NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

It is seen in Figure 4.23 that the performance of the nonlinear H1 solution
and the nonlinear H 2 solution provide similar performance, with the robust design
being slightly inferior, similar to the linearized case. The question becomes now,
what exactly is gained by using such 'robust' design methodologies? As is shown
in Chapter 5, the H1 designs do provide better performance on the hardware, a
vindication of robust design methodology.
4.3 Tabulated Results
Table 4.1 shows how the numbers compare for the various control strate-
gies. The linearized H 2 was easily the best performer, while the passivity-based
control yielded the worst results. The backstepping algorithm was the best oscillation
damper, despite its high rst-state energy, but it also used a lot more control e ort
than the other designs. Disappointingly, the nonlinear control laws do not particu-
larly stand out as notably superior to the linearized ones: perhaps the TORA system
is too easily stabilized and not appropriate for a nonlinear benchmark problem.
Table 4.1: Tabular Comparison of Simulated Results
LQR Lin. H1 PBC Backstep HJB HJI
R y(t) 2 dt(cm 2 ) 3.06 5.72 11.2 6.03 4.12 5.28
R u(t) 2 dt(V 2 ) 4.05 4.39 .945 21.12 4.5 1.366
4.4 Tuning and Ease of Implementation
The easiest controls to tune are the linearized optimal control laws. Both LQR
and the optimal H1 require only the adjustment of the weighting matrix Q, and to
rapidly test the new values is as simple as loading the new feedback gain vector, Kc,
onto the software workspace. These controls are also the easiest to implement, as they
require only the linearization of the state-space model, and the solution of a Riccati
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