This paper presents experimental investigation results of an electric variable valve timing (EVVT) actuator using linear parameter varying (LPV) system identification and control. For the LPV system identification, a number of local system identification tests were carried out to obtain a family of linear time-invariant (LTI) models at fixed engine speed and battery voltage. Using engine speed and battery voltage as time-varying scheduling parameters, the family of local LTI models is translated into a single LPV model. Then, a robust gain-scheduling (RGS) dynamic output-feedback (DOF) controller with guaranteed H performance was synthesized and validated experimentally. In contrast to the vast majority of gain-scheduling literature, scheduling parameters are assumed to be polluted by measurement noises and the engine speed and battery voltage are modeled as noisy scheduling parameters. Experimental and simulation results show the effectiveness of the developed approach.

References

References
1.
Moriya
,
Y.
,
Watanabe
,
A.
,
Uda
,
H.
,
Kawamura
,
H.
,
Yoshioka
,
M.
, and
Adachi
,
M.
,
1996
, “
A Newly Developed Intelligent Variable Valve Timing System-Continuously Controlled Cam Phasing as Applied to a New 3 Liter Inline 6 Engine
,”
SAE
Paper No. 960579.
2.
Rugh
,
W. J.
, and
Shamma
,
J. S.
,
2000
, “
Research on Gain Scheduling
,”
Automatica
,
36
(
10
), pp.
1401
1425
.
3.
White
,
A.
,
Ren
,
Z.
,
Zhu
,
G.
, and
Choi
,
J.
,
2013
, “
Mixed H2/H∞ Observer-Based LPV Control of a Hydraulic Engine Cam Phasing Actuator
,”
IEEE Trans. Control Syst. Technol.
,
21
(
1
), pp.
229
238
.
4.
Ren
,
Z.
, and
Zhu
,
G. G.
,
2011
, “
Integrated System ID and Control Design for an IC Engine Variable Valve Timing System
,”
ASME J. Dyn. Syst. Meas. Control
,
133
(
2
), pp.
1
10
.
5.
Ren
,
Z.
, and
Zhu
,
G. G.
,
2009
, “
Pseudorandom Binary Sequence Closed-Loop System Identification Error With Integration Control
,”
J. Syst. Control Eng.
,
223
(6), pp.
877
884
.
6.
Oliveira
,
R. C.
, and
Peres
,
P. L.
,
2009
, “
Time-Varying Discrete-Time Linear Systems With Bounded Rates of Variation: Stability Analysis and Control Design
,”
Automatica
,
45
(
11
), pp.
2620
2626
.
7.
Caigny
,
J.
,
Camino
,
J.
,
Oliveira
,
R.
,
Peres
,
P.
, and
Swevers
,
J.
,
2010
, “
Gain Scheduled H2 and H∞ Control of Discrete-Time Polytopic Time-Varying Systems
,”
IET Control Theory Appl.
,
4
(
3
), pp.
362
380
.
8.
Wei
,
X.
, and
del Re
,
L.
,
2007
, “
Gain Scheduled H∞ Control for Air Path Systems of Diesel Engines Using LPV Techniques
,”
IEEE Trans. Control Syst. Technol.
,
15
(
3
), pp.
406
415
.
9.
Lee
,
M.
, and
Sunwoo
,
M.
,
2012
, “
Modelling and H∞ Control of Diesel Engine Boost Pressure Using a Linear Parameter Varying Technique
,”
J. Automob. Eng.
,
226
(
2
), pp.
210
224
.
10.
Postma
,
M.
, and
Nagamune
,
R.
,
2012
, “
Air-Fuel Ratio Control of Spark Ignition Engines Using a Switching LPV Controller
,”
IEEE Trans. Control Syst. Technol.
,
20
(
5
), pp.
1175
1187
.
11.
Chen
,
X.
,
Wang
,
Y.
,
Haskara
,
I.
, and
Zhu
,
G.
,
2014
, “
Optimal Air-to-Fuel Ratio Tracking Control With Adaptive Biofuel Content Estimation for LNT Regeneration
,”
IEEE Trans. Control Syst. Technol.
,
22
(
2
), pp.
428
439
.
12.
Zhang
,
F.
,
Grigoriadis
,
K. M.
,
Franchek
,
M. A.
, and
Makki
,
I. H.
,
2008
, “
Transient Lean Burn Air-Fuel Ratio Linear Parameter-Varying Control Using Input Shaping
,”
Int. J. Model. Identif. Control
,
3
(
3
), p.
318
.
13.
Zhang
,
F.
,
Grigoriadis
,
K. M.
,
Franchek
,
M. A.
, and
Makki
,
I. H.
,
2007
, “
Linear Parameter-Varying Lean Burn Air-Fuel Ratio Control for a Spark Ignition Engine
,”
ASME J. Dyn. Syst. Meas. Control
,
129
(
4
), pp.
404
414
.
14.
Zope
,
R. A.
,
2011
, “
Model-Based Estimation and Control in Spark Ignition Engines Using LPV Techniques
,”
Ph.D. dissertation
, University of Houston, Houston, TX.http://gradworks.umi.com/35/00/3500063.html
15.
White
,
A.
,
Zhu
,
G.
, and
Choi
,
J.
,
2011
, “
Hardware-in-the-Loop Simulation of Robust Gain-Scheduling Control of Port-Fuel-Injection Processes
,”
IEEE Trans. Control Syst. Technol.
,
19
(
6
), pp.
1433
1443
.
16.
Lu
,
B.
, and
Wu
,
F.
,
2004
, “
Switching LPV Control Designs Using Multiple Parameter-Dependent Lyapunov Functions
,”
Automatica
,
40
(
11
), pp.
