This paper addresses control of structural vibrations using semi-active actuators that are capable of manipulating stiffness and∕or producing variable stiffness. Usually vibration suppression is achieved using damping devices rather than stiffness ones. However, stiffness devices can produce large forces and have significant advantages for shock isolation purposes. In this work we use a passivity approach to establish the requirements for the control law for a structure equipped with semi-active stiffness devices. We also solve an optimal control problem that demonstrates that our passive, resetting feedback control law approximates the optimal control. Simulation and experimental results are presented in support of the proposed approach.

1.
Kobori
,
T.
, and
Kamagata
,
S.
, 1991, “
Dynamic Intelligent Buildings: Active Seismic Response Control
,”
Intelligent Structures; Monitoring and Control
,
Y. K.
Wen
, ed.,
Elsevier
,
New York
, pp.
279
282
.
2.
Onodo
,
J.
, and
Minesugi
,
K.
, 1996, “
Alternative Control Logic for Type-II Variable Stiffness System
,”
AIAA J.
0001-1452,
34
(
1
), pp.
207
209
.
3.
Patten
,
W. N.
, and
Sack
,
R. L.
, “
Semiactive Control of Civil Engineering Structures
,”
Proc. of 1994 ACC
,
Baltimore
,
Omnipress
,
Madison, WI
, pp.
1078
1082
.
4.
Bobrow
,
J. E.
,
Jabbari
,
F.
, and
Thai
,
K.
, 2000, “
A New Approach to Shock Isolation and Vibration Suppression Using a Resetable Actuator
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
122
, pp.
570
573
.
5.
Gavin
,
H. P.
,
Hanson
,
R. D.
, and
Filisko
,
F. E.
, 1996, “
Electro-Rheological Damper: 1. Analysis and Design, 2, Testing and Modeling
,”
ASME J. Appl. Mech.
0021-8936,
63
(
3
), pp.
669
682
.
6.
Gavin
,
H. P.
, 1997, “
The Effect of Particle Concentration Inhomogeneities on the Steady Flow of Electro- and Magneto-Rheological Materials
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
71
(
3
), pp.
165
182
.
7.
Wang
,
X. J.
, and
Gordaninejad
,
F.
, 1999, “
Flow Analysis of Field-Controllable, Electro- and Magneto-Rheological Fluids Using Herschel-Bulkley Model
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
10
(
8
), pp.
601
608
.
8.
Dyke
,
S. J.
,
Spencer
,
B. F.
,
Sain
,
M. K.
, and
Carlson
,
J. D.
, “
Seismic Response Reduction Using Magneto-Rheological Dampers
,”
Proc. of the 1996 IFAC 13th Congress
,
San Francisco
,
Elsevier
,
New York
, pp.
145
150
.
9.
Utkin
,
V. I.
, 1977, “
Variable Structure Systems With Sliding Modes
,”
IEEE Trans. Autom. Control
0018-9286,
22
(
2
), pp.
212
222
.
10.
Nemir
,
D.
,
Lin
,
Y.
, and
Osegueda
,
R.
, 1994, “
Semi-Active Motion Control Using Variable Stiffness
,”
Adv. Environ. Res.
1093-0191,
12
(
4
), pp.
1291
1306
.
11.
Bobrow
,
J. E.
,
Jabbari
,
F.
, and
Thai
,
K.
, 1995, “
An Active Element and Control Law for Vibration Suppression
,”
Smart Mater. Struct.
0964-1726, pp.
264
269
.
12.
Bobrow
,
J. E.
, “
High Performance Damping With a Semi-Active Spring
,”
1997 ASME Design Technical Conferences
, Sacramento, Sept., ASME Paper No. DETC97∕VIB-3826.
13.
Ramaratnam
,
A.
,
Jalili
,
N.
, and
Dawson
,
D. M.
, 2004, “
Semi-Active Vibration Control Using Piezoelectric Based Switched Stiffness
,” ACC04, Boston, June, pp.
5461
5466
.
14.
Yang
,
J. N.
,
Li
,
Z.
, and
Wu
,
J. C.
, 1996, “
Control of Seismic Excited-Buildings Using Active Variable Stiffness System
,”
Eng. Struct.
0141-0296,
18
(
8
), pp.
589
596
.
15.
Leitmann
,
G.
, and
Reithmeirer
,
E.
, 1993, “
Semiactive Control of a Vibrating System by Means of Electro-Rheological Fluids
,”
Dyn. Control
0925-4668,
3
(
1
), pp.
7
34
.
16.
Jabbari
,
F.
, and
Bobrow
,
J. E.
, 2002, “
Vibration Suppression with a Resetable Device
,”
J. Eng. Mech.
0733-9399,
128
(
9
), pp.
916
924
.
17.
Leavitt
,
J. L.
,
Bobrow
,
J. E.
,
Jabbari
,
F.
, and
Yang
,
J. N.
, 2005, “
Application of a High-Pressure Gas Semi-Active Resetable Damper to the Benchmark Smart Base-Isolated Buildings
,”
Journal of Structural Control and Health Monitoring
, Vol. 13, pp.
748
757
.
18.
Leavitt
,
J.
, “
Motion Sensing and Control of a Pneumatically Actuated Hopping Robot and a Semi-Active Vibration Damper
,” Ph.D. dissertation, University of California, Irvine, October 2006.
19.
Yang
,
J. N.
,
Bobrow
,
J. E.
,
Jabbari
,
F.
,
Leavitt
,
J. L.
,
Cheng
,
C. P.
, and
Lin
,
P. Y.
, “
Full Scale Experimental Verification of Resetable Semi-Active Stiffness Dampers
,” Journal of Earthquake Engineering and Structural Dynamics (submitted).
20.
McDonell
,
B.
, and
Bobrow
,
J.
, 1998, “
Modeling, Identification, and Control of a Pneumatically Actuated, Force Controllable Robot
,”
IEEE Trans. Rob. Autom.
1042-296X,
14
, pp.
732
742
.
21.
Dunn
,
J. C.
, and
Bertsekas
,
D. P.
, 1989, “
Efficient Dynamic Programming Implementations of Newton’s Method for Unconstrained Optimal Control Problems
,”
J. Optim. Theory Appl.
0022-3239,
63
(
1
), pp.
23
38
.
22.
Athans
,
M.
, and
Falb
,
P. L.
, 1966,
Optimal Control; An Introduction to the Theory and Its Applications
,
Mcgraw-Hill
,
New York
.
23.
Khalil
,
H. K.
, 1996,
Nonlinear Systems
,
2nd ed.
,
Ptrentice-Hall
,
Englewood Cliffs, NJ
.
24.
Beker
,
O.
,
Hollot
,
C. V.
,
Chait
,
Y.
, and
Han
,
H.
, 2004, “
Fundamental Properties of Reset Control Systems
,”
Automatica
0005-1098,
40
, pp.
905
916
.
25.
Inaudi
,
J. A.
,
Leitmann
,
G.
, and
Kelly
,
J. M.
, 1994, “
Single Degree of Freedom Nonlinear Homogeneous Systems
,”
J. Eng. Mech.
0733-9399,
120
(
7
), pp.
1543
1562
.
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