Subbarao Varigonda

A nonlinear observer design for fuel cell hydrogen estimation

We present an observer design to estimate the partial pressure of hydrogen in the anode channel of a fuel cell. A precise knowledge of this pressure is of importance to ensure reliable and efficient operation of the fuel cell power system. Our design makes use of a monotonic nonlinear growth property of the voltage output on hydrogen partial pressures at the inlet and at the exit of the channel. By treating the slowly varying inlet partial pressure as an unknown parameter, an adaptive observer is developed that employs a nonlinear voltage injection term. We then study the robustness of this observer against variations in the inlet partial pressure, and analyze its sensitivity to other modeling errors. We also prove a robustness property of the observer against the parameter estimation error, which means that it can be implemented with alternative parameter estimator designs.

Dynamics of relay relaxation oscillators

Relaxation oscillators can usually be represented as a feedback system with hysteresis. The relay relaxation oscillator consists of relay hysteresis and a linear system in feedback. The objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators. In particular, we give a complete analysis for the case of unimodal periodic orbits, and illustrate the presence of degenerate and asymmetric orbits. We also discuss how complex orbits can arise from bifurcation of unimodal orbits. Finally, we focus on oscillators with an integrator as the linear component, and study the entrainment under external forcing, and phase locking when such oscillators are coupled in a ring.

Control of natural gas catalytic partial oxidation for hydrogen generation in fuel cell applications

A fuel processor that reforms natural gas to hydrogen-rich mixture to feed the anode field of fuel cell stack is considered. The first reactor that generates the majority of the hydrogen in the fuel processor is based on catalytic partial oxidation of the methane in the natural gas. We present a model-based control analysis and design for a fuel processing system (FPS) that manages natural gas flow and humidified atmospheric air flow in order to regulate 1) the amount of hydrogen in the fuel cell anode and 2) the temperature of the catalytic partial oxidation reactor during transient power demands from the fuel cell. Linear feedback analysis and design is used to identify the limitation of a decentralized controller and the benefit of a multivariable controller. Further analysis unveils the critical controller cross coupling term that contributes to the superior performance of the multivariable controller.

Control of stationary and transportation fuel cell systems: Progress and opportunities

Abstract Fuel cell power systems have witnessed intense development in the recent years as they offer a clean and efficient alternative for power generation in stationary and transportation applications. In this paper, we present an overview of recent work on dynamic modeling and control design for stationary and transportation fuel cell systems including the research at United Technologies Corporation. The use of equation oriented modeling framework for system level dynamic modeling enabled by tools, such as Dymola and gPROMS is described. It is demonstrated that the non-linear system level models readily allow linear model derivation and the application of advanced control analysis and design techniques that provide more insight into the system level dynamic and control issues in fuel cell systems. The dynamic modeling and advanced control design research performed at UTC for a hydrogen fed PEMFC power plant for a bus and a natural gas fed PEMFC power plant for stationary power generation is described. We also identify, for future research, the challenges and opportunities in several areas relating to fuel cell systems ranging from power management and freeze startup to system level modeling, control, diagnostics and hardware-in-the-loop validation of the control system. The emphasis is on polymer electrolyte membrane fuel cell (PEMFC) systems but phosphoric acid fuel cell (PAFC) systems are also briefly discussed.

Numerical solution of the optimal periodic control problem using differential flatness

Optimal periodic control (OPC) is of interest in many engineering applications. In practice, the numerical solution of the OPC problem has been found to be quite challenging. In this note, we present a method which uses differential flatness for the solution of OPC problems. The OPC problem is reformulated using the flatness of the underlying dynamical system to eliminate the differential equations and the periodicity constraints, resulting in simpler and generally more efficient computation. The effect of point-wise constraints and the analytical computation of the Jacobian matrix are also discussed. The approach is demonstrated using two examples.

