  The scope of inverted pendulum has been widely studied as one of the notable
research with respect to standing in balance. The concept of this pendulum is
similar to missile guidance, meaning that the center of drag is ahead that of
gravity. Mathematical model of inverted pendulum on a cart is moreover
presented in this paper. Various rewarding parameters are proposed from the
displacement of the pivot, angular rotation, to external force exerted on the
carriage so as to gain its equilibrium points and the linearized systems. Due
to the severe risk of instability, a reliable closed-loop state feedback
controller is designed to stabilize in upright position, even with large
deviations. The specific concept proposed is to apply the canonical form of
computing the determinant of gain $K$ leading to $K_d$. The results show that
the constructed design can maintain the stability of the system by applying
three sorts of initial condition and choosing sampling time $T$ under $0.2$
with small possible degrading performance.