1973
1980
.
17.
Daafouz
,
J.
,
Bernussou
,
J.
, and
Geromel
,
J.
,
2008
, “
On Inexact LPV Control Design of Continuous Time Polytopic Systems
,”
IEEE Trans. Autom. Control
,
53
(
7
), pp.
1674
1678
.
18.
Sato
,
M.
, and
Peaucelle
,
D.
,
2013
, “
Gain-Scheduled Output-Feedback Controllers Using Inexact Scheduling Parameters for Continuous-Time LPV Systems
,”
Automatica
,
49
(
4
), pp.
1019
1025
.
19.
Sato
,
M.
,
2010
, “
Gain-Scheduled State-Feedback Controllers Using Inexactly Measured Scheduling Parameters: Stabilizing and H∞ Control Problems
,”
SICE J. Control Meas. Syst. Integr.
,
3
(
4
), pp.
285
291
.
20.
Al-Jiboory
,
A. K.
,
Zhu
,
G.
, and
Choi
,
J.
,
2016
, “
Guaranteed Performance State-Feedback Gain-Scheduling Controllers With Uncertain Scheduling Parameters
,”
ASME J. Dyn. Syst. Meas. Control
,
138
(
1
), p.
014502
.
21.
Sato
,
M.
,
2016
, “
Gain-Scheduled Model-Matching Flight Controller Using Inexact Scheduling Parameters
,”
IFAC-PapersOnLine
,
49
(
17
), pp.
88
93
.
22.
Al-Jiboory
,
A. K.
, and
Zhu
,
G.
,
2016
, “
Robust Gain-Scheduling Control With Guaranteed Performance
,”
Tenth IFAC Symposium on Nonlinear Control Systems
(
NOLCOS
), Monterey, CA, Aug. 23–25, Paper No. WeB01.2
23.
Ren
,
Z.
, and
Zhu
,
G. G.
,
2014
, “
Modeling and Control of an Electric Variable Valve Timing System
,”
ASME J. Dyn. Syst. Meas. Control
,
136
(
2
), p.
021015
.
24.
Ljung
,
L.
,
1998
,
System Identification
,
Springer
, New York.
25.
Codrons
,
B.
,
Anderson
,
B. D.
, and
Gevers
,
M.
,
2002
, “
Closed-Loop Identification With an Unstable or Nonminimum Phase Controller
,”
Automatica
,
38
(
12
), pp.
2127
2137
.
26.
Zhu
,
G. G.
,
Skelton
,
R. E.
, and
Li
,
P.
,
1995
, “
Q-Markov Cover Identification Using Pseudo-Random Binary Signals
,”
Int. J. Control
,
62
(
6
), pp.
1273
1290
.
27.
Zhu
,
G. G.
,
2000
, “
Weighted Multirate q-Markov Cover Identification Using PRBS—An Application to Engine Systems
,”
Math. Probl. Eng.
,
6
(
2–3
), pp.
201
224
.
28.
Yang
,
J. J.
,
Zhang
,
S.
,
Song
,
R.
, and
Zhu
,
G. G.
,
2015
, “
LPV Model Identification of an EVVT System
,”
American Control Conference
(
ACC
), Chicago, IL, July 1–3, pp.
4723
4728
.
29.
Lacerda
,
M. J.
,
Tognetti
,
E. S.
,
Oliveira
,
R. C.
, and
Peres
,
P. L.
,
2016
, “
A New Approach to Handle Additive and Multiplicative Uncertainties in the Measurement for H∞ LPV Filtering
,”
Int. J. Syst. Sci.
,
47
(
5
), pp.
1042
1053
.
30.
Agulhari
,
C. M.
,
de Oliveira
,
R. C. L. F.
, and
Peres
,
P. L. D.
,
2012
, “
Robust LMI Parser: A Computational Package to Construct LMI Conditions for Uncertain Systems
,”
XIX Brazilian Conference on Automation
(
CBA
), Paraiba, Brazil, Sept. 3, pp.
2298
2305
.http://www.eletrica.ufpr.br/anais/cba/2012/Artigos/99195.pdf
31.
Löfberg
,
J.
,
2004
, “
YALMIP: A Toolbox for Modeling and Optimization in MATLAB
,” IEEE International Symposium on Computer Aided Control Systems Design (
CACSD
), New Orleans, LA, Sept. 2–4, pp.
284
289
.
32.
Sturm
,
J.
,
1999
, “
Using SeDuMi 1.02, A MATLAB Toolbox for Optimization Over Symmetric Cones
,”
Optim. Methods Software
,
11
(
1–4
), pp.
625
653
.
33.
Oliveira
,
R. C. L. F.
,
Bliman
,
P.
, and
Peres
,
P. L. D.
,
2008
, “
Robust LMIs With Parameters in Multi-Simplex: Existence of Solutions and Applications
,”
47th IEEE Conference on Decision and Control
(
CDC
), Cancun, Mexico, Dec. 9–11, pp.
2226
2231
.
34.
Chesi
,
G.
,
Garulli
,
A.
,
Tesi
,
A.
, and
Vicino
,
A.
,
2007
, “
Robust Stability of Time-Varying Polytopic Systems Via Parameter-Dependent Homogeneous Lyapunov Functions
,”
Automatica
,
43
(
2
), pp.
309
316
.
35.
Tóth
,
R.
,
2010
, “
Discretization of LPV Systems
,”
Modeling and Identification of Linear Parameter-Varying Systems
,
Springer
, Berlin, pp.
143
169
.
This content is only available via PDF.
You do not currently have access to this content.