An adaptive observer design for fuel cell hydrogen estimation

We present an observer design to estimate the partial pressure of hydrogen in the anode channel of a fuel cell. Our design makes use of a monotonic nonlinear growth property of the voltage output on hydrogen partial pressures at the inlet and at the exit of the channel. By treating the slowly-varying inlet partial pressure as an unknown parameter, an adaptive observer is developed that employs a nonlinear voltage injection term. We then prove robustness of this observer against variations in the inlet partial pressure, and analyze its sensitivity to measurement errors in the voltage.

Optimal periodic control of a drug delivery system

Abstract Administration of certain drugs at a steady rate results in deterioration of drug effect, also known as drug tolerance. Periodic delivery is an attractive option for minimizing tolerance and maximizing the desired effect of such drugs. In this paper, periodic drug infusion strategies for maximizing a time-averaged measure of drug effect are investigated. A simple pharmacokinetic–pharmacodynamic (PKPD) model of a system exhibiting tolerance is considered and optimal periodic control theory is employed. First, regions of PKPD parameter space in which periodic infusion provides a locally improved average effect compared to steady infusion are characterized using the so-called π -test. Then, optimal drug delivery strategies, obtained using two different computational approaches, are presented for a representative set of parameter values, and insight is provided into the results. The first method, proposed by the authors, is based on the notion of differential flatness, while the second is based on a standard shooting method for dynamic optimization problems.

Graph decomposition methods for uncertainty propagation in complex, nonlinear interconnected dynamical systems

Uncertainty propagation in complex, interconnected dynamical systems can be performed more efficiently by decomposing the network based on the hierarchy and/or the strength of coupling. In this paper, we first present a structural decomposition method that identifies the hierarchy of subsystems. We briefly review the notion of horizontal-vertical decomposition (HVD) or strongly connected components (SCC) decomposition of a dynamical system and describe algorithms based on Markov chain theory and graph theory to obtain the HVD from the equation graph of the system. We also present a non-structural decomposition method to identify the weakly connected subsystems of a system based on the Laplacian of a graph derived from the Jacobian. While most of prior efforts in this direction concentrated on stability, robustness and concrete results were limited to linear systems, we use it for uncertainty propagation and study of asymptotic behavior of nonlinear interconnected systems. We illustrate the two methods using a fuel cell system example. These two methods provide a framework for efficient propagation of uncertainty in complex nonlinear systems.

Control-Oriented Model of an Integrated Fuel Cell Stack and Fuel Processor System

Abstract A control-oriented dynamic model of a catalytic partial oxidation-based fuel processor is developed using physics-based principles. The fuel processor converts a hydrocarbon fuel to a hydrogen rich mixture that is directly feed to the PEM-FC. Cost and performance requirements of the total powertrain typically lead to highly integrated designs and stringent control objectives. Physics based component models are extremely useful in understanding the system level interactions, implications on system performance and in model-based controller design. The model can be used in a multivariable analysis to determine characteristics of the system that might limit performance of a controller or a control design. The model can also be used to assist in measurement selection and to develop a plant observer to predict or estimate critical plant variables and conditions.

Optimal Periodic Control of a Drug Delivery System

Abstract Administration of certain drugs at a steady rate results in a deterioration of the drug effect due to a phenomenon known as tolerance. Periodic drug delivery is an attractive option for maximizing the effect of drugs exhibiting tolerance. In this paper, periodic drug infusion strategies for maximizing an averaged measure of the drug effect are investigated. A simple pharmacokinetic-pharmacodynamic model of a system exhibiting tolerance is considered and optimal periodic control theory is employed. The regions in the parametric space where periodic infusion gives better drug effect than steady infusion are characterized using the scalled π test. The optimal drug delivery strategy obtained using two different computational approaches are presented for a representative set of parameter values and insight is provided into the results. The first method, proposed by the authors, is based on the notion of differential flatness and the second, is based on the standard shooting method for dynamic optimization problems.