ANALISIS KETEROBSERVASIAN SISTEM GERAK KERETA SEDERHANA DENGAN DUA PENDULUM TERBALIK

Amanto Amanto

Abstract


There are three main consepts in mathematical system theory, which are : stability, controllability, and
observability. In this paper we will focus on observability. Given time-invariant differential systems
x& = Ax + Bu, y = Cx + Du ; with x n m Î R ,u Î R and p y Î R and we will be indicated the system by (A,B,C,D).
Observability is completely determined by the matrices A and C and therefore we will discuss the
observability of the pair (C,A). The system (A,B,C,D) is observable if and only if the observability matrix,
[ n ]T W C CA CA CA 2 1 = ... - has rank = n. In the case of a single output system, W is square matrix, then (C,A)
is observable if W is non singular. Moreover, we will investigate observability of system of motion cart
with inverted pendulums. The result, the system is observable.
Keywords: Observable, observability matrix, pendulums.

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