Stabilization of Double Inverted Pendulum (DIP) on a Cart using Optimal Adaptive Sliding Mode Control (OASMC)

The potential application of an inverted pendulum in different domains is the primary source of motivation for researchers to initiate innovative and new development. A DIP system is a nonlinear, inherently unstable, and underactuated system. It has a single input and multiple outputs. The mathematical model of this system is normally formulated either through Newtonian or Euler-Lagrange dynamic approaches. This article aims to analyze the stability of a DIP through optimal adaptive sliding mode control (OASMC) and for the purpose of comparison, an LQR controller is also developed. The linear model of DIP is used as a base to design the controllers. Then, the developed controllers are simulated with the nonlinear model of DIP using MATLAB/Simulink. To demonstrate the effectiveness of OASMC over LQR, the performance of LQR and OASMC controllers are analyzed. Besides, the performance outcomes were compared in terms of robustness and reference tracking with and without external disturbances (white noise and sine wave disturbances). The simulation test results indicate that the OASMC controller has better transient performance and disturbance rejection capabilities than the LQR controller.