Joel A. Paulson

A combined canonical variate analysis and Fisher discriminant analysis (CVA-FDA) approach for fault diagnosis

Abstract This paper proposes a combined canonical variate analysis (CVA) and Fisher discriminant analysis (FDA) scheme (denoted as CVA–FDA) for fault diagnosis, which employs CVA for pretreating the data and subsequently utilizes FDA for fault classification. In addition to the improved handling of serial correlations in the data, the utilization of CVA in the first step provides similar or reduced dimensionality of the pretreated datasets compared with the original datasets, as well as decreased degree of overlap. The effectiveness of the proposed approach is demonstrated on the Tennessee Eastman process. The simulation results demonstrate that (i) CVA–FDA provides better and more consistent fault diagnosis than FDA, especially for data rich in dynamic behavior; and (ii) CVA–FDA outperforms dynamic FDA in both discriminatory power and computational time.

Layer Number Dependence of MoS2 Photoconductivity Using Photocurrent Spectral Atomic Force Microscopic Imaging

Atomically thin MoS2 is of great interest for electronic and optoelectronic applications because of its unique two-dimensional (2D) quantum confinement; however, the scaling of optoelectronic properties of MoS2 and its junctions with metals as a function of layer number as well the spatial variation of these properties remain unaddressed. In this work, we use photocurrent spectral atomic force microscopy (PCS-AFM) to image the current (in the dark) and photocurrent (under illumination) generated between a biased PtIr tip and MoS2 nanosheets with thickness ranging between n = 1 to 20 layers. Dark current measurements in both forward and reverse bias reveal characteristic diode behavior well-described by Fowler-Nordheim tunneling with a monolayer barrier energy of 0.61 eV and an effective barrier scaling linearly with layer number. Under illumination at 600 nm, the photocurrent response shows a marked decrease for layers up to n = 4 but increasing thereafter, which we describe using a model that accounts for the linear barrier increase at low n, but increased light absorption at larger n creating a minimum at n = 4. Comparative 2D Fourier analysis of physical height and photocurrent images shows high spatial frequency spatial variations in substrate/MoS2 contact that exceed the frequencies imposed by the underlying substrates. These results should aid in the design and understanding of optoelectronic devices based on quantum confined atomically thin MoS2.

Real-time model predictive control for the optimal charging of a lithium-ion battery

Li-ion batteries are widely used in industrial applications due to their high energy density, slow material degradation, and low self-discharge. The existing advanced battery management systems (ABMs) in industry employ semiempirical battery models that do not use first-principles understanding to relate battery operation to the relevant physical constraints, which results in conservative battery charging protocols. This article proposes a Quadratic Dynamic Matrix Control (QDMC) approach to minimize the charge time of batteries to reach a desired state of charge (SOC) while taking temperature and voltage constraints into account. This algorithm is based on an input-output model constructed from a first-principles electrochemical battery model known in the literature as the pseudo two-dimensional (P2D) model. In simulations, this approach is shown to significantly reduce charging time.

Fast stochastic model predictive control of high-dimensional systems

Probabilistic uncertainties and constraints are ubiquitous in complex dynamical systems and can lead to severe closed-loop performance degradation. This paper presents a fast algorithm for stochastic model predictive control (SMPC) of high-dimensional stable linear systems with time-invariant probabilistic uncertainties in initial conditions and system parameters. Tools and concepts from polynomial chaos theory and quadratic dynamic matrix control inform the development of an input-output formulation for SMPC with output constraints. Generalized polynomial chaos theory is used to enable efficient uncertainty propagation through the high-dimensional system model. Galerkin projection is used to construct the polynomial chaos expansion for a general class of linear differential algebraic equations (DAEs), so that the SMPC algorithm is applicable to both regular and singular/descriptor systems. The fast SMPC approach is applied for control of an end-to-end continuous pharmaceutical manufacturing process with approximately 8000 states. The on-line computational cost of the proposed probabilistic input-output SMPC algorithm is independent of the state dimension and, therefore, alleviates the prohibitive computational costs of control of uncertain systems with large state dimension.

Stability for receding-horizon stochastic model predictive control

A stochastic model predictive control (SMPC) approach is presented for discrete-time linear systems with arbitrary time-invariant probabilistic uncertainties and additive Gaussian process noise. Closed-loop stability of the SMPC approach is established by appropriate selection of the cost function. Polynomial chaos is used for uncertainty propagation through system dynamics. The performance of the SMPC approach is demonstrated using the Van de Vusse reactions.

