Luís Gustavo Soares Longhi

On the positivity of multivariable scalar functions

The determination of local and global positivity (or negativity) of general nonlinear functions plays a fundamental role in several applied mathematical areas. In this work, this subject is addressed by the presentation of a new theorem that allows to determine the sign of a function and furnishes an estimate of the local region maintaining this sign. Applications to Lyapunov stability theory and nonlinear H-infinity control are presented as examples of the applicability of the theorem.

A Possible Approach to Solve Nonlinear H-Infinity Control Problem⋄

Abstract Robustness is fundamental to any control system. Furthermore, there exist situations where a fixed linear controller cannot be used to control a process. When this occurs, it is necessary to use nonlinear control techniques to design the controller. The nonlinear H-infinity control theory allows the design of nonlinear robust control laws. However, this theory suffers a strong lack for methods to solve the οJI (Hamilton-Jacobi-Isaacs) inequality that arise in this problem in the same way the Riccati inequality arise in the linear H-infinity theory. In this work, an approach to easily solve the nonlinear H-infinity control problem is proposed. This approach is based on theoretical results obtained in former works and furnishes not only a local solution to the problem but also an estimate for the state space region where this solution is valid. Finally, the resulting method is applied in two examples: a pure mathematical dynamical system and a chemical reactor system.

Control Loop Performance Assessment and Improvement of an Industrial Hydrogen Generation Unit

Abstract This paper describes the CLPA (Control Loop Performance Assessment) and improvement of an industrial hydrogen generation unit (HGU) located at Alberto Pasqualini – REFAP S.A., a petroleum refinery (whose capacity is 189,000 barrels per day) located at the south of Brazil, subsidiary of Petroleo Brasileiro S.A. (PETROBRAS), and also belonged to REPSOL YPF. At first, we describe the HGU unit and its process purpose. After, we introduce the motivation for the CLPA for this unit and describe the main tool used to carry out this task. This tool is entitled BRPerfX (petroBRas PERFormance indeX) and it was developed by the Federal University of Rio Grande do Sul, Trisolutions enterprise and CENPES (the PETROBRAS research center). The necessary capital to develop this tool was supported by PETROBRAS. A base case was developed for comparison. This base case is composed by a time interval of typical operation before the project startup. This allows showing the improvements made after the control loop assessment is finished. The main steps of the work methodology are also presented, with focus on the planned and implanted actions to improve the dynamical performance of the unit. Finishing the paper, we present the main results achieved. These include not only the better dynamic behavior of the loops but also the economic results related to the index online monitored in the CLPA tool.

Modeling of Ammonia Removal in RBCs: An Industrial Case

Abstract This paper describes the mathematical modeling of a set of rotating biological contactors (RBC) used for ammonia removal by nitrification of the wastewater stream that comes from a petroleum refinery. The entire biological wastewater treatment unit is composed by an aerated facultative lagoon, four sets of RBCs, and a pair of clarification decanters. In this paper we are concerned with the nitrification step. It has two sequential biochemical pathways (nitritation and nitratation) for the nitrification process and the existence of two distinct biological agents, related to Nitrobacter and Nitrosomonas autotrophic bacteria. We discuss some characteristics about the kinetics and important points that should be concerned for such a study. We also propose an alternative way to model the spatial distribution on the rotating bioreactor, with necessary simplifications and the discussion on their limitations. Available data sets from on-line analyzers for ammonium, composed by 3-hours sampled input and output, were used for parameter estimation and model validation. The process modeling, dynamic simulation, and parameter estimation were completely accomplished in the software EMSO. The results show the good prediction capability of the proposed model. It is expected to use the developed model for monitoring the wastewater treatment and for operator training. Meanwhile, the acquired knowledge obtained during the model development has improved the efficiency and the operational procedures of the industrial unit.