  In this work we present a workflow for designing two linear control
techniques applied to the dynamic system quadruple inverted pendulum mounted on
a cart (QIP) where the steady state error on cart position is eliminated
through a precompensation gain. The first control law designed was based on
LQR, technique that stabilizes the system states based on a minimization of the
total energy of the system states and the second control technique was pole
placement by 2nd order system approximation, this method allowed to define a
settling time and overshoot of the desired response of the plant, for this
control the system was considered SISO, being the only output of the plant the
horizontal position of the cart. To eliminate the steady-state error generated
by both linear controllers, an analysis of the stationary response of the
system under control in the Laplace Domain was performed. The simulation
environment used to validate the results presented in this paper was Simscape
of Matlab, it is a simulation environment that allowed to simulate the dynamic
of nonlinear mechanical systems. The results obtained indicate that both
controllers are able to stabilize the plant and move the cart position to the
desired setpoint. Finally, we discuss about the performances of both linear
control techniques.