Guaranteed active fault diagnosis for uncertain nonlinear systems

An input design method is presented to actively isolate faults for polynomial or rational systems in the presence of unknown-but-bounded uncertainties. For active fault isolation, the input is required to lead to outputs consistent with at most one fault model despite disturbances, measurement noise, and parametric uncertainty. This task is posed in terms of a bilevel optimization problem where the inner program verifies, for a given input, that the outputs are consistent with at most one model, while the outer program determines the minimally harmful input. Because of the nonlinear dynamics, we propose to replace the inner program with a convex relaxation that can be efficiently solved while still guaranteeing fault detection and isolation. The approach is numerically demonstrated on a two-tank system with three fault models.

Receding-horizon Stochastic Model Predictive Control with Hard Input Constraints and Joint State Chance Constraints

ABSTRACT This article investigates model predictive control (MPC) of linear systems subject to arbitrary (possibly unbounded) stochastic disturbances. An MPC approach is presented to account for hard input constraints and joint state chance constraints in the presence of unbounded additive disturbances. The Cantelli–Chebyshev inequality is used in combination with risk allocation to obtain computationally tractable but accurate surrogates for the joint state chance constraints when only the mean and variance of the arbitrary disturbance distributions are known. An algorithm is presented for determining the optimal feedback gain and optimal risk allocation by iteratively solving a series of convex programs. The proposed stochastic MPC approach is demonstrated on a continuous acetone–butanol–ethanol fermentation process, which is used in the production of biofuels.This article investigates model predictive control (MPC) of linear systems subject to arbitrary (possibly unbounded) stochastic disturbances. An MPC approach is presented to account for hard input ...

Plant-wide model predictive control for a continuous pharmaceutical process

Integrated continuous manufacturing offers ample opportunities for efficient and cost-effective pharmaceutical processes. Plant-wide control is required for meeting the stringent regulatory requirements on quality attributes of products in continuous pharmaceutical manufacturing processes. This paper investigates plant-wide model predictive control (MPC) of an end-to-end continuous pharmaceutical manufacturing process with nearly 8000 state variables. The process includes two series of chemical synthesis and crystallization steps, followed by tablet formation steps. A subspace identification approach is adopted to obtain a linear low-dimensional description of the complex plant-wide dynamics. Quadratic dynamic matrix control algorithm is used to enable input-output formulation of the control problem, whose online computational cost is independent of the state dimension. The performance of the plant-wide MPC system is evaluated in a closed-loop setting with an existing nonlinear plant simulator equipped with a stabilizing control layer. The closed-loop simulation results demonstrate the ability of plant-wide MPC to facilitate flexible process operation and effective regulation of quality attributes of tablets.

An Analytical Solution for Exciton Generation, Reaction, and Diffusion in Nanotube and Nanowire-Based Solar Cells

Excitonic solar cells based on aligned or unaligned networks of nanotubes or nanowires offer advantages with respect of optical absorption, and control of excition and electrical carrier transport; however, there is a lack of predictive models of the optimal orientation and packing density of such devices to maximize efficiency. Here-in, we develop a concise analytical framework that describes the orientation and density trade-off on exciton collection computed from a deterministic model of a carbon nanotube (CNT) photovoltaic device under steady-state operation that incorporates single- and aggregate-nanotube photophysics published earlier (Energy Environ Sci, 2014, 7, 3769). We show that the maximal film efficiency is determined by a parameter grouping, α, representing the product of the network density and the effective exciton diffusion length, reflecting a cooperativity between the rate of exciton generation and the rate of exciton transport. This allows for a simple, master plot of EQE versus film thickness, parametric in α allowing for optimal design. This analysis extends to any excitonic solar cell with anisotropic transport elements, including polymer, nanowire, quantum dot, and nanocarbon photovoltaics.

An Adaptive Model Predictive Control Strategy for Nonlinear Distributed Parameter Systems using the Type-2 Takagi–Sugeno Model

This paper proposes an adaptive model predictive control (MPC) strategy for nonlinear distributed parameter systems (DPSs) based on the online-tuning interval Type-2 Takagi-Sugeno (IT2 T–S) model. First, the infinite dimension DPS is approximated in a finite dimensional space via the finite difference method, and from this model, training data are generated. Principal component analysis is then used to project the finite, but still high, dimensional spatiotemporal training data into a low-dimensional time series using spatial basis functions. Next, an online-tuning IT2 T–S fuzzy model is proposed to predict the low-dimensional time series with a high accuracy by computing an optimal time-varying weight parameter. Furthermore, a new method for simplifying controller design is presented by transforming the control objective from the high-dimensional spatial outputs reaching their set points to the lower dimensional time outputs reaching their set points. These novel contributions increase the accuracy of the prediction model (thus improving control performance) and reduce the computational cost of the underlying MPC optimization. Lastly, simulations are presented on a typical DPS to demonstrate the accuracy and effectiveness of the proposed methods.