec feedback) o each design is different o safety component have to be added Not user friendly o low inertia o nearly a integrator Help yourself!!!! 4

5 Differences electric and fluid power drives (2/3) Other architectures of hydraulic drives command Mechanic Power Load Low bandwidth High bandwidth desired command angular position Not user friendly Electric Power Load High bandwidth Low bandwidth High bandwidth 5

6 Differences electric and fluid power drives (3/3) Pneumatic drives command Pneumatic Power Load High bandwidth Low bandwidth o ~ no sensor (mech/elec feedback) o low efficiency o each design is different o safety component to be added Not user friendly o low inertia o low pressure dynamic Help yourself!!!! 6

7 Simplicity of control Why electrical drive are so user-friendly? Servo/Prop. Hydraulic Act. EHA/ displacement pump The intelligence is in the box Plug & Play Nearly no computation capacity embedded Not Plug & Play EHA/ variable speed Electric MA Servo Pneumatic Act. User-friendly control 7

8 How to make the control easier? The physical variables are not always the best for control purposes : o On mechanical side Speed o On fluid side (pneumatic) Displacement 2 commands : q mp up,p P q mn un,p N q mn inversion P N u N = ψ 1 q mn, P N u P = ψ 1 q mp, P p 8

9 The AT transform (1/2) 2 different phenomena o The differential pressurization : Force o The symmetric pressurization : do not modify the force Let us consider the following coordinate transformation: q mp q mn q ma = active flow q mt = pressurization flow with (*) * Note : this transformation can easily be extended to non-symmetric cylinder 9

10 The AT transform (2/2) Make the really interesting variables appear in the equations F pneu =S. P P P N = S.Δp P T = P N + P P 2 10

11 The AT transform (2/2) Make the really interesting variables appear in the equations Decoupling Force generation from Pressurization 11

12 The AT transform (2/2) Make the really interesting variables appear in the equations Speed Displacement Active flow Pressurization flow P T ~ Actuator Stiffness 12

13 Pressure difference DP [bar] Virtual flow rates [g/s] Mean pressure P T [bar] Experimental validation Open-loop : variation on q mt variation of 4 bars q mt q ma = 0 variation of 0.7 bars 13

14 Pressure difference DP [bar] Virtual flow rates [g/s] Mean pressure P T [bar] Experimental validation Open-loop : variation on q ma variation < 0.05 bar q mt = 0 q ma variation max of 0.8 bars 14

15 AT Transform vs. Park Transform AT Transform o change of variables for control purpose: Park Transform o change of variables for control purpose: o original flows of power modulator change in : virtual active flow qma Force control virtual presurization flow qmt o original voltages of power modulator change in : virtual voltage Vd Displacement and force generation Mean pressure control Actuator stiffness Torque control virtual voltage Vq Magnetic flux control 15

16 Laboratoire Ampère Unité Mixte de Recherche CNRS Génie Électrique, Électromagnétisme, Automatique, Microbiologie Environnementale et Applications Applications of the AT Transform Trajectory control (Y-P T control) Energy saving (Y-P Topti control) Displacement / Stiffness (Y-K control) Position oberver (at 0 speed) Mono-distributor 16

17 Application of the AT Transform Active flow Pressurization flow q ma q mt Pressure difference Speed Displacement Pressurization control (Y-P T control) Energy saving (Y-P Topti control) Stiffness (Y-K control) Position oberver (at 0 speed) Mono-distributor 17

18 Virtual flow rates [g/s] Displacement [mm] Mean pressure P T [bar] Trajectory control (Y-P T control) Control synthesis : Backstepping desired trajectory yd desired trajectory P Td measured trajectory y measured trajectory P T q ma q mt Same results to what was achieved with other control techniques 18

19 Energy saving (Y-P Topti control) Control synthesis : o q ma is imposed (y trajectory) o minimize with q ma = V 0. q mp V P q mn V N If V N smaller than V P, less flow is required to produce q ma if q mn is used If V P smaller than V N, less flow is required to produce q ma if q mp is used if as q mt = V 0. q mp V P + q mn V N if Optimal control is obtained for : if 19

20 Stiffness (Y-K control) Stiffness control: o reject or not disturbances in open-loop (do not required fast closed loop) o variable compliance Control synthesis : o q ma is imposed (y trajectory) o Actuator stiffness natural behavior of the actuator to come back to its equilibrium point 20

21 Displacement [mm] Virtual flow rates [g/s] Stiffness [N/m] Load [N] Stiffness (Y-K control) Control synthesis : Backstepping Close loop stiffness desired K pneu measured K pneu K pneu = 1, N/m K pneu = 2, N/m K pneu = 3, N/m measured displacement y Static error decreasing with K pneu at impact q ma desired position yd K pneu = 1, N/m K pneu = 2, N/m K pneu = 3, N/m 21

22 Position observer at standstill Position observer at standstill (v=0) : y, q ma, q mt not known position estimation error estimated system inputs From pressure sensors only : F pneu and P T can be calculated, the full state can be obtained by differentiation: Procedure o change slightly q mt with q ma = 0 theoritically F pneu do not change (or < dry friction) the piston do not move (v=0) 22

23 Displacement [mm] Force F pneu [N/m] Load [N] Displacement [mm] Position observer at standstill [N/(m.s)] Observer synthesis : Sliding mode o 5 Hz Sinusoisal trajectory on P T derivative of F pneu estimated position y real position ym measured K pneu 23

24 Conclusion Active flow Pressurization flow q ma q mt Pressure difference Speed Displacement Pressurization control (Y-P T control) Energy saving (Y-P Topti control) Stiffness (Y-K control) What else? Position oberver (at standstill) Mono-distributor 24

25 Thanks a lot for your kind attention References : 1. Frédéric Abry, Xavier Brun, Sylvie Sesmat, Eric Bideaux. Non-linear position control of a pneumatic actuator with closed-loop stiffness and damping tuning, ECC, Jul 2013, Zürich, Switzerland. pp , Frédéric Abry, Xavier Brun, Michaël Di Loreto, Sylvie Sesmat, Eric Bideaux. Piston position estimation for an electro-pneumatic actuator at standstill, Control Engineering Practice, Elsevier, 2015, 41 (8), pp