© The Institution of Engineering and Technology
Controllers in the linear parameter-varying (LPV) framework are commonly designed in continuous time (CT) requiring accurate and low-order CT models of the system. However, identification of CT-LPV models is largely unsolved, representing a gap between the available LPV identification methods and the needs of control synthesis. In order to bridge this gap, direct identification of CT-LPV systems in an input–output setting is investigated, focusing on the case when the noise part of the data generating system is an additive discrete-time (DT) coloured noise process. To provide consistent model parameter estimates in this setting, a refined instrumental variable (IV) approach is proposed and its properties are analysed based on the prediction-error framework. The benefits of the introduced direct CT-IV approach over identification in the DT case are demonstrated through a representative simulation example inspired by the Rao–Garnier benchmark.
References
-
-
1)
-
R. Johansson
.
Identification of continuous–time models.
IEEE Trans. Signal Process.
,
4 ,
3887 -
897
-
2)
-
R. Pintelon ,
J. Schoukens ,
Y. Rolain
.
Box–Jenkins continuous–time modeling.
Automatica
,
7 ,
983 -
991
-
3)
-
G.C. Goodwin ,
S. Graebe ,
M.E. Salgado
.
(2001)
Control system design.
-
4)
-
L. Ljung
.
(1999)
System identification: theory for the user.
-
5)
-
H. Gariner ,
M. Mensler ,
A. Richard
.
Continuous-time model identification from sampled data: implementation issues and performance evaluation.
Int. J. Control
,
13 ,
1337 -
1357
-
6)
-
Tóth, R., Heuberger, P.S.C., Van den Hof, P.M.J.: `Flexible model structures for LPV identification with static scheduling dependency', Forty-Seventh IEEE Conf. on Decision and Control, December 2008, Cancun, Mexico, p. 4522–4527.
-
7)
-
M.G. Wassink ,
M. van de Wal ,
C.W. Scherer ,
O. Bosgra
.
LPV control for a wafer stage: beyond the theoretical solution.
Control Eng. Pract.
,
231 -
245
-
8)
-
Østergaard, K.Z., Stousturp, J., Barth, P.: `Rate bounded linear parameter varying control of a wind turbine in full load operation', 17thIFAC World Congress, July 2008, Seoul, Korea.
-
9)
-
R. Tóth
.
(2010)
Modeling and identification of linear parameter-varying systems.
-
10)
-
F. Wu ,
K. Dong
.
Gain-scheduling control of LFT systems using parameter-dependent Lyapunov functions.
Automatica
,
39 -
50
-
11)
-
K. Zhou ,
J.C. Doyle
.
(1997)
Essentials of robust control.
-
12)
-
R. Murray-Smith ,
T.A. Johansen ,
R. Shorten
.
On the interpretation of local models in blended multiple model structures.
Int. J. Control
,
620 -
628
-
13)
-
Ljung, L.: `Experiments with identification of continuous-time models', Fifteenth IFAC Symp. on System Identification, July 2009, Saint-Malo, France.
-
14)
-
A. Marcos ,
G.J. Balas
.
Development of linear-parameter-varying models for aircraft.
J. Guid. Control Dyn.
,
2 ,
218 -
228
-
15)
-
M. Campi ,
T. Sugie ,
F. Sakai
.
An iterative identification method for linear continuous-time systems.
IEEE Trans. Autom. Control
,
7 ,
1661 -
1669
-
16)
-
Tóth, R., Felici, F., Heuberger, P.S.C., Van den Hof, P.M.J.: `Discrete time LPV I/O and state space representations, differences of behavior and pitfalls of interpolation', European Control Conf., July 2007, Kos, Greece, p. 5418–5425.
-
17)
-
T. Söderström ,
P. Stoica
.
(1983)
Instrumental variable methods for system identification.
-
18)
-
Laurain, V., Gilson, M., Garnier, H., Young, P.C.: `Refined instrumental variable methods for identification of Hammerstein continuous-time Box-Jenkins models', Forty-Seventh IEEE Conf. on Decision and Control, December 2008, Cancun, Mexico.
-
19)
-
K.E. Atkinson
.
(1989)
An introduction to numerical analysis.
-
20)
-
Ljung, L.: `Initialisation aspects for subspace and output-error identification methods', European Control Conf. (ECC'2003), September 2003, Cambridge, UK.
-
21)
-
G. Rao ,
H. Garnier
.
Identification of continuous-time systems: direct or indirect?.
Syst. Sci.
,
3 ,
25 -
50
-
22)
-
Tóth, R., Lovera, M., Heuberger, P.S.C., Van den Hof, P.M.J.: `Discretization of linear fractional representations of LPV systems', Forty-Eighth IEEE Conf. on Decision and Control, December 2009, Shanghai, China, p. 7424–7429.
-
23)
-
R. Tóth ,
P.S.C. Heuberger ,
P.M.J. Van den Hof
.
Discretisation of linear parameter-varying state-space representations.
IET Control Theory Appl.
,
10 ,
2082 -
2096
-
24)
-
P. Apkarian ,
P. Gahinet
.
A convex characterization of gain-scheduled H∞ controllers.
IEEE Trans. Autom. Control
,
5 ,
853 -
864.
-
25)
-
Wijnheijmer, F., Naus, G., Post, W., Steinbuch, M., Teerhuis, P.: `Modeling and LPV control of an electro-hydraulic servo system', IEEE Int. Conf. on Control Applications, October 2006, Munich, Germany, p. 3116–3120.
-
26)
-
H. Garnier ,
L. Wang
.
(2008)
Identification of continuous-time models from sampled data.
-
27)
-
P.C. Young
.
The refined instrumental variable method: unified estimation of discrete and continuous-time transfer function models.
J. Eur. Syst. Autom.
,
149 -
179
-
28)
-
G.P. Rao ,
H. Unbehauen
.
Identification of continuous-time systems.
IEE Proc., Control Theory Appl.
,
2 ,
185 -
219
-
29)
-
Dettori, M., Scherer, C.: `LPV design for a CD player: an experimental evaluation of performance', Fortieth IEEE Conf. on Decision and Control, December 2001, Orlando, Florida, USA, p. 4711–4716.
-
30)
-
V. Laurain ,
M. Gilson ,
R. Tóth ,
H. Garnier
.
Refined instrumental variable methods for identification of LPV box-jenkins models.
Automatica
,
6 ,
959 -
967
-
31)
-
P.C. Young
.
(1984)
Recursive estimation and time-series analysis.
-
32)
-
M. Gilson ,
P. Van den Hof
.
Instrumental variable methods for closed-loop system identification.
Automatica
,
2 ,
241 -
249
-
33)
-
M. Gilson ,
H. Garnier ,
P.C. Young ,
P. Van den Hof
.
Optimal instrumental variable method for closed-loop identification.
IET Control Theory Appl.
-
34)
-
P. Young ,
H. Garnier ,
M. Gilson ,
H. Garnier ,
L. Wang
.
(2008)
Refined instrumental variable identification of continous-time hybrid Box–Jenkins models, Identification of continuous-time models from sampled data.
-
35)
-
Rao, G., Garnier, H.: `Numerical illustrations of the relevance of direct continuous-time model identification', Fifteenth IFAC World Congress, 2002, Barcelona, Spain.
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