In real-world applications, a nominal model is often used to approximate the design of an industrial system. This approximation could make the traditional design method less effective due to the existence of model uncertainty. In this paper, a novel stability-based approach is proposed to design the system ensuring robust stability under model uncertainty. First, the design variables and their variation bounds are configured to make the system stable. Then, a robust design is developed to incorporate system eigenvalues that are less sensitive to model uncertainty. Finally, the tolerance of the design space will be maximized under given performance constraints. A simulation example is conducted to demonstrate the effectiveness of the proposed robust design method.

1.
Choi
,
H. J.
, and
Allen
,
J. K.
, 2009, “
A Metamodeling Approach for Uncertainty Analysis of Nondeterministic Systems
,”
ASME J. Mech. Des.
0161-8458,
131
(
4
), p.
041008
.
2.
Lu
,
X. J.
, and
Li
,
H. X.
, 2009, “
Perturbation Theory Based Robust Design for Model Uncertainty
,”
ASME J. Mech. Des.
0161-8458,
131
(
11
), p.
111006
.
3.
Hong
,
Y. P.
, and
Li
,
H. X.
, 2003, “
Comparative Study of Fluid Dispensing Modeling
,”
IEEE Trans. Electron. Packag. Manuf.
1521-334X,
26
(
4
), pp.
273
280
.
4.
Liu
,
G. P.
, and
Patton
,
R. J.
, 1998,
Eigenstructure Assignment for Control System Design
,
Wiley
,
New York
.
5.
Blanco
,
A. M.
, and
Bandoni
,
J. A.
, 2003, “
Interaction Between Process Design and Process Operability of Chemical Processes: An Eigenvalue Optimization Approach
,”
Comput. Chem. Eng.
0098-1354,
27
(
8–9
), pp.
1291
1301
.
6.
Lu
,
X. J.
, and
Li
,
H. X.
, 2009, “
Stability Based Robust Eigenvalue Design for Tolerance
,”
ASME J. Mech. Des.
0161-8458,
131
(
8
), p.
081007
.
7.
El-Kady
,
M. A.
, and
Al-Ohaly
,
A. A.
, 1997, “
Fast Eigenvalue Sensitivity Calculations for Special Structures of Matrix Derivatives
,”
J. Sound Vib.
0022-460X,
199
(
3
), pp.
463
471
.
8.
Ralph
,
B.
, and
Stephen
,
G. N.
, 1989, “
Approaches to Robust Pole Assignment
,”
Int. J. Control
0020-7179,
49
(
1
), pp.
97
117
.
9.
Kautsky
,
J.
,
Nichols
,
N. K.
, and
Dooren
,
P. V.
, 1985, “
Robust Pole Assignment in Linear State Feedback
,”
Int. J. Control
0020-7179,
41
(
5
), pp.
1129
1155
.
10.
Hu
,
S.
, and
Wang
,
J.
, 2002, “
A Gradient Flow Approach to On-Line Robust Pole Assignment for Synthesizing Output Feedback Control System
,”
Automatica
0005-1098,
38
, pp.
1959
1968
.
11.
Ting
,
K. L.
, and
Long
,
Y. F.
, 1996, “
Performance Quality and Tolerance Sensitivity of Mechanisms
,”
ASME J. Mech. Des.
0161-8458,
118
(
1
), pp.
144
150
.
12.
Zhu
,
J. M.
, and
Ting
,
K. L.
, 2001, “
Performance Distribution Analysis and Robust Design
,”
ASME J. Mech. Des.
0161-8458,
123
(
1
), pp.
11
17
.
13.
Caro
,
S.
,
Bennis
,
F.
, and
Wenger
,
P.
, 2005, “
Tolerance Synthesis of Mechanisms: A Robust Design Approach
,”
ASME J. Mech. Des.
0161-8458,
127
(
1
), pp.
86
94
.
14.
Chen
,
W.
,
Allen
,
J. K.
,
Tsui
,
K. L.
, and
Mistree
,
F.
, 1996, “
A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors
,”
ASME J. Mech. Des.
0161-8458,
118
(
4
), pp.
478
493
.
15.
Li
,
M.
,
Azarm
,
S.
, and
Boyars
,
A.
, 2006, “
A New Deterministic Approach Using Sensitivity Region Measures for Multi-Objective Robust and Feasibility Robust Design Optimization
,”
ASME J. Mech. Des.
0161-8458,
128
, pp.
874
883
.
16.
Parkinson
,
A.
, 1995, “
Robust Mechanical Design Using Engineering Models
,”
ASME J. Mech. Des.
0161-8458,
117
, pp.
48
54
.
17.
Al-Widyan
,
K.
, and
Angeles
,
J.
, 2005, “
A Model-Based Formulation of Robust Design
,”
ASME J. Mech. Des.
0161-8458,
127
(
3
), pp.
388
396
.
18.
Choi
,
H.
,
Mcdowell
,
D. L.
,
Allen
,
J. K.
,
Rosen
,
D.
, and
Mistree
,
F.
, 2008, “
An Inductive Design Exploration Method for Robust Multiscale Materials Design
,”
ASME J. Mech. Des.
0161-8458,
130
, p.
031402
.
19.
Stewart
,
G. W.
, and
Sun
,
J. G.
, 1990,
Matrix Perturbation Theory
,
Academic
,
Boston, MA
.
You do not currently have access to this content.