through modeling of an srg using both simulation and experimentation , it can be determined that the optimal - efficiency turn - off angles for a given srg can be characterized as a function of power and speed level . within the closed - loop power controller according to the present invention , the optimal - efficiency turn - off angle is firstly determined from an analytic curve fit . the turn - on angle is then used as the degree of freedom necessary to regulate the power produced by the srg . given that the turn - off angle is initially selected for being associated with optimal - efficiency at each speed and power point , overall operation of the srg is achieved at optimal - efficiency . in the following description , the srg , inverter and control system is modeled in simulink in the first example to demonstrate the operation of the system when implemented within a voltage regulation system , i . e ., an automotive ic engine driven environment . in the second example , the control technique is then applied to an actual experimental srg system . experimental operation documents that the technique provides for efficient operation of the srg system through tuning the controller at only four operating points . the method does not need machine modeling or extensive simulations . the algorithm relies on experimental characterization at only four operating points , representing all combinations of low speed , high speed , low power and high power . because these operating points can be characterized experimentally , it is not necessary to characterize them analytically . the algorithm is easy to implement and does not need look up tables for excitation parameters . implementation of the method and included algorithm , shown in fig1 , is demonstrated in simulation and experiment for a four phase srg when implemented as part of a voltage regulation system on a 1 . 8 kw srg drive . the objectives of the algorithm are best explained through consideration of the linear inductance profile for the srm shown in fig1 . the minimum inductance region is defined by the angular interval over which the rotor poles do not overlap the stator poles . the maximum inductance region is defined by the angular interval over which there is complete overlap between the stator and rotor poles . the regions of increasing and decreasing inductance correspond to varying overlap between the stator and rotor poles . for operation of the srm as a motor , phase current must be present in the phase winding as the inductance is increasing in the direction of rotation . for operation of the srm as a generator , phase current must be present in the phase winding as the inductance is decreasing in the direction of rotation . the polarity of current is immaterial , so we assume that the phase current is always positive . as we operate the generator above base speed , i . e ., 2000 rpm , the magnitude and shape of the phase current directly depends on the turn - on and turn - off angles . the amount of power generated is dictated by the phase current and its relative position with respect to inductance profile . in order to produce a map of power production for a given speed , turn - on and turn - off angles , the srg is modelled using finite element magnetization data and the generator system is simulated for every 1000 rpm between 3000 rpm and 10 , 000 rpm with turn - on and turn - off angles taking on all combinations of turn - on angle and turn - off angle in increments of 2 electrical degrees . fig2 , 3 , and 4 show dc power generation versus excitation angles at 3000 rpm . among all simulated data , the optimum turn - on and turn - off angles are selected for a given speed and power level . the criteria is to find the excitation angles that produce the required power at a given speed with minimum mechanical power for the specified srg being simulated . fig5 and 6 show the optimal - efficiency excitation angles as a function of speed and power level . it would require an extensive look up table to experimentally implement the optimum excitation angles , not to mention the time required to experimentally determine the optimum values of the turn - on and turn - off angles . also due to the discrepancy between the actual system and the motor model and the constant changes in system parameters during the operation of the system , it is very difficult to achieve power control under open loop conditions prescribed by a look up table . further , it will be appreciated by one skilled in the art that the use of a look up table creates issues associated with interpolation among discreet points within the table and the amount and speed of memory required in the controller to store the look up table . as shown in the figures , the optimum turn - off angles are a function of operating speed and average output power . the optimum turn - off angles can be represented as eq . 1 : θ off = k 1 ωp + k 2 ω + k 3 p + k 4 where ω is rotor speed , “ p ” is the output power and k 1 - 4 are curve fit parameters . for our simulation work , the curve fit parameters are based on a least squares fit to the collection of optimal turn - off angles over all operating points above base speed . for our experimental work the curve fit parameters are based on the optimized data for four operating points representing all combinations of low speed , high speed , low power and high power . fig7 , 8 , and 9 show the curve fit of the turn - off angles using all data and data from only four operating points . as seen from these figures the curve fit using only four data gives results that are close to the actual optimized turn - off angles . for lower speeds and power levels , there can be observed some deviation between the optimized turn - off angles and the angles predicted by the curve fit . this is a reflection of the inconsistency in the efficiency - optimal turn - off angles determined through simulation . however , due to the general nature of the srm we know that small changes in excitation parameters will not cause a significant change in the achieved efficiency . further , at lower speeds and power levels there are more combinations of excitation parameters that support a particular operating point . finally , we satisfy ourself that the trend in turn - off angle is consistent with eq . 