Control of an Inverted Pendulum

It can be seen that for the tasks of stabilizing an inverted pendulum
located on a trolley, the LQR regulator demonstrated the highest efficiency
. This controller has excellent stability and is able
to effectively control non-linear systems. While modal
control requires detailed and careful parameter settings to achieve
the desired results, the LMI controller provides the ability to determine
the optimal degree of stability of the system, which makes it an attractive
choice in certain application situations.
A study of the LQG regulator was conducted, which successfully
stabilized the nonlinear system. This regulator was developed based on
a linear model, and despite its linear foundations, it has demonstrated
high efficiency in controlling a nonlinear system. Although using
a linear model greatly simplifies and reduces the necessary calculations, it
cannot provide an absolute guarantee of stability when working with
nonlinear systems, which highlights the potential limitations of this
approach.
The compensation task has been successfully solved: the regulator is effective
compensated for the effects of an external harmonic disturbance. Besides,
The tracking task has been completed, in which the controller accurately tracked and
corresponded to the set fluctuations of the system, thus ensuring accurate
compliance with the set motion parameters