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Design of Flight Controllers based on Simplified LPV model of a UAV
Kannan Natesan, DaWei Gu, Ian Postlethwaite and Jianchi Chen
Abstract
—In this paper, two strategies for the design of
controllers based on a simplified LPV model of a UAV
(longitudinal flight dynamics) are presented. The simplified
LPV model is first derived from a UAV LPV model over the
entire range of the cruise speed. The dependence of the LPV
model on the varying parameter is reformulated in terms of a μ
synthesis problem. A straight μ design and a gainscheduling μ
control scheme have been considered. Simulation results of the
closed loop system comprising the controllers and original
statespace models are presented and compared.
I.
INTRODUCTION
ain scheduling is an important and intrinsic part of any
flight controller design process. While the classical
gainscheduling techniques use a family of equilibrium
operating points for obtaining the corresponding controllers,
the alternative continuous gain scheduling approach has
gained increasing attention in recent years. This approach
directly exploits the dependence of the linear statespace
models on the scheduling parameter. Such systems known as
Linear ParameterVarying (LPV) systems can be expressed
as:
()
() (
)
)
u
t
D
x
t
C
y
u
t
B
x
t
A
x
θ
+
=
+
=
&
(
1
)
where
θ
(t) is the varying parameter [1]. The main aim in the
control of LPV systems is to guarantee closedloop stability
and performance for all possible varying parameters. In
[2,3], the scaled small gain theorem is used for the design of
controllers for LPV systems that can be expressed in LFT
form. While [2,3] use a modification of the small gain
theorem to prove stability, performance in the sense of L
2
norm is guaranteed in
[4,5] by obtaining a single quadratic
Lyapunov function for all possible variations of the plant. It
is however assumed that the parameters enter the LPV
model in an affine fashion. In [6], the derivation technique is
extended using the bounded real lemma formulation of H
∞
performance. The controller is then obtained by solving a
system of Linear Matrix Inequalities (LMIs). Again the
parameter dependence is assumed to be affine and the time
varying parameter
θ
is assumed to vary over a polytope of
vertices. Recent approaches to controller synthesis for LPV
systems include the use of unstructured scaling matrices at
different vertices of the parameter region [7] and quadratic
LFT Lyapunov functions and fullblock multipliers [8].
Manuscript received March 8, 2006. This research work is supported by
the BAE Systems and UK Engineering and Physical Sciences Research
Council.
The authors are with the Department of Engineering, University of
Leicester, LE1 7RH, UK. Phone: +441162560; fax: +
44116
2522619
; email: dag@leicester.ac.uk.
While the satisfaction of robust stability and performance
for LPV systems is the ultimate goal in controller synthesis,
the modeling of LPV systems in itself is an important task.
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 Spring '11
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