In the present investigation, we have derived an efficient reduced-order model of the low-voltage cascade electroosmotic micropump. This model can be combined with the equivalent circuit model of straight microchannels to construct a complete model for a microfluidic device, which can be employed to implement modern control schemes. To demonstrate the efficiency of the reduced-order model we employ it to estimate the zeta potentials of many subchannels in the micropump cascade using velocity measurements, which is a preliminary step to the implementation of modern control schemes. It is found that a conjugate gradient procedure employing the reduced-order model estimates accurately the zeta potential variation in the subchannels, which may be caused by adhesion of biomolecules, even with noisy velocity measurements.