(490e) Dual Set-Point Cascade Control for Water Management in Methanol Fuel Cells

Direct methanol fuel cells (DMFCs) are highly promising candidates for powering portable
devices because they have high energy density, low operational temperatures, and can be realized
in a compact design [4]. Figure1 shows a schematic diagram of the DMFC system considered in
this work. The device includes a mixing tank containing a diluted methanol solution, and an
associated cascade feedback loop shown with standard instrumentation indicated by the symbols
LT and LC to denote level transmitter and level controller, and a fan that operates as the final
control element. The area between the anode flow channel (AFC) and the cathode flow
channel (CFC) represents a stack of fuel cells, including the polymer exchange membrane
(PEM).

An electrochemical reaction takes place at the anode region inside the fuel-cell stack, where the
methanol and water are consumed via the electro-oxidation reaction

CH3OH+H2O -→ CO2+6H +6e " src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage">

(1)

while on the cathode side oxygen is consumed by the electro-reduction reaction

6H +6e + 2O2 -→ 3H2O " src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage">

(2)

The protons produced in (1) migrate from the anode to the cathode, passing through the PEM. In
addition, some methanol transports through the membrane from the anode to the cathode, where
it undergoes the undesirable crossover reaction

CH3OH+ -O2 - → 2H2O + CO2 2 " src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage">

(3)

The water balance in the membrane is affected by liquid water that moves through membrane
pores from the anode to the cathode via an electro-osmotic drag flux J_EO, while at the same time
some of the liquid water produced at the cathode returns to the anode in the form of a
hydraulic-pressure back-convection flux J_BX through small laser-drilled holes across the membrane.
Water vapor losses are incurred through venting into the CFC (J_H2O,v) and at the gas/liquid
separator.

The control instrumentation shown in Figure 1 implements a water management strategy
involving two proportional-integral (PI) controllers configured in a cascade mode. The master
controller is denoted as LC and the slave as TC. An original control goal was to deploy the cascade
scheme for the purpose of maintaining the liquid-level in the mixing tank at a fixed set point L^SP .
The control objective of the original design is to regulate the liquid-level in the tank by adjusting
the fuel cell stack temperature using the fan [2]. This scheme succeeds in maintaining the liquid
level at the set point, though this is accomplished by continuously manipulating the temperature of
the stack.

The master control law is described by

T = ¯T + KP e(t) + KI e(τ)dτ 0 " src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage">

(4)

where T is the bias temperature (the desired temperature of operation), e(t) = L^SP (t) -L(t) is the
error of the liquid-level L(t), while K_P and K_I are the proportional and integral gains,
respectively. This original control scheme is in principle able to keep the mixing tank level at set
point. However, this is done at the cost of constantly adjusting the set point T^SP for the fuel cell
stack. Hence, the operating temperature is a function of the liquid level, a scenario that is not
conducive to optimal power generation.

In this work, we introduce a new cascade control policy, with the goal of decoupling, at least
temporarily, the liquid-level control from the control of the temperature of the stack. This allows
the introduction of periods of operation where the stack temperature can be maintained at an
optimal constant value. The novelty introduced is the modification of the master-controller
equation (4) in the form

T = T + f(t) Kpe (t) + KI e(τ)dτ 0 " src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage">

(5)

where the switching function

f(t) = 1 PI ON " src="https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/..." class="documentimage">

(6)

is a binary signal. The state f(t) = 0 implements a regime where the master PI controller is on the
off mode, and produces the constant output T^SP = T. On the other hand, the state f(t) = 1
returns the control law (5) to its previous state (4).

Figure 2 illustrates the algorithm for switching f(t) between its two states. We refer to this
technique as a dual-threshold scheme. The figure shows an upper threshold r, a lower threshold r,
and a set point for liquid-level r(t) = L^SP (t). Suppose that, as indicated in the figure, during an
initial period between t₀ and t₂, the liquid-level is in a rising mode. In such case f(t) = 0 and the
master-controller PI of equation (5) is in the off (manual) mode, as indicated by the label “OFF” in
the figure. During the period of time up to the instant t₂ the output of (5) is the constant
temperature target T^SP = T, which allows the operator to specify a desirable stack operating
temperature T that remains constant up to instant t₂. When the liquid level reaches the upper
threshold, at instant t₂, the switching function changes its state to f(t) = 1, and placing the
controller into the automatic (on) mode. The label “ON” at instant t₃ illustrates the sate of
the controller. The controller remains in the on mode until it brings the liquid level
into a dead-band zone labeled 2b around the liquid level set point r. The dead-band is
intended to make the algorithm less sensitive to measurement noise, and the parameter b
is adjusted based on the standard-deviation of the noise. Once inside the dead-band,
the switching function changes to f(t) = 0, placing the controller back into manual
mode. This is illustrated in the figure by the label “OFF” shown at instant t₄. Hence, the
dual-threshold algorithm allows the fuel cell stack to operate at desirable temperature, from the
beginning to the instant t₂, and then again for another period that begins at instant t₄. An
analogous logic applies to the case where the liquid level reaches the lower threshold
r.

In this study we compare and contrast the performance of the original cascade scheme involving
Equation (4) with the switching dual-threshold scheme described by Equation (5). The analysis is
done in a simulation environment using the MATLAB and Simulink software packages. The
dynamics of DMFC model used in the simulation has been validated experimentally by our
research group [1, 3]. The simulation involves introducing a step disturbance in the relative
humidity RH, and recording the closed loop responses of the two controllers. The desired
temperature of operation is set at T = 60^oC.

Simulation results for the original cascade control scheme show that the liquid-level of the tank
can be regulated successfully to the set point, but during the entire period of operation the target
fuel cell temperature of 60^oC is never realized since it fluctuates between 51 and 57^oC.
In contrast, the dual-threshold cascade control results show that the desired constant
temperature of operation is realized for an extended period, essentially for most simulation
duration.

Figure 3 shows the results of electrical generation under both control schemes. The original
cascade control algorithm (denoted by SC in the graph) generates electrical current and power
outputs with fluctuating behavior. In contrast, the dual-threshold controller values are constant for
long periods of time. The improved performance of the dual-threshold algorithm is a consequence
of the fact that the current and power outputs of the DMFC are strong functions of temperature.
During the simulation length the controller succeeds in keeping the fuel cell stack at the optimal
target temperature of 60^oC. Furthermore, the total energy produced under dual-threshold control
is higher than the original controller by approximately 11%. Another advantage of the
dual-threshold control scheme is that by operating at the optimal temperature for long
(though intermittent) periods of time, the DMFCs capability of avoiding flooding and
dry-out conditions in the membrane improves. The liquid-level in the tank is adjusted
satisfactorily by the dual-threshold controller during the relatively short period that it in the
“ON” state. The original cascade scheme is effective in keeping the mixing tank liquid
level near the set point, a result that is obtained at the expense of reduced electrical
performance.

Figure 3: Simulation results showing the electrical current (I) and electrical power
as a function of time for the original master controller (SC) and the dual-threshold controller
(DT).