Inverted Pendulum Stabilization Using Fractional-Order Direct Model Reference Adaptive Control Combined with a Fractional-Order PID Controller

This paper presents a combined fractional-order control strategy for stabilizing a cart–inverted pendulum system at its upright equilibrium while regulating the cart position. The proposed strategy combines a fractional-order direct model reference adaptive controller (FODMRAC) for cart-position regulation with a fractional-order proportional–integral–derivative (FOPID) controller for pendulum-angle stabilization. Particle swarm optimization (PSO) is used to tune the FO-PID controller gains and the FODMRAC gains, orders of integration and adaptive controller parameters respectively. The control problem is challenging because the system is underactuated and unstable, and the cart and pendulum dynamics are coupled through a single control input. The combined strategy is evaluated through numerical simulations using a model of the Feedback Instruments inverted pendulum platform. The reported results demonstrate better upright stabilization and cart-position regulation performance. Also, the control effort is evaluated to characterize the actuation requirements. These findings support the feasibility of combining fractional-order adaptive control and FO-PID control for the stabilization of an underactuated mechanical system.