A self-adaptive fractional order PID controller for the particle velocity regulation in a pneumatic conveying system

This paper presents the methodical development of a state-error-driven self-adaptive fractional-order proportional–integral–derivative (AFOPID) control algorithm to efficiently regulate the velocity of pneumatically conveyed particles at the desired set point and to prevent the blockage of particles in a pipe due to an imbalanced combination of their velocity and corresponding mass flow rate. The proposed fractional control law is constituted by adaptively modulating fractional orders of the integral and differential operators in the control based on the state-error variations in the velocity of solid particles. The particle’s velocity is measured and updated via electrostatic sensors in conjunction with cross-correlation signal processing algorithms. All the other fixed hyper-parameters associated with the proportional–integral–derivative (PID) control scheme are meta heuristically optimized by using a genetic algorithm. The proposed AFOPID is benchmarked against conventional integer-order PID and the fractional-order proportional–integral–derivative (FOPID) controllers. Experiments are performed on a laboratory-scale test rig to comparatively analyze the aforesaid control schemes, where each controller is examined for three velocity set points and three disturbance levels. The experimental results validate the superior time optimality and robustness of the proposed AFOPID controller against bounded disturbances and abrupt velocity set-point variations by manifesting relatively faster settling time, low overshoots (and undershoots), and smaller steady-state fluctuations.