Errata: In Example 6.8, the state error should be \xi and the input should be F
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Location: page 192, line 4-14
The symbol z represents both the system state and the state error, and the symbol u should be the input forces F. The correct text should read
Lettingand
, the linearized system is given by
It can be verified that the system is reachable.
To compute a linear quadratic regulator for the system, we write the cost function as
where
and
. We begin with diagonal matrices for the state and input costs:
This gives a control law of the form
, which can then be used to derive the control law in terms of the original variables:
As computed in Example 5.4, the equilibrium points have
and
.
(Contributed by C.-H. Choi, 7 Dec 2010)
