NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

Figure 2.1: Photograph of Flexible Beam System
torque constant of .001 Nm/Amp. The motor served as the only input to the system,
however a strain gauge placed near the xed end of the exible beam senses the
beam's de ection, and an encoder on the motor senses the angular position the proof
mass. The strain gauge is calibrated to give 1 Volt per inch, and the encoder uses a
1024 count disc which in quadrature results in a resolution of 4096 counts/revolution.
The FBS can be mounted in two con gurations, with the exible beam vertically or
horizontally mounted. We choose to mount the beam horizontally so that gravity will
be acting perpendicular to the motion of the system, thus making stabilization more
di cult.
2.2 Derivation of the Mathematical Model
Obtaining an adequate mathematical model for the FBS, one that was not too
complex to be useful nor one that was too simple to be accurate, is a challenge. The
rst step is representing the physical system in a simpler way. Figure 2.2 shows a
simple mechanical model of the system. Here the rigid beam structure is modeled as a
single rigid beam with a point mass (m) located at one end and a motor at the other.
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