This paper deals with adaptive super-twisting (STW) sliding mode control (SMC) algorithm to manage chaotic supply chain system. A multi-echelon supply chain system having parametric perturbations and disturbances is presented to demonstrate chaotic nonlinear dynamical behaviours. When changing input variables slightly in the supply chain system, the predicted outputs will be completely different due to chaotic behaviours with bifurcation. In addition, various uncertainties along with exogenous disturbances make the system dynamics more complex to manage as they propagate both upstream and downstream of the supply chain networks. Particularly, the adaptive STW SMC algorithm has been designed for chaos suppression and synchronisation of the supply chain system. Next, the robust control algorithm with adaptive law for the closed-loop system has been proved by using Lyapunov stability theorem. Then, extensive numerical simulations are conducted to demonstrate the validity of the active control synthesis for optimal operations management of chaotic supply chain networks. The control algorithm based on system theory provides satisfactory performance on achieving chaos suppression and synchronisation of the chaotic supply system. The control system theory can be expanded into new integration software applications for operations management of supply chain networks. Finally, the presented control synthesis with dynamical analysis is essential for strategic decision-makers in the modern supply chain management.

This paper deals with the PID control synthesis with robust (H_∞) loop shaping framework to manage MIMO reverse osmosis (RO) desalination plants. This new method takes advantage of the robust controller which has a fixed low order of conventional PID scheme guaranteeing robust stability and performance under large parametric uncertainties, external disturbances, and sensor noises. The coprime factor uncertainty description in H_∞ loop shaping methodology can cover a wide variety of uncertainties over all frequencies for the RO plants. The test results demonstrate that the achieved controller has high stability margin, showing disturbance and noise attenuation abilities. Furthermore, most interactions between control channels have been decoupled in the complete control system. The presented control approach can help reduce membrane cleaning, save energy, and reduce product water costs for the RO plants. Note that weather changes increase unstableness in RO plants but the water treatment facilities are only dimensioned for PID control. In addition, this study addresses control robustness as well as performance of a RO system against uncertainties, disturbances, and noises. Finally, the present control method can be utilized for efficiently controlling water quality (including quantity) and managing water facility of the RO desalination plants.

Control of the activated sludge process (ASP) is a challenging problem due to the complexity of the biological and chemical reactions, and large variations in the influent flow.