(398c) Control of a Fuel-Cell Powered DC Electric Vehicle Motor

The control structure of a fuel-cell system connected to an electric motor has been investigated. The modeled system comprised a fuel cell, a DC/DC buck-boost converter, and a DC electric motor. The objective of the control strategy is to control the torque produced by the engine according to a randomly generated reference, in spite of disturbances represented by the vehicle speed and the counter-electromotive force it causes in the motor. It has been found that, if the problem is adequately posed, control analysis and synthesis can be very simple.

To find a suitable reference for our control problem, the New European Driving Cycle has been considered. It is a standard used to represent common driving patterns of automobiles, and it has been used to calculate the power requirement in an average car. A first approach would have been to find the sequence of values for the manipulated variable that would have yielded the best tracking performance using these data, but such an approach would have only optimized the control action for the specific cycle. Therefore, the cycle data was transformed into the frequency domain with a Fast Fourier Transform, and a linear transfer function was obtained; feeding this transfer function with randomly-generated white noise produces a pattern similar in shape and size to the NEDC, but not predictable. This approach allows to design a controller that will be able to deal with likely values of reference and disturbance.

The power in the system is ultimately produced by a fuel cell. While fuel cells today are extensively researched, dynamic models are in relatively short supply. They are also often modeled in the V=f(i,t) form, since many are used in conjunction with galvanostats in laboratories. However, without another external source of power, it is normally not possible to directly manipulate the current passing through a fuel cell. Real-life operation of fuel cells requires models that can take realistic inputs, and models in the literature often require an adaptation in order to be useful in a control-theory context. The simplest dynamic model of a fuel cell must take into account the losses due to internal resistance and to catalytic overvoltage. Mass-transport overvoltage can usually be embedded in the latter through the Butler-Volmer equation.

An important aspect in this analysis is that the different components of the fuel cell's voltage loss, namely the internal resistance and the catalytic overvoltage, behave differently under varying conditions. The voltage loss across the internal resistance will instantaneously follow the variation in current, while the catalytic overvoltage will change continuously with time, with a transient whose time constants can vary between 0.1 to 10 seconds, depending on the reaction rate and the current flowing through the cell. Investigating the evolution of transients in the V-i phase plane yields the result that transients in fuel cells, under the quite general condition of operating at currents below the one corresponding to the maximum power output, result in some power overshoot; this makes it in theory possible to achieve perfect control of the system, if an appropriate manipulated variable is available.

Fuel-cell powered vehicles are actually electric vehicles with a fuel cell, instead of a battery, as its power source. It is therefore important to know the structure and the dynamics of the motor in order to be able to control its behavior. It has been chosen to model DC motors, as they are the most common choice for controllable drives; their model can also be applied to other motors, such as the brushless DC motor, which is in actuality an AC motor with a DC interface.

The voltage fed to the electric motor will be considered the manipulated variable. The voltage input to most common electrical motors is beyond what can be achieved by a reasonably sized fuel-cell stack, and the possibility of choosing any voltage, above or below the stack voltage, is therefore necessary. A buck-boost DC/DC converter can achieve this, and it has been assumed that such a converter has been fitted with an appropriate control system. It is known from the literature that sliding-mode control of the output voltage of such converters yields time constants of about 0.1 to 1 ms. Modeling the actuator dynamics as a simple pole with a time constant of 1 ms, the control problem can be reduced into very simple terms.

The controlled variable will be the current passing through the motor's armature windings. It is known that this current is proportional to the torque exerted by the motor, and therefore proportional to the force applied on the vehicle. Assuming some parameters for the size of the vehicle, it is easy to calculate what force the motor has to output, thereby providing a reference. The main disturbance is the counter-electromotive force of the motor, caused by the rotation of the motor shaft. It is proportional with angular velocity, and therefore to the vehicle's speed.

Using this structure, it was found that a PID controller, tuned according to simple rules such as the Ziegler-Nichols rule set, performed satisfactorily when tested against randomly-generated driving patterns.