This paper develops general theoretical results about an input–output model-following methodology for linear systems, as an optimal control problem. A control law is obtained by minimizing a quadratic index that takes into account the matching errors and the control inputs. The control is obtained from the Lagrange multiplier method and can be interpreted as an extension of the linear quadratic regulator, with finite and infinite horizon formulations. The major contribution of the paper is the development of solutions involving plant output feedback. The method is illustrated with an application to a nonlinear flexible aircraft with nonstationary aerodynamics and nine flexible modes. Simulations compare state and output feedback solutions. In the proposed example, when taking into account unmodeled flexible dynamics and parametric uncertainties, the best results are given by the proposed output feedback.
AndersonBDOMooreJB (1971) Linear Optimal Control, Englewood Cliffs NJ: Prentice-Hall.
2.
AsseoSJ (1970) Application of optimal control to perfect model following. Journal of Aircraft7(4): 308–313.
3.
BiskriDEBotezRMStathopoulosNThérienSDickinsonMRatheA (2008) Aeroservoelasticity analysis method based on an error analytical form applied on a business aircraft. Journal of Vibration and Control14(8): 1217–1230.
4.
da SilvaAL (2010) Non linear optimal model following control of flexible aircraft. PhD Thesis, Brazil: Aeronautical Institute of Technology.
5.
da SilvaALPaglionePYoneyamaT (2010a) Conceptual flexible aircraft model for modeling, analysis and control studies. AIAA Atmospheric Flight Mechanics Conference.Toronto, Canada. 2–5 August 2010.
6.
da Silva AL, Yoneyama T and Paglione P (2010b) Controllability analysis and stabilization of flexible aircrafts, XIII Congresso Brasileiro de Automática, Bonito, Brazil, pp. 3452–3457, 12–16 September 2010.
7.
da SilvaALPaglionePYoneyamaT (2012) Cruising autopilot for a flexible aircraft with internal loop of model following. Journal of Aerospace Engineering.. DOI: 10.1061/(ASCE)AS.1943-5525.0000277.
8.
Di BenedettoMDGrizzleJW (1994) Asymptotic model matching for nonlinear systems. IEEE Transactions on Automatic Control39(8): 1539–1550.
9.
Di BenedettoMDIsidoriA (1986) The matching of nonlinear models via dynamic state-feedback. SIAM Journal on Control and Optimization24(5): 1063–1075.
10.
GadewadikarJLewisFAbu-KhalafM (2006) Necessary and sufficient conditions for H-infinity static output-feedback control. Journal of Guidance, Control, and Dynamics29(4): 915–920.
11.
GomanMGDemenkovMN (2004) Computation of controllability regions for unstable aircraft dynamics. Journal of Guidance, Control, and Dynamics27(4): 647–656.
12.
Guimaraes NetoAB (2008) Dinâmica e controle de aeronaves flexíveis com modelagem aerodinâmica pelo método doublet lattice, Brazil: Graduation Final Work, Aeronautical Institute of Technology.
13.
HermannR (1994) C-O-R Generalized Functions, Current Algebras, and Control, Brookline, MA: Math Sci Press.
14.
KaseW (2001) Model following control system for nonminimum phase plants using Taylor's expansion. 40th IEEE Conference on Decision and Control. Orlando, USA, 4–7 December 2001, pp. 4897–4902.
15.
KirkDE (2004) Optimal Control Theory, an Introduction, Mineola: Dover Publications.
16.
KoJStrganacTWJunkinsJLAkellaMRKurdilaAJ (2002) Structured model reference adaptive control for a wing section with structural nonlinearity. Journal of Vibration and Control8(5): 553–573.
17.
KreindlerERothschildD (1976) Model-following in linear-quadratic optimization. AIAA Journal14(7): 835–842.
18.
LaubAJ (2005) Matrix Analysis for Scientists and Engineers, Philadelphia, PA: Society for Industrial and Applied Mathematics.
19.
LawrenceDA (1999) Approximate model matching for nonlinear systems. 38th IEEE Conference on Decision and Control. Phoenix, AZ, 7–10 December 1999, pp. 720–725.
20.
LeeKWSinghSN (2012) l1adaptive control of a nonlinear aeroelastic system despite gust load. Journal of Vibration and Control.. DOI: 10.1177/1077546312452315.
21.
LewisFLSyrmosVL (1995) Optimal Control, 2nd ed. New York: John Wiley and Sons.
22.
MilneRD (1964) Dynamics of the deformable aeroplane, London, UK: Reports and Memoranda No. 3345, Her Majesty's Stationery Office.
23.
OgataK (1997) Modern Control Engineering, 3rd ed. Upper Saddle River, NJ: Prentice-Hall, pp. 722–736.
24.
PieperJKBaillieSGoheenKR (1996) Linear quadratic optimal model-following control of a helicopter in hover. Optimal Control Applications and Methods17(2): 123–140.
25.
PreidikmanSMookD (2000) Time domain simulations of linear and nonlinear aeroelastic behaviour. Journal of Vibration and Control6(8): 1135–1175.
26.
SatoM (2009) Robust model-following controller design for LTI systems affected by parametric uncertainties: a design example for aircraft motion. International Journal of Control82(4): 689–704.
27.
SilvestreFJPaglioneP (2008) Dynamics and control of a flexible aircraft. 2008 AIAA Atmospheric Flight Mechanics Conference and Exhibit.Honolulu, HI: AIAA Paper 2008-6876. 18–21 August 2008.
28.
StevensBLLewisFL (2003) Aircraft Control and Simulation, 2nd ed. New York: John Wiley and Sons.
29.
VincentTLLeeCS (1983) Parametric optimization with dynamic systems. Applied Mathematics and Computation12(2–3): 169–185.
30.
WangFHuoSYueZQianW (2011) Further study on aeroelastic response of aircraft wing with freeplay. Journal of Vibration and Control.. DOI: 10.1177/1077546311424306.
31.
WaszakMRSchmidtDK (1988) Flight dynamics of aeroelastic vehicles. Journal of Aircraft25(6): 563–571.
32.
YuGR (2006) Explicit model-following design of propulsion control aircraft using genetic algorithms. 2006 IEEE International Conference on Systems, Man, and Cybernetics. Taipei, Taiwan, 8–11 October 2006, pp. 4348–4353.
33.
ZongRChangBCYehHHBandaSS (1995) An approximate I/O linearization via nonlinear H∞ model matching. 34th IEEE Conference on Decision and Control. New Orleans, LA, 13–15 December 1995, pp. 345–346.
