Natural Frequency based Swing up of Rotary Inverted Pendulum and its Stabilization

This paper aims at the applications of natural frequency of inverted pendulum and Takagi-Sugeno (TS) fuzzy control in the swing up and stabilization of Rotary inverted pendulum (RIP) respectively. RIP is one of the important multivariable system in control to test the performance of any controller due to its nonlinear, unstable, non-minimum phase and under actuated nature. Many techniques based on state variable of pendulum are used for swing up of pendulum from down hanging position to vertical upright position. But a more simple way to swing up is based on natural frequency of pendulum. It can be calculated either experimentally or based on equation of time period of pendulum. During swing up pendulum change its direction at every half of time period of pendulum except very first time where it changes its direction at one fourth of its time period. If we apply constant control input to the arm of pendulum based on this time period, we can swing up the pendulum without any feedback from RIP system. The advantage of fuzzy logic controller is its aptitude to deal with nonlinearities, uncertainties without accurate mathematical model of the system. TS fuzzy controllers are close to gain scheduling approaches. Several linear controllers are defined, each valid in one particular region of the controller's input space. In between the swing up and stabilization a mode controller is used which is basically a condition check on the angle of the pendulum rod. Finally Simulink based experimental results are used to verify and validate the performance of the above controllers on RIP system.