The Runge-Kutta methods are an important family of iterative methods that were designed to imitate the Taylor series method. These methods are good for the approximation of the solutions to ordinary differential equations. The initial value problem for the Taylor series is that the second order, third order derivatives, etc. need to be taken by differentiating a function before the Taylor series is applied. The Runge-Kutta method, more specifically the classical fourth-order Runge-Kutta method, is commonly used in many applications to solve initial-value problems.

Switched reluctance motors use an embedded Runge-Kutta scheme in to operate efficiently. A reluctance motor is a type of electric motor which generates torque through non-permanent magnetic poles. The switched reluctance motors (SRM) are reluctance of a special form; SRMs have a more simple structure—fewer poles and a lack of magnets. Switched reluctance motors can be found in some washing machine designs and control rod drive mechanisms of nuclear reactors. A particular feature of SRMS is that the phase windings of the SRM are isolated from each other, so the fault tolerance is relatively higher than AC motors, which means that instead of the machine failing over; it “gracefully degrades” or operates at a lower output level over time.

Embedded Runge-Kutta schemes are used in a pulse-width modulation (PWM) in order to control the motor torque of the SRM. The PWM has to use current positions of the motor and sampling of torque rate in order to calculate duty ratios to be provided. The PWM has to compensate for changes in the motor speeds. The Runge-Kutta method is used to interpolate sample current and position measurements in order for the PWM to allocate duty ratios. The embedded Runge-Kutta method allows the PWM to solve the drive model efficiently over the complete speed range with little monitoring.

https://archive.ugent.be/retrieve/2804/yrs2006.pdf

http://en.wikipedia.org/wiki/Runge-Kutta#Usage

http://en.wikipedia.org/wiki/Reluctance_motor#Switched_reluctance_or_variable_reluctance_motor