Analysis of improved fractional backstepping and lyapunov strategies for stabilization of inverted pendulum

Controlling an inverted pendulum towards an upright position is a difficult task. Backstepping control is an emerging tool for assisting this extremely nonlinear system to stabilize. Since several studies demonstrated fractional modern strategies with Oustaloup approximation, this current work proposes a novel fractional backstepping rule with improved biquadratic equiripple approximation method to stabilize the system with superior accuracy. On the basis of study in the frequency domain, a suitable fractional order is established. Closed-loop performances and control efforts between proposed fractional and conventional backstepping controllers are illustrated based on time domain analysis from a real-time perspective. By abruptly changing the system's parameters, the effectiveness of the proposed controller is also verified. A further fractional Lyapunov improved architecture is proposed to investigate control efficacy with proposed fractional backstepping strategy. The selection of tuning parameters of all control strategies is addressed analytically in depth. It is explored that the suggested fractional backstepping control scheme outperforms the conventional backstepping and fractional Lyapunov stability rules by effectively tracking desired position. This enhanced performance is achieved with relatively smooth control action. On the basis of error measurements, quantitative performance analysis is also subjected to all control strategies.