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Inverted Pendulum Modeling and Control

In this research shows to stabilize a Inverted Pendulum. Primarily, there are two control problems: the cart's position and the pendulum's angle in the inverted positions. Stabilization of Inverted pendulum System can be accomplished through several methods. We did LQR, PID(trial and error method, Zieger-Nichols Method, Relay Autotuning). First of all, Equations of Inverted Pendulum System are non-linearity equations. So, We must linearize the Inverted Pendulum System equations. We dealed with in two ways. First, The linearization Using Jacobian matrix at Lagrange’s Equation. Second, The linearization Using Taylor series and They are expressed as the Transfer function and State-Space equation. And then we add the dynamics of the DC-motor to equation. We did control angle of the Inverted pendulum using PID method at the Transfer function. Because Transfer Function is difficult to express the MIMO system. And then We did control of the angle of the Inverted pendulum and position of cart using LQR method at the State-Space equation. We did the simulation for the Inverted Pendulum System using MATLAB M-file and Simulink and compared the specification performance between PID controller and LQR controller. Finally, We tried to make Cart Type. But Cart Type was so unstable. We changed a plan to make ​​the Linear Type. We made the Inverted Pendulum(Linear Type) using the PID control. So, Actually We had to only controlled the angle of the pendulum. A detailed description of the code is to be posted on NAVER blog and Github. Github - https://github.com/angelkim88 NAVER blog - https://blog.naver.com/angelkim88