EF2000 Control Laws - Phase 4 Optimisation of Feedback Gains (Pitch)

Transcription

1 Optimisation of Feedback Gains (Pitch) Some DA & IPA are flying with the Phase 4 Claws Pilot comments: (improved Handling Qualities/Agility (flying like a true fighter aircraft Optimisation program to design the feedback gains (Pitch) Optimisation of Feedback Gains 1

2 Personnel Background in Optimisation Studium der Mathematik & Physik in Würzburg (Prof. Knobloch) Jungwissenschaftler bei der DLR Oberpfaffenhofen (Dr. Well) Trajectory optimization with TOMP Extension TOMP TOMP2 Optimization Kernel SLLSQP (Kraft/Schittkowski) MBB Vorentwicklung (TKF) Routenplaner für UTA EADS MT62/MT66(FJT) EF: Foreplane schedule supersonic Feedback Gain Optimisation Optimisation of Feedback Gains 2

3 SLLSQP! min = f(x) G(x) = 0 H(x) 0 x L x x U f skalar, G, H vektorwertig, 2x stetig differenzierbar reverse communication, benötigt f X, G X, H X. Liefert lokale Minima! Beispiel aus Variationsrechnung: Welcher Quader vorgegebenen Volumens besitzt die kleinste Oberfläche? x=(l,b,h), f(x) = 2*(l*b + b*h + l*h); G(x) = l*b*h V 0 ; H 0 Lösung: Würfel: l * = b * = h * = V 1/3 0 Optimisation of Feedback Gains 3

4 Differential PI-Algorithm in Phase 4 Control Laws (Pitch) Optimisation of Feedback Gains 4

5 Plant Optimisation of Feedback Gains 5

6 Feedback Gain Optimisation (Pitch) Design Criteria v v Multi-Konfig Optimierung eine Design-Konfig + mehrere Rand -Konfigs Frequenzbereichsanalyse + Eigenwertbetrachtung 9 Stabilität, Dämpfung, Dynamik Nichols PITCH(MLC) s027,14.0t,33.4%, 8.0g Einzelne Kriterien: 1) Stabilitätsradius (Ellipse) (=1 für 5.6dB & 35 ) 2) Upper Gain Margin -6dB (keine AERO oder ADS-Tol.) 3) Phase Margin 20 & Lower Gain Margin 2dB 4) FCS Mode Dämpfung z FCS ) Integrator Pol s I / Einschwingzeit T I T I =1, s I-dem = -1/T I = -1 für Design-Konfig σ I - σ I-dem klein für Rand -Konfigs ( erleichtert Vorwärtspfad-Design) Gain [db] SS SG1: medium mass, aft cg SC Phase [deg] (Veas,Mach,Alfa)=(400,0.85,14) Optimisation of Feedback Gains

7 Design Criteria (cont.) Minimum SP damping cubic spline between (3.5, 0.73) and (10, 0.45) ) Minimum Short Period Damping 0.73 up to 3.5[rad/s], 0.45 above 10[rad/s] cubic spline in between ) Short Period Frequency close to Level 1* value of CAP criterion (Note: σ I & ω SP from PT3 approx. to transfer function: Stick 8) Small Feedback Gains short period frequency [rad/sec] Alfa) 9) Gain Ratio KEA/(KDA*xdia) and KEQ/(KDQ*xdia) close to 1 (Idea: Same actuator rates for TEF & FP) 10) x L and x U from 3 rd order model considerations with certain ranges for s I t SP w SP ; upper limit for KDQ from end-to-end gain limitations 0.4 Optimisation of Feedback Gains 7

8 3 Stage Optimisation Scheme Stage 1 x = (JD, KDA, KDQ, KEA, KEQ, x 6, x 7, x 8 ) (x 6, x 7 may e.g. vary in [0.3, 3], x 8 in [0.1, 1.2] ) Set s I-dem = -1 Stage 1: Maximise r subject to: x 6 = x 4 / (x 2 *xdia), x 7 = x 5 / (x 3 *xdia), r = x 8 s I (1) = s I-dem x L x x U frequency responses in Nichols plots outside ellipse with radius r upper gain margin -6 db phase margin 20, lower gain margin 2 db z FCS 0.25 Optimisation of Feedback Gains 8

9 Stage 2 Stage 2: Maximise r subject to: x 6 = x 4 / (x 2 *xdia), x 7 = x 5 / (x 3 *xdia), r = x 8 s I (1) = s I-dem x L x x U frequency responses in Nichols plots outside ellipse with radius 1 upper gain margin -6 db phase margin 20, lower gain margin 2 db z FCS 0.25 z SP r*min_sp_damp(w SP ) Optimisation of Feedback Gains 9

