Ett naturligt steg i framtiden blir att implementera styrlagarna, d˚a framf¨orallt Explicit MPCAPN, i en mer omfattande modell. Sedan kommer en m¨angd tester g¨allande robusthet, stabilitet, prestanda p˚a varierande h¨ojd m.m. som alltid att beh¨ovas.
Litteraturf¨orteckning
[1] J. C. Andersson. Kondenserad modell av styrautomat och skrov. Teknisk rapport RRS-73-88:01, Saab Missiles Combitech Group, 1991.
[2] A. Bemporad. Short Course on Model Predictive Control and Hybrid Systems, September 2004. Link¨oping.
[3] A. Bemporad, M. Morari, V. Dua och E.N. Pistikopoulos. The Explicit Linear Quadratic Regulator for Constrained Systems. Automatica, 38:3–20, 2002. [4] N. Bergman. Parallella filter f¨or detektering av flygplansman¨ovrer. Master’s
thesis LiTH-ISY-EX-1598, Department of Electrical Engineering, Link¨oping University, Link¨oping, Sweden, 1995.
[5] W.R. Chadwick och P. Zarchan. Interception of Spiraling Ballistic Missiles. I Proceedings of the American Control Conference, ss 4476–4482, Seattle, Washington, Juni 1995.
[6] H. Frank. Definitions related to air-to-air performance. Teknisk rapport RT- R03:9017(I), Saab Bofors Dynamics AB, 2003.
[7] T. Glad, S. Gunnarsson, L. Ljung, T. McKelvey, A. Stenman och J. L¨ofberg. Digital Styrning Kurskompendium. Instutionen f¨or systemteknik, Link¨oping, Sweden, 2003.
[8] T. Glad och L. Ljung. Reglerteknik. Grundl¨aggande teori. Studentlitteratur, Lund, Sweden, 2a utg˚ava, 1989.
[9] T. Glad och L. Ljung. Reglerteori. Flervariabla och olinj¨ara metoder. Stu- dentlitteratur, Lund, Sweden, 2a utg˚ava, 2003.
[10] G. Hexner, T. Shima och H. Weiss. An LQG Guidance Law with Bounded Ac- celeration Command. I Proceedings of the 42nd IEEE Conference on Decision and Control, band 1, ss 715–720, Maui, Hawaii USA, December 2003. [11] H. Johansson. Gain scheduled missile control using robust loop shaping. Mas-
ter’s thesis LiTH-ISY-EX-3291-2002, Department of Electrical Engineering, Link¨oping University, Link¨oping, Sweden, 2003.
[12] K.B. Kim, T.W. Yoon och W.H. Kwon. Receding Horizon Guidance Laws for Constrained Missiles with Autopilot Lags. Control Engineering Practice, 9:1107–1115, 2001.
[13] M. Kvasnica, P. Grieder, M. Baoti´c och M. Morari. Multi Parametric Tool- box (MPT). I Hybrid Systems: Computation and Control, Lecture Notes in Computer Science, mar 2004.
http://control.ee.ethz.ch/∼mpt.
[14] C.F. Lin. Modern Navigation, Guidance, and Control Processing. Prentice- Hall, Inc., 1991.
[15] J. Lundgren, M. R¨onnqvist och P. V¨arbrand. Linj¨ar och ickelinj¨ar optimering. Studentlitteratur, 2001.
[16] I. Rusnak. Advanced Guidance Laws for Acceleration-Constrained Missile, Randomly Maneuvering Target and Noisy Measurements. IEEE Transactions on Aerospace and Electronic Systems, 32(1):456–464, 1996.
[17] I. Rusnak och L. Meir. Optimal Guidance for Acceleration Constrained Missile and Maneuvering Target. IEEE Transactions on Aerospace and Electronic Systems, 26(4):618–624, 1990.
[18] P.O.M. Scokaert och J.B. Rawlings. Constrained Linear Quadratic Regula- tion. IEEE Transactions on Automatic Control, 38(8):1163–1169, 1998. [19] A. S¨oderberg. Styrlagar f¨or en h¨oghastighetsrobot. Master’s thesis LiTH-ISY-
EX-3362-2003, Department of Electrical Engineering, Link¨oping University, Link¨oping, Sweden, 2003.
[20] T. Svantesson. FoT. moderna slutfasstyrningsalgoritmer - etapp 7. Teknisk rapport RT-R04:9013(F¨oretagshemlig), Saab Bofors Dynamics AB, 2004. [21] P. Tøndel, T.A. Johansen och A. Bemporad. An Algorithm for Multi-
Parametric Quadratic Programming and Explicit MPC Solutions. Automa- tica, 39:489–497, 2003.
[22] P. Tøndel, T.A. Johansen och A. Bemporad. Evaluation of Piecewise Affine Control via Binary Search Tree. Automatica, 39:945–950, 2003.
Bilaga A
Notationer
Operatorer och funktioner
E{·} V¨antev¨ardesoperatorn. p Deriveringsoperatorn d/dt. X\Y Snittet mellan X och Y .
A 0 Positivt semidefinit matris, xTAx≥ 0, ∀x 6= 0.
F¨orkortningar
AFMM Adaptive Filtering through Multiple Models APN Augmented Proportional Navigation EKF Extended Kalman Filter
EMPC Explicit Model Predictive Control FCZ Fighter Center Zone
IMM Interactive Multiple Models IR Infrared
KKT Karush-Kuhn-Tucker LQ Linear Quadratic
LQAPN Linear Quadratic Augmented Proportional Navigation MICOS Missile Combat Simulator
mp-QP multi-parametric Quadratic Programming MPC Model Predictive Control
MPCAPN Model Predictive Control Augmented Proportional Navigation MPCT Model Predictive Control Toolbox
MPT Multi-Parametric Toolbox
MRAAM Medium Range Air-to-Air Missiles OBA Off Boresight Angle
OGL Optimal Guidance Law PN Proportional Navigation QP Quadratic Programming RHC Receding Horizon Control SOG Simplified Optimal Guidance-law TCZ Target Center Zone
Bilaga B
Matlabkod exempel
Matlabkod f¨or exemplet i kapitel 2 (Exempel 7.1 fr˚an [3]).
mpt_init % Initierar toolboxen
% Ett andra ordningens system, samplingstid 0.1s A = [0.7326 -0.0861;0.1722 0.9909]; B = [0.0609;0.0064]; C = [0 1.4142]; % N_y = N_u = N N = 2; % Viktmatriser Q=eye(2); R=0.01; sysStruct.A = A; sysStruct.B = B; sysStruct.C = C; sysStruct.D = 0; sysStruct.ymax = inf; sysStruct.ymin = -inf; sysStruct.umax = 2; sysStruct.umin = -2; sysStruct.dumax = inf; sysStruct.dumin = -inf; probStruct.N = N; probStruct.Q = Q; 61
probStruct.R = R; probStruct.norm = 2;
probStruct.P_N = dlyap(A,Q); % Viktmatris f¨or $x_N$
probStruct.Tconstraint = 0; % Medf¨or inget terminal constraint set probStruct.subopt_lev = 0; % Optimeran m.a.p. viktfunktionen
[ctrlStruct] = mpt_control(sysStruct, probStruct) % Skapar mp-QP l¨osningen figure(1)
mpt_plotPartition(ctrlStruct); axis([-1.5 1.5 -1.5 1.5]);
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