This paper proposes several easy-to-implement control strategies when seven-phase axial flux brushless DC machines with trapezoidal back electromotive forces operate in normal and faulty modes by taking into account constraints on voltage and current. The constraints are related to the converter and machine design in terms of maximum values of current and voltage. The considered faults are cases in which one or two phases of the machine are open-circuited. Numerical computations based on analytical formulations are applied to obtain torque-speed characteristics, including the fluxweakening operation. The methods determine current references to ensure the torque optimizations while currents and voltages are within their limits. The usefulness of the methods is verified by numerical results.