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  1. Free, publicly-accessible full text available December 1, 2022
  2. Appeared in the proceedings of the 2021 IFAC Workshop on Time-Delay Systems This paper establishes a PIE (Partial Integral Equation)-based technique for the robust stability and H∞ performance analysis of linear systems with interval delays. The delays considered are time-invariant but uncertain, residing within a bounded interval excluding zero. We first propose a structured class of PIE systems with parametric uncertainty, then propose a Linear PI Inequality (LPI) for robust stability and H∞ performance of PIEs with polytopic uncertainty. Next, we consider the problem of robust stability and H∞ performance of multidelay systems with interval uncertainty in the delay parameters and show this problem is equivalent to robust stability and performance of a given PIE with parametric uncertainty. The robust stability and H∞ performance of the uncertain time-delay system are then solved using the LPI solver in the MATLAB PIETOOLS toolbox. Numerical examples are given to prove the effectiveness and accuracy of the method. This paper adds to the expanding field of PIE approach and can be extended to linear partial differential equations.
  3. This paper addresses a critical question pertaining to manufacturing sustainability: is it economically viable to implement an island microgrid to power a flow shop system under power demand and supply uncertainty? Though many studies on microgrid sizing are available, the majority assume the microgrid is interconnected with main grid. This paper aims to size wind turbine, photovoltaic and battery storage to energize a multi-stage flow shop system in island mode. A mixed-integer, non-linear programming model is formulated to optimize the renewable portfolio and capacity with the goal of minimizing the levelized cost of energy. The island microgrid is tested in three locations with diverse climate profiles. The results show that net zero energy flow shop production is economically feasible in the areas where the average wind speed exceed 8 m/s at 80-meter tower height, or the battery cost drops below $100,000/MWh. Sensitivity analyses are further carried out with respect to installation cost, demand response program, production scalability, and weather seasonality.