1 ( above ) even for a curve fit based on only four operating points , and that the curve fit improves as speed and power levels increase . as explained earlier , only the turn - on and turn - off angles have control over power generation for operation above base speed . from the above studies the efficiency - optimal turn - off angles for a given specified srg are easily determined through simulation . once the turn - off angle is selected , the closed loop power control can then provide the turn - on angle . since the turn - off angle is optimum for a given speed and power , the turn - on angle being output by the power controller is then guaranteed to be efficiency - optimal as well . approached in this manner , closed - loop control of output power is maintained while enforcing optimal efficiency . this is based on the premise that while there are multiple turn - on and turn - off angle combinations that will provide the same output power at a particular operating speed , only one pair will yield the highest efficiency . fig1 shows the closed loop power control algorithm . adjustment of the turn - on angle is constrained ( as shown as θ cond ) to prevent continuous conduction of the phase currents . in the fig1 algorithm , the power requirement p * is summed , through the σ function , with the available power p and passed through a proportional integral controller 2 to assess the trend of successive power requirements and adjust the turn - on angle accordingly . where there is a power surplus , the turn - on angle is increased proportionally , where there is a power deficit the turn - on angle is decreased proportionally . this power requirement is then used , in conjunction with the θ on result set in accord with θ cond , to select the optimum turn - on angle subject to a limiter function 4 . the limiter is used to prevent destructive changes in the operation of the switched reluctance generator . the algorithm previously described was implemented in simulation to confirm proper operation before an actual prototype was constructed . the specified srg to which the simulation is applied is a 16 / 12 four - phase srm designed for a 1 . 8 kw 12 v automotive application ; table 1 gives the parameters of the srg used in this simulation work . the srg magnetics are modeled analytically based on data collected through finite element analysis . fig1 shows the result of the proposed power control technique for 1600 w reference power and varying speed profile . fig1 shows the simulation results of the implemented control technique where speed is ramped to 5000 rpm in 0 . 15 s and kept constant . the power reference is changed from 1600 w to 300 w at 0 . 25 s . these figures show the control technique provides the commanded ( demanded ) power by adjusting the excitation angles . to the extent that the turn - off angle corresponds to that required for peak efficiency based on the control algorithm , the required power is produced with the highest efficiency possible . the performance of the controller is experimentally verified through a 16 / 12 four - phase srg designed for a 1 . 8 kw 12 v automotive application . the control algorithm according to the present invention is implemented using an analog devices admc401 digital signal processor . the srg is coupled to an induction motor , which acts as constant speed mechanical power source using an adjustable speed drive . a resolver with resolver to digital converter circuitry provides 12 bit position information to the dsp . the 12 v battery and load resistors are connected in parallel to the inverter . fig1 shows the block diagram of the experimental setup for the tests . we experimentally determined the optimum turn - off angles for four operating points representing all combinations of low and high speed with low and high power . fig1 shows the input shaft torque versus turn - off angles at 3000 and 6000 rpm with low and high power levels . the turn - off angle providing the desired power with the minimum torque is the most efficient one . the turn - off angles of interest are those that minimize shaft torque while supporting the required output power at speed . having the most efficient excitation angles for four operating points we determine the turn - off angles for any given point using eq . 1 . fig1 shows the dependence of turn - off angle on speed and power using experimental data from the four operating points . in an automotive application , the power produced by the srg is used to regulate the voltage of the electrical system . accordingly , voltage control is implemented as an outer control loop that is responsible for establishing the setpoint for the power controller . the voltage controller commands the reference power necessary to drive the output voltage to the required level . in order not to harm mechanical components , i . e , overwhelming the supplied torque and stalling the ic engine , and to control the charging rate of the battery , a rate limiter is implemented . the rate limiter interacts with the pi controller to keep the integrator out of saturation . table 2 provides the parameters used in the voltage and power controllers . fig1 shows the block diagram of the voltage controller applied experimentally . fig1 shows the response of the experimental system where the load is changed from 300 w to 1600 w . the rate of change of power is limited to 600 w / s . fig1 shows the response of the system where the speed is changed from 2000 rpm to 6000 rpm .