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Design of a linear feedback control system for an Inverted Pendulum

Michailidis Sokratis

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Summary

The objective of this thesis is the study of the inverted pendulum system. For this, a bibliographic analysis was carried out on subjects similar to that of the inverted pendulum problem and the mathematical model of such a system was developed. Thus, it was possible to carry out simulations for the non-linear model. In these simulations, different scenarios were carried out to study the behavior of the pendulum without the presence of control. Afterwards, the model was linearized and configured in a state space model so that the corresponding simulations could be carried out as well. Then, the open-loop and closed-loop models were developed. In the closed-loop model, simulations and comparisons between different ways of constructing controllers were carried out. The simulations were performed in the presence of discrete time and an observer. The programming environment used is Matlab. The controllers designed and compared are linear feedback controller and quadratic linear controller. From the simulations carried out it was realized that the quadratic linear controller is more efficient as it takes into account the energy consumption, but at the same time the deviation of the system from the desired position. Also, in the presence of discrete time, the differences in controller design and the differences in the input signals of the systems were noticed compared to the presence of continuous time. The presence of the observer helped to predict the state of the system through the output and input of the system. From the simulations carried out it was possible to compare the responses of the system without an observer and the system with an observer.

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