| Summary: | <p> The discipline of control engineering has been applied for thousands of years. As long as humans have needed a system to vary automatically, different devices, electronics and algorithms have been designed to attain system control and stability. This study intends on implementing the theory developed my mathematicians such as Henri Poincaré, Aleksandr Lyapunov, Rudolf E. Kálmán and many others in an attempt to stabilize an unstable system: a cart and inverted pendulum. In order to stabilize the inverted pendulum system, control designs consisting of both classical and modern approaches will be explored to design effective PID and LQR controllers. Furthermore, an adaptive controller will be designed as well for a one-degree-of-freedom unstable system. For accurate control design, linear and non-linear system identification techniques will be used to attain mathematical dynamic system models. Multiple tuning techniques will be utilized to achieve the most stable system possible. A micro-processor (Arduino) will be used in conjunction with a computer for data communication and digital control algorithms. The utilization of an Arduino will require the design and implementation of digital control systems, digital tuning techniques, and digital filtering. If successful, the implemented theory will result in the stabilization of a multiple degree of freedom system with chaotic potential.</p>
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