Control of a Pem Fuel Cell Cooling System

Previous research has assumed that a perfect Proton Exchange Membrane Fuel Cell (PEMFC) body temperature manager is available. Maintaining this temperature at a desired value can ensure a high reaction efficiency over all operation. However, fuel cell internal body temperature control has not been specifically presented so far. This work presents such control, using a Multiple Input Single Output (MISO) fuel cell cooling system to regulate the internal body temperature of a PEMFC intended for transportation. The cooling system plant is taken from a recently developed hydrogen/air PEMFC total system model. It is linearized and used to design a series of controllers via μ-synthesis. μ-synthesis is chosen since system nonlinearities can be handled as parameter uncertainties. A controller must coordinate the desired fuel cell internal temperature and commanded mass flow rates of the coolant and cooling air. Each linear controller is created for a segment of the expected current density range. Plant parameters are expected to vary over their linearized values in each segment. Also, a common set of μ-synthesis weighting functions has been developed to ease controller design at different operating points. Thus, the nonlinear cooling subsystem can be controlled with a series of current density scheduled linear controllers. Current density step change simulations are presented to compare the controller closed loop performance and open loop response which uses cooling system flow rates taken from an optimal steady state solution of the whole fuel cell system. Furthermore, a closed loop sinusoid response is also given. These show that the closed loop driven ∗Address all correspondence to this author. 1 internal fuel cell temperature will vary little during operation. However, this will only be true over the range that the cooling system is required to be active. NOMENCLATURE cv Average specific heat at constant volume (J/kg K) CV Control volume d Exogenous input e Error fS Factor of safety m Mass (kg) P Plant T Temperature (K) u Control input W Weighting function x State vector y System output δ Difference, δa = a−ao, a a variable ∆ Deviation μ Structured singular value ω Rotational speed (rad/s) Subscripts act Actuator bw Bandwidth cds Current density segment clt Coolant dist Disturbance Copyright c © 2006 by ASME f an Cooling fan f c Fuel cell ha Humidified air hex Heat exchanger max Maximum min Minimum mu Multiplicative uncertainty o Operating point per f Performance snois Sensor noise unc Uncertain INTRODUCTION The PEMFC is a device that produces electrical power via oxidation and reduction half reactions that are separated in space. In this case, the fuel is hydrogen gas and the oxidant is ambient air. PEMFC systems have emerged as a possible replacement for internal combustion engines due to their efficiency, zero emission potential, and use of renewable fuels. Those used in transportation applications will experience unpredictable and widely varying power demand changes just like internal combustion engines in the majority of present vehicles. However, PEMFC systems are not currently cost effective; increasing their potential power density can improve their attractiveness. Moreover, hydrogen gas has a low density compared to liquid fuels, and even when pressurized can consume a significant volume. Thus it is advantageous to minimize the amount required for acceptable vehicle range. A simple way to accomplish these goals is to operate the PEMFC at its maximum allowed temperature. This has the effect of shifting the polarization curve upward; the reaction produces more power than at a lower temperature and requires no additional fuel or oxidant [1]. Previous authors [2–4] have assumed that a controller is available to perfectly maintain the fuel cell at its operating temperature. Unfortunately, the fuel cell cooling management work to date has been focused on modeling rather than control [5, 6]. There has been past work in internal combustion engine thermal management [7] and heat exchanger [8] control. Engine thermal management methods may be applied but require modification since: a fuel cell cooling system has less actuators; nearly all of the fuel cell waste heat must be rejected by the cooling system unlike an engine which rejects most of its waste heat with exhaust; there is a smaller temperature difference between the powerplant and surroundings which makes heat rejection more difficult; and the fuel cell power output and working life are greatly influenced by its operating temperature so its precise control is imperative. Next, the heat exchanger control was developed with the assumption that the fluid to be cooled is maintained at a constant mass flow rate. This approach will waste valuable fuel cell power. Thus, it is of primary interest to develop a fuel cell cooling system controller and validate the assumption that 2 the fuel cell temperature can be maintained without large excursions when subject to fuel cell output power changes and other disturbances. The objective of the work presented here is to develop a linear controller (or series of them) that can regulate the coolant and cooling air mass flow rates in an effort to ensure that the fuel cell internal temperature is maintained at a set value in the presence of noise and disturbance. Also, it is desired to find a set of μ-synthesis weighting functions, dependent only upon the linearization point, which can always give a suitable controller. The use of a general form speeds series controller construction since it becomes only a matter of application. Furthermore, performance of the resulting controllers is evaluated with simulation. MODEL DEVELOPMENT A complete modern fuel cell system model intended for transportation applications has previously been developed and simulated by Meyer and Yao [9]. The complete model is composed of four submodels: anode control volume, cathode control volume, fuel cell body, and cooling system. The cooling system referred to in this work combines the previous cooling system submodel and a modified fuel cell body submodel. They are joined together since it is desired to regulate the body temperature with the cooling system actuators. The states Tf c, Tclt, f c, Tclt,hex, Tha,hex, and Thex make up this new system. Their relationship is shown in Figure 1. The original fuel cell body submodel is the Tf c state nonlinear equation. States other than those listed here appear in it and their effect is lumped together in a disturbance term, dTf c . Sensor dynamics are not included since it is assumed that thin wire thermocouples are used; they can have a bandwidth over 300 rad/s [10]. The cooling system is in nonlinear state space form. To eventually apply μ-synthesis controller design it must be linearized. The linearized state space formulation models the response about an operating point: δẋ = Aδx + Bδu + BddTf c (1)