We present a new method to compute output gain-scheduled controllers for nonlinear systems. We use structured H-control to precompute an optimal controller parametrization as a reference. We then propose three practical methods to implement a control law which has only an acceptable loss of performance with regard to the optimal reference law. Our method is demonstrated in longitudinal flight control, where the dynamics of the aircraft depend on the operational conditions velocity and altitude. We design a structured controller consisting of a PI-block to control vertical acceleration, and another I-block to control the pitch rate.

References

References
1.
Becker
,
G.
, and
Mantz
,
R.
,
1994
, “
Robust Performance of Linear Parametrically Varying Systems Using Parametrically-Dependent Linear Feedback
,”
Syst. Control Lett.
,
23
, pp.
205
213
.10.1016/0167-6911(94)90006-X
2.
Apkarian
,
P.
, and
Gahinet
,
P.
,
1995
, “
A Convex Characterization of Gain-Scheduled H∞ Controllers
,”
IEEE Trans. Autom. Control
,
40
, pp.
853
864
.10.1109/9.384219
3.
Apkarian
,
P.
,
Gahinet
,
P.
, and
Becker
,
G.
,
1995
, “
Self-Scheduled H∞ Control of Linear Parameter-Varying Systems: A Design Example
,”
Automatica
,
31
(
9
), pp.
1251
1261
.10.1016/0005-1098(95)00038-X
4.
Zhang
,
Y. S.
, and
SaadatMehra
,
A.
,
2012
, “
Hinfty PID Control for Multivariable Networked Control Systems With Disturbance Noise Attenuation
,”
Int. J. Robust Nonlinear Control
,
22
(
2
), pp.
183
204
.10.1002/rnc.1688
5.
Lu
,
B.
, and
Wu
,
F.
,
2004
, “
Switching LPV Control Design Using Multiple Parameter-Dependent Lyapunov Functions
,”
Automatica
,
40
, pp.
1973
1980
.10.1016/j.automatica.2004.06.011
6.
Lu
,
B.
,
Wu
,
F.
, and
Kim
,
S.
,
2006
, “
Switching LPV Control of an F-16 Aircraft via Controller State Reset
,”
IEEE Trans. Control Syst. Technol.
, pp.
267
277
.
7.
Mattei
,
M.
,
2001
, “
Robust Multivariable PID Control for Linear Parameter Varying Systems
,”
Automatica
,
37
(
12
), pp.
1997
2003
.10.1016/S0005-1098(01)00156-X
8.
Bolea
,
Y.
,
Puig
,
V.
, and
Blesa
,
J.
,
2008
, “
Gain-Scheduled Smith PID Controllers for LPV Systems With Time Varying Delay: Application to an Open-Flow Canal
,”
Proceedings of IFAC
, Korea, pp.
14564
14569
.
9.
Mattei
,
M.
, and
Scordamaglia
,
V.
,
2008
, “
A Full Envelope Small Commercial Aircraft Flight Control Design Using Multivariable Proportional- Integral Control
,”
IEEE Trans. Control Syst. Technol.
,
16
(
1
), pp.
169
176
.10.1109/TCST.2007.903098
10.
Jenie
,
S. D.
, and
Budiyono
,
A.
,
2006
,
Automatic Flight Control System—Classical Approach and Modern Control Perspective
(Lecture Notes), Bandung Institute of Technology, Indonesia.
11.
Stevens
,
B.
, and
Lewis
,
F. L.
,
1992
,
Aircraft Control and Simulation
,
John Wiley and Sons, Inc.
,
New York
.
12.
Sonneveldt
,
L.
,
2006
,
Nonlinear F-16 Model Description
,
Faculty of Aerospace Engineering, Delft University of Technology
,
Delft, The Netherlands
.
13.
Magni
,
J.
,
Bennani
,
S.
, and
Terlouw
,
J.
,
1997
,
Robust Flight Control: A Design Challenge
, Vol.
224
(Lecture notes in Control and Information Sciences),
Springer
,
Berlin
.
14.
Zolghadri
,
A.
,
2000
, “
A Redundancy-Based Strategy for Safety Management in a Modern Civil Aircraft
,”
Control Eng. Pract.
,
8
, pp.
545
554
.10.1016/S0967-0661(99)00172-0
15.
Robust toolbox of Matlab R2010b, MathWorks, Natick, MA.
16.
Apkarian
,
P.
, and
Noll
,
D.
,
2006
, “
Nonsmooth H∞-Control
,”
IEEE Trans. Autom. Control
,
51
(
1
), pp.
71
78
.10.1109/TAC.2005.860290
17.
Noll
,
D.
,
Prot
,
O.
, and
Rondepierre
,
A.
,
2008
, “
A Proximity Control Algorithm to Minimize Nonsmooth and Nonconvex Functions
,”
Pacific J. Optim.
,
4
(
3
), pp.
569
602
.
19.
Pottmann
,
H.
,
Krasauskas
,
R.
,
Hamann
,
B.
,
Joy
,
K.
, and
Seibold
,
W.
,
2000
, “
On Piecewise Linear Approximation of Quadratic Functions
,”
J. Geom. Graphics
,
4
(
1
), pp.
31
53
.
20.
Keviczky
,
T.
, and
Balas
,
G. J.
,
2006
, “
Receding Horizon Control of an F-16 Aircraft: A Comparative Study
,”
Control Eng. Pract.
,
14
, pp.
1023
1033
.10.1016/j.conengprac.2005.06.003
21.
Hassin
,
R.
, and
Levin
,
A.
,
2006
, “
A Better-Than-Greedy Approximation Algorithm for the Minimum Set Cover Problem
,”
SIAM J. Comput.
,
35
, pp.
189
200
.10.1137/S0097539704444750
22.
Shamma
,
J.
, and
Athans
,
M.
,
1990
, “
Analysis of Gain Scheduled Control for Nonlinear Plants
,”
IEEE Trans. Autom. Control
,
35
(
4
), pp.
898
907
.10.1109/9.58498
23.
Helton
,
J.
, and
James
,
M. R.
,
1999
,
Extending H∞ Control to Nonlinear Systems
,
SIAM Advances in Design and Control
,
Philadelphia, PA
.
24.
Gabarrou
,
M.
,
Alazard
,
D.
, and
Noll
,
D.
,
2010
, “
Structured Flight Control Law Design Using Non-Smooth Optimization
,”
18th IFAC Symposium on Automatic Control in Aerospace
.
You do not currently have access to this content.