10 Stage 3 Stage 3: Maximise f(x) subject to: x 6 = x 4 / (x 2 *xdia), x 7 = x 5 / (x 3 *xdia), r = x 8 s I (1) = s I-dem x L x x U frequency responses in Nichols plots outside ellipse with radius r upper gain margin -6 db phase margin 20, lower gain margin 2 db z FCS 0.25 z SP 1*min_sp_damp(w SP ) f(x) is build as a weighted sum of different design aims: a) stability radius b) small gains c) gain ratio close to 1 d) increase FCS mode damping (to some extent) e) move short period frequency towards level 1* value ( CAP) f) reduce spread around the demanded integrator pole position Optimisation of Feedback Gains 10

11 Example Optimisation result Start Stage 1 Stage 3 12 Mon Jun Nichols PITCH(MLC) s000,14.3t,30.6%, 1.0g s000,12.2t,27.2%, 1.1g s000,17.0t,28.1%, 0.8g 12 Mon Jun Nichols PITCH(MLC) s000,14.3t,30.6%, 1.0g s000,12.2t,27.2%, 1.1g s000,17.0t,28.1%, 0.8g 12 Wed Jun Nichols PITCH(MLC) s000,14.3t,30.6%, 1.0g s000,12.2t,27.2%, 1.1g s000,17.0t,28.1%, 0.8g s027,12.2t,33.4%, 1.1g s027,12.2t,33.4%, 1.1g s027,12.2t,33.4%, 1.1g s027,14.0t,33.4%, 1.0g s027,14.0t,33.4%, 1.0g s027,14.0t,33.4%, 1.0g s027,18.9t,32.5%, 0.7g 9 s027,18.9t,32.5%, 0.7g 9 s027,18.9t,32.5%, 0.7g 9 Gain [db] SS SG1: nominal SC00, light+heavy FWD SC00, light+medium+heavy AFT SC wgt_gain = 0 wgt_rtio = 0 wgt_damp = 0 wgt_dwsp = 0 wgt_sigi = <= NZ <= 1.13 [g] radius = <= -1/Ti <= [rad/s] <= wnsp <= [rad/s] <= zesp <= <= zefcs <= Gain [db] SS SG1: nominal SC00, light+heavy FWD SC00, light+medium+heavy AFT SC wgt_gain = 0 wgt_rtio = 0 wgt_damp = 0 wgt_dwsp = 0 wgt_sigi = <= NZ <= 1.13 [g] radius = <= -1/Ti <= [rad/s] <= wnsp <= [rad/s] <= zesp <= <= zefcs <= Gain [db] SS SG1: nominal SC00, light+heavy FWD SC00, light+medium+heavy AFT SC wgt_gain = wgt_rtio = 0.5 wgt_damp = 0.5 wgt_dwsp = 0.5 wgt_sigi = <= NZ <= 1.13 [g] radius = <= -1/Ti <= [rad/s] <= wnsp <= [rad/s] <= zesp <= <= zefcs <= Par: JD KDA KDQ KEA KEQ KEA/(KDA*xdia) KEQ/(KDQ*xdia) RAD low: P0: P : upp: act:!!!!!!!!!!!!!!!!!!!!!!!! Phase [deg] (Veas,Mach,Alfa)=(350,0.6,4) -12 Par: JD KDA KDQ KEA KEQ KEA/(KDA*xdia) KEQ/(KDQ*xdia) RAD low: P0: P : upp: act:!!!!!!!!!!!!!!!!!!!!!!!! Phase [deg] (Veas,Mach,Alfa)=(350,0.6,4) -12 Par: JD KDA KDQ KEA KEQ KEA/(KDA*xdia) KEQ/(KDQ*xdia) RAD low: P0: P : upp: act:!!!!!!!!!!!!!!!!!!!!!!!! Phase [deg] (Veas,Mach,Alfa)=(350,0.6,4) Optimisation of Feedback Gains 11

12 Scheduled Versions of the Optimisation Program Subsonic Range: Gains are tabulated in Speed, Mach, AoA; Da = 2 To get a smooth schedule (over AoA) slope restrictions between neighbouring AoAs are introduced guaranteeing that an AoA error of 1 (or 2 ) does not produce a loss in gain margin greater than 1.5 db. Supersonic Range: Gains are tabulated in Speed, Mach, AoA; Da = 4 Starting with e.g. a=4 and determining the gains at next a=8 the interpolated gain values must fulfil the constraints at a=6. Optimisation of Feedback Gains 12

13 Conclusion The Feedback Gain Optimisation Program has proven to be a valuable tool for the Control Law Designers Developed in close contact with the designers (R. Osterhuber) All feedback gains are obtained simultaneously Stability aspects are fully covered, but damping and A/C dynamics, too (improves A/C handling and facilitates forward path design) It works reliable and fast enough (even for thousands of constraints) Reduces the workload put on the designer Allows quick reaction on model data changes (e.g. aerodynamics) Optimisation of Feedback Gains 13