Compensation of an Input-Dependent Hydraulic Input Delay for a Cascaded Microfluidic Process Governed by Zweifach-Fung Effect

In this paper, we consider the control problem of a microfluidic process designed for the separation operations of a fluid containing particles in suspension, such as blood. We consider the case of several cascaded bifurcations, traveled by the fluid, to maximize the fractionation capabilities of the device for instance. We control the ratio of the flowrates in each branch, affecting the fractionation nonlinearly, through the Zweifach-Fung effect. This process can be modeled as a cascaded nonlinear dynamics, subject to input-dependent input delays of hydraulic type, corresponding to the transportation time along the branches. In this paper, we generalize our previous design for a single-bifurcation system, based on inputdelay compensation, and establish sufficient conditions for input-delay compensation and exponential stabilization.