Sliding mode controls based on adaptive closed-loop transfer function tuning for a rotary inverted pendulum

There are some tuning techniques for sliding mode controls based on perturbation observers, on neuro-fuzzy systems and on discontinuous adaptive gains. It should be interesting to propose an alternative tuning technique not based on perturbation observers, neuro-fuzzy systems or discontinuous adaptive gains. This alternative could be the tuning technique utilising the adaptive closed-loop transfer function, which is commonly applied in proportional integral derivative (PID) controls with satisfactory results. This work aims to apply the tuning technique utilising the adaptive closed-loop transfer function in two continuous sliding mode controls called first order sliding mode control and second order sliding mode control, where this tuning technique uses continuous time functions in the transfer functions. Particularly, this work addresses how to apply the continuous sliding mode controls for stabilisation of a rotary inverted pendulum with perturbation.