Received: 1 December 2016 Revised: 31 July 2017 Accepted: 29 October 2017
Piecewise affine approximations for quality modeling and
control of perishable foods
Rudy R. Negenborn
School of Electrical Engineering,
Zhengzhou University, Zhengzhou
Department of Maritime and Transport
Technology, Delft University of
Technology, Delft, Netherlands
Jianbin Xin, Department of Automation,
School of Electrical Engineering,
Zhengzhou 450001, China.
China Postdoctoral Science Foundation,
Grant/Award Number: 2016M592311;
National Natural Science Foundation of
China, Grant/Award Number: 61703372;
China Scholarship Council, Grant/Award
This paper proposes a new methodology for modeling and controlling qual-
ity degradation of perishable foods when zero-order kinetics are considered.
This methodology approximates the nonlinear model of the zero-order qual-
ity kinetics using the piecewise affine (PWA) modeling representation. For
obtaining a proper PWA model, two state-of-the-art methods are discussed, and
eventually, a hybrid identification-based PWA model is considered after the
comparison. This PWA model is then transformed into a computational mixed
logical dynamical model, based on which an optimal control strategy is proposed
that balances food quality and associated energy consumption. Furthermore, a
model predictive control is proposed for improving energy efficiency when a
dynamical weather environment is considered. Simulation experiments illus-
trate the potentials of the proposed optimal controller and the model predictive
controller in a case study involving the bighead carp.
optimal control, perishable food control, piecewise affine approximation, quality kinetics
Roughly, one-third of food for human consumption in the world is wasted,
and therefore, maintaining high food quality
has become a crucial factor for managing the entire food supply chain from producers to customers. Facing the growth
of global population, this wastage problem motivates the society to optimize the quality of perishable foods.
Food quality is a very broad concept, and modeling food perishability is diversified according to its featuring aspects.
Briefly, for a particular type of perishable food, quality modeling can be classified into kinetic models for a single product
and production-distribution planning models for multiple products.
For a single product, various quality indicators can be described explicitly regarding either a particular food attribute
(eg, color, texture, and vitamins) or a global index for multiple attributes.
For these quality indicators, quantitative
kinetic models that describe a particular quality index as a function of conditions (typically temperature) over time have
been developed (see the work of van Boekel
for a comprehensive review). Typical quality kinetic models are nonlinear
described in terms of the zero-order form or the first-order form, in which key parameters are identified from conducting
a number of experiments.
After identifying these kinetic models, food quality can be further estimated and controlled,
and an analytical optimal control (OC) approach has been proposed for the quality of perishable goods.
Based on the kinetic models of a single product, research on quality control of perishable goods has been extended
into each actor in the food logistics chains from producers toward consumers leading to intelligent food logistics. In the
intelligent food logistics, 1 research direction is to monitor and evaluate food quality using data collected from the sensor
860 Copyright © 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/oca Optim Control Appl Meth. 2018;39:860–872.