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be adjusted and Eqs.(17)-(19) should be used. In this connection, the function "MINCX" in the LMI
toolbox of MATLAB can be used conveniently to design both KfcB-EB and HaB-PB controllers.
APPLICATION TO BENCHMARK CABLE-STAYED BRIDGE
A benchmark model for a cable-stayed bridge has been established [Dyke et al (2002)] in order to
investigate the effectiveness of control systems during an episode of earthquake. The benchmark
cable-stayed bridge is the Missouri 74-fllinois 146 bridge spanning the Mississippi River near Girardau,
Missouri, and a schematic drawing of the bridge is shown in Fig.l. A control system has been suggested
and a sample LQG controller has been worked out in the benchmark paper to serve as a reference for the
comparison of control performances with that of the other control strategies. In this control system,
actuators are installed between the deck and two towers (a total of 4 locations) as well as between the
deck at both ends and the pier and abutment, respectively. A total of 24 hydraulic actuators are installed
symmetrically with respect to the centerline of the bridge at a total of 8 locations as shown by the dotted
areas in Fig.2. The number of actuators installed at each location is indicated in parentheses next to the
dotted area. All actuators are identical and each has a capacity of lOOOkN. Three earthquakes records
have been considered as the input excitations in the longitudinal direction of the bridge, i.e., El Centro
NS, Gebze NS and Mexico earthquakes.
The performance indices are defined by Jj to Jig, where Jj = maxi. base shear of tower; ^2 = maxi.
deck shear; Js = maxi. base moment of tower; 14 = maxi. deck moment; Js = maxi. cable force deviation;
Jg = maxi. deck displacement; Jy = norm base shear of tower; Jg - norm deck shear; 19 = norm base
moment of tower; JIQ = norm deck moment; Jn= norm cable force deviation; Ji2~ maxi. control force;
Jn = maxi. actuator stroke; Ji4= maxi. actuator power; ]\s= total actuator power; Jig = number of
actuators; Jn = number of sensors; and Jig = control resources. The norm Ml of a response quantity is
-468' -1150' -468' 1870'
I
I
Bent 1 Pier 2
to
I
I
Pier 3 Pier 4
Fig. 1: Drawing of the Cape Girardeau Bridge [Drawing Courtesy of Dyke et al (2002)].
/Protective Devices
Ill ( 2 )
S:S ( 4 )^— Number of Ac;tuators N ted (4) w mN V^l^:
Illinois> Approach " ^
Bentl Pier 2 Pier 3
Fig. 2: Locations of Protective Devices in the Cable-Stayed Bridge.