Linear Quadratic Regulators Optimal Control of Rotary Double Parallel Inverted Pendulum

In this research, a new kind of first-order rotary inverted pendulum system is proposed. This new model, which is not popularly considered, is rotary double parallel inverted pendulum (RDPIP). This model is constructed by adding one more link parallel to the old link, which is placed at the ends of the arm. The RDPIP is not only rarely considered in reality but also in simulation. Due to the complexity of RDPIP, it is a far less researched subject than other pendulum models such as RIP, RDSIP, etc., and it is also difficult to find documents about RDPIP. So, this research will focus on studying the mathematical equations of RDPIP and applying the LQR controller to balance this model in Matlab/Simulink toolbox.