Control of real time furuta inverted pendulum system with lqr and pole placement

Inverted Pendulum systems are an important engineering system used in the solution of many engineering problems and motion analysis with the application of control techniques. Real-time balancing of these systems has been very challenging and important for modern control theory. Studies on these systems shed light on the design and control algorithms of many systems ranging from automotive, aircraft, spatial vehicles, defense vehicles, missile launchers to human marches, load bearing robots and earthquake resistant building designs. Furuta-Pendulum is one of the most important basic systems used in control engineering. In this study, firstly, a mathematical model for the system was created. A mathematical model is a mathematical equation representing a process or the behavior of a system. The dynamic equations expressing these equations were obtained by Lagrange method. Furuta-Pendulum is a nonlinear system. The state-space model has been obtained by linearization of the obtained equations. State-space model is the expression of the differential equations of any system in the time domain by means of "state-space transformation". State equations and state variables were obtained by using State-Space model. In addition, the controllability and observability of the system were investigated depending on the state variables. In accordance with these observations, transfer function, characteristic equation, poles, zeros and singular points have been found in order to make the control analysis of Furuta-Pendulum system properly. The control analysis of the system was performed with these data. Afterwards, LQR (Linear Quadratic Regulator) control and Pole-Placement control algorithms were designed for real-time Furuta-Pendulum in the Robotics and Mechatronics Laboratory of Fırat University. Finally, the performance of these control methods designed and applied were examined and the necessary control analyzes were performed and the results were obtained.