LQR, LQG, Extremum Seeking and Sliding Mode controls combined with Fuzzy for a rotary inverted pendulum stabilization

This study considers the stabilization performance of a rotary type inverted pendulum (rotary inverted pendulum, RIP) using fuzzy control combined with linear quadratic regulator (LQR), linear quadratic Gaussian (LQG), extremum seeking and sliding mode controllers, respectively. Stability on the controlled systems is verified by a Lyapunov stability function. The performances of developed systems are visualized using Simscape Multibody in Matlab®’s environment. The control and statistical performances such as overshoot, root mean square, integral time absolute, integral square, and integral absolute errors are presented to show the success of the developed systems. This study mainly contributes to modeling the RIP with 3D visualization using Simscape Multibody to verify the success of the applied control schemes and to show the improvement of fuzzy control modified with some controls over the control techniques without fuzzy. In addition, the swing-up control scheme adopted the homoclinic orbit strategy and was presented via the hardware in the loop (HIL) mechanism.