NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

compared to the uncontrolled oscillator, and to require limited control e ort. A
passivity-based control design is also described that uses the control to simulate a
damped pendulum absorber. The International Journal of Robust and Nonlinear
Control published a special issue devoted exclusively to the NLBP (volume 8, 1998)
and the 1995 American Control Conference contained an invited session in which six
papers were submitted on the topic of the Nonlinear Benchmark Problem.
The literature devoted to the TORA system was used as the basis for the
designs presented in this thesis. In particular, the passivity-based control strategy
comes mainly from the implementation described in [9], while a more complete ex-
planation of passivity-based control of Euler-Lagrange systems can be found in [10]
or in [11]. The integrator backstepping controller was mainly derived from [1] where
they supply the necessary variable substitutions and transformations to derive acas-
cade controller. It should be noted that the cascade controller presented in [1] is
almost identical to the one derived in this thesis, and this controller is a special case
of the full controller one obtains using integrator backstepping as described in [12].
The linearized optimal H 2 controller was derived by the well known solution to the
Riccati equation. A concise overview of the theory and application of optimal linear
control can be found in [13]. The linearized H1 controller was also designed by the
well known robust control technique as described in Chapter 6 of [14].
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