Compensation of input-dependent hydraulic input delay for a model of a microfluidic process under Zweifach–Fung effect

We consider a model of a microfluidic process under Zweifach-Fung effect, which gives rise to a second-order nonlinear, non-affine system with control input that affects the plant both without delay and with an input-dependent delay defined implicitly through an integral of the past input values (that arises from a transport process with transport speed being the control input itself). We construct a predictorfeedback control law that exponentially stabilizes the output to a desired reference point. This is the first time that a predictor-feedback design is constructed that achieves complete input delay compensation for such a type of input delay and despite that control input affects the plant also without delay. This is attributed to the particular structure of the nonlinear system considered, which allows to deriving an implementable formula for the predictor state at the proper prediction horizon. We then identify a class of nonlinear systems with input-dependent input delay of hydraulic type for which complete delay compensation, through construction of an exact predictor state, is achievable.