Hybrid Control of a Double Linear Inverted Pendulum using LQR-Fuzzy and LQR-PID Controllers

The principle of inverted pendulums (IP) has been used to design and stabilize different systems. A double linear inverted pendulum (DLIP) system is a type of IP system that is a nonlinear, multivariable, inherently unstable, and under-actuated mechanical system. The DLIP dynamics can be developed with the Euler-Lagrange and the Newtonian approaches. This paper presents the control of a DLIP using two-hybrid controllers: LQR-FLC and LQR-PID. The comparative study of the hybrid controllers together with classical controllers such as PID and LQR is performed through simulations. The results show the superior performance of the developed hybrid controllers (in terms of dynamic and steady-state performance over the classical ones. In addition, the controllers were also simulated under the effect of a pulse disturbance, and the obtained results indicate the hybrid and LQR controllers are robust.