Tracking control of air flow based on a fractional-order model of the lung impedance

Abstract

Abstract A fractional order output feedback controller for a lung ventilator is designed. This is based on a state-of-the-art electrical analogue model of the human respiratory system in the form of a network of resistors and fractional capacitors. The electrical input impedance of the adopted analogue can be suitably tuned to fit experimental ventilation impedance data. Furthermore, it can explicitly account for the different physiological fractal type characteristics associated with lung formation such as branching morphogenesis associated to the treelike tubular network and alveolar differentiation associated with the generation of specialized epithelial cells for gas exchange. A description of this electrical analogue in pseudo-state space is then proposed. The aim is to finally provide a control methodology within the scope of output feedback control, when the measured output which is the airflow through the trachea is directed to follow a specified reference. The control provides adequate air pressure input to generate this nominal airflow. The proposed control design includes a pseudo-state observer and a double leaky integrator. The gains involved are designed using constraints imposed through linear matrix inequalities (LMIs), which enforce a regional allocation of eigenvalues. The robustness of the control loop is analysed through an uncertainty matrix analysis linked directly to the model. It is observed that the proposed design can tolerate a relatively wide variation in physiological parameters ( $$\pm 15\%$$ ). The proposed formulation advances current control design approaches for mechanical ventilators and provides a generic methodology for the control of complex system with emergent responses as encountered in bioengineering.