We present a model predictive control framework for a class of nonlinear systems affected by additive stochastic disturbances with (possibly) unbounded support. We consider hard input constraints and chance state constraints and we employ the unscented transform method to propagate the disturbances over the nonlinear dynamics in a computationally efficient manner. The main contribution of our work is the establishment of sufficient conditions for stability and recursive feasibility of the closed-loop system, based on the design of a terminal cost and a terminal set. We focus here on a special class of nonlinear systems that exhibit contractive properties in the dynamics. By assuming this property, we propose a novel approach to efficiently compute the terminal conditions without the need of performing any linearization of the dynamics. Finally, we provide an illustrative example to corroborate our theoretical findings.

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Differential mobility analyzers (DMAs) are widely used to determine the size of aerosol particles, and to probe their size-dependent physicochemical properties when two are employed in tandem. A limitation of tandem DMA (TDMA) systems is their long measuring cycle when the properties of more than one monodisperse population of particles need to be probed. In this work, we propose a simple modification of the classical cylindrical DMA by including three monodisperse-particle outlets in its central electrode (namely, the 3MO-DMA), with the objective of using it as the first DMA in TDMA systems for reducing their measuring cycle. The performance of the 3MO-DMA at different flow conditions was evaluated using laboratory-generated aerosol particles, and compared with theoretical predictions. The theory predicted accurately (i.e., within 3%) the geometric mean diameters of the three distinct populations, as well as the resolutions of the first and the third outlet, under all experimental conditions. For the second outlet, the resolution was 10% to 74% lower than that predicted theoretically depending on the sheath-to-aerosol flow ratio. Nevertheless, the geometric standard deviation of the monodisperse aerosol from all the outlets was less than 1.09, which is sufficient for using the 3MO-DMA designed and tested in this work as a first DMA to produce a monodisperse aerosol flow containing three distinct particle populations in TDMA systems.@en

Hygroscopic Tandem Differential Mobility Analyzers (HTDMAs) are widely used to measure the water uptake characteristics of aerosol particles. As has been shown experimentally in the past, potential differences in the relative humidity (RH) between the aerosol and the sheath flow of the second Differential Mobility Analyzer (DMA) can lead to erroneous estimates of the apparent hygroscopic behavior of the sampled particles. A prompt phase transition, for example, may become smeared and be erroneously interpreted as non-prompt. Using a particle-tracking model, here we simulate the trajectories and the state of the particles classified in a DMA with non-uniform RH and temperature profiles. Our simulations corroborate earlier observations proving that such an experimental artifact can induce particle growth within the second DMA. Given the importance of maintaining uniform RH and temperature inside the second DMA of HTDMA systems and the limitations of existing RH and temperature sensors, we further provide suggestions for their operation.@en

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