a brushless motor control apparatus is shown in fig1 . reference numeral 1 denotes a brushless motor , numeral 2 denotes a rotation angle sensor , such as a well known resolver for detecting electrical angle , numeral 3 denotes a controller , and numeral 4 denotes a current sensor . the controller 3 comprises a drive circuit 31 , a pwm conversion unit 32 , a two - phase to three - phase conversion circuit 33 , a three - phase to two - phase conversion circuit 34 , a d - axis pi control unit 35 and a q - axis pi control unit 36 that perform well known pi ( proportional and integral ) control , subtraction circuits 37 and 38 , an instruction value arithmetic unit 39 , an electrical angle arithmetic unit 61 , an angular velocity arithmetic unit 64 , and an overheat protection arithmetic unit 65 , wherein a construction except for the overheat protection arithmetic unit 65 is the same as that of a known brushless motor control apparatus . the controller 3 includes a known microcomputer with an internal a / d ( analog / digital ) converter . the controller 3 may however be constructed with an exclusive hardware circuit . as is well known , the drive circuit 31 includes a three - phase inverter circuit as shown in fig2 . reference numerals 311 – 316 denote mos power transistors , symbol d a flywheel diode , numeral 311 a u - phase upper arm element , numeral 312 a u - phase lower arm element , numeral 313 a v - phase upper arm element , numeral 314 a v - phase lower arm element , numeral 315 a w - phase upper arm element , and numeral 316 a w - phase lower arm element , wherein each of the elements 311 – 316 is connected to the flywheel diode d in reverse parallel individually . between a low electric potential power supply line ll and a high electric potential power supply line lh , a battery voltage is applied through an unillustrated smoothing circuit , and three - phase alternating voltages outputted from the drive circuit 31 ( namely , a three - phase inverter ) are applied to each end of a u - phase winding 11 , a v - phase winding 12 and a w - phase winding 13 of the motor 1 , individually . the electrical angle arithmetic unit 61 generates a rotation angle signal θ from an analog rotation angle signal outputted from the rotation angle sensor , and outputs it to both the two - phase to three - phase conversion circuit 33 and the three - phase to two - phase conversion circuit 34 . the controller 3 performs pwm control of the three - phase brushless motor 1 based on the above phase current , the rotation angle signal and a torque instruction value externally applied . the three - phase to two - phase conversion circuit 34 converts the applied three - phase current iu , iv and iw into the q - axis current and the d - axis current based on the rotation angle signal ωt outputted from the rotation angle sensor 2 . the instruction value arithmetic unit 39 converts the torque instruction value externally applied into a q - axis current instruction value . the subtraction circuit 38 performs pi conversion of a difference δi q between the q - axis current i q and the q - axis current instruction value i qc in the q - axis pi control unit 36 , and outputs it to the two - phase to three - phase conversion circuit 33 . the subtraction circuit 37 performs pi conversion of a difference δi d between the d - axis current i d and the d - axis current instruction value i dc in the d - axis pi control unit 35 , and outputs it to the two - phase to three - phase conversion circuit 33 . the two - phase to three - phase conversion circuit 33 converts pi control quantities of δi q and δi d applied from the d - axis pi control unit 35 and the q - axis pi control unit 36 , respectively , based on the rotation angle signal outputted from the rotation angle sensor 2 to target three - phase voltages vu , vv and vw ( phase voltage instruction value ) through two - phase to three - phase conversion , and outputs them to the pwm conversion unit 32 . the pwm conversion unit 32 outputs pwm signals , i . e ., pwmu , pwmv and pwmw , each of which has a duty ratio corresponding to the applied target three - phase voltages vu , vv and vw to the mos power transistors 311 – 316 of the drive circuit 31 . the drive circuit 31 drives the motor 1 by outputting the three - phase alternating voltages vu , vv and vw to the motor 1 . each of pwmu , pwmv and pwmw of the pwm signals includes two pwm signals having mutually opposite signs . to be more precise , the pwm signals include six signals ( gate voltages ) of a pwmu upper signal , a pwmu lower signal , a pwmv upper signal , a pwmv lower signal , a pwmw upper signal and a pwmw lower signal . these signals are applied to the elements as follows : the pwmu upper signal to the u - phase upper arm element 311 , the pwmu lower signal to the u - phase lower arm element 312 , the pwmv upper signal to the v - phase upper arm element 313 , the pwmv lower signal to the v - phase lower arm element 314 , the pwmw upper signal to the w - phase upper arm element 315 and the pwmw lower signal to the w - phase lower arm element 316 . since a drive system itself of the three - phase brushless motor by the pwm control described above and its various variations are well known , further detailed explanation is omitted . the motor overheat protection processing will be described using fig1 and the flowchart of fig3 . this processing is repeatedly performed in the controller 3 . first , each of the phase current of the u - phase , v - phase and w - phase windings of the motor 1 is detected by the current sensor 4 ( s 1 ), and subsequently the electrical angle ωt is calculated in the electrical angle arithmetic unit 61 based on the rotation angle of the motor 1 detected by the rotation angle sensor 2 ( s 2 ). then , the kwon three - phase to two - phase conversion is performed using the formula 3 based on the phase current values detected in the three - phase to two - phase conversion unit 34 to obtain the q - axis current i q ( s 3 ). the angular velocity is calculated in the angular velocity arithmetic unit 64 ( s 4 ) based on the rotation angle of the motor 1 detected by the rotation angle sensor 2 . the angular velocity can be calculated from a change in the rotation angle per unit time . the overheat protection arithmetic unit 65 , first , multiplies a squared value of the q - axis current i q by a previously stored electric resistance r of each phase winding of the motor 1 to calculate the most recent basic electric power po of the phase winding resulting from the q - axis current i q ( s 5 ). next , whether the motor 1 is in the lock state is determined . this is done as follows : when the angular velocity obtained in the above is less than a predetermined value or when the angular velocity is less than a predetermined value and a value of the q - axis current exceeds a predetermined value , the motor 1 is determined to be in the lock state ; and otherwise , the motor 1 is determined to be rotating ( s 6 ). when the motor 1 is in the lock state ( s 6 : yes ), a predetermined coefficient ko multiplied by a sine component ( sin ωt ) of the electrical angle ωt of each phase is specified as a coefficient k ( s 7 ). when the motor 1 is determined to be rotating ( s 6 : no ), a predetermined coefficient ko ( e . g ., ko = 1 ) multiplied by ½ is specified as a coefficient k common to all phases : u - phase , v - phase and w - phase ( s 8 ). a product obtained by multiplying the most recent basic electric power po calculated previously by the coefficient obtained in the above is specified as the most recent electric power p ( s 9 ). the most recent value p is added to stored past history data of electric power and this history data is substituted into a previously stored calculation formula to calculate the temperature t of the phase winding ( s 10 ). then , when any one of the calculated temperatures t of the phase windings exceeds a predetermined threshold temperature tth stored in advance ( s 11 : yes ), the overheat protection arithmetic unit 65 sends a predetermined signal to the instruction value arithmetic unit 39 . the instruction value arithmetic unit 39 receives the signal and sends a value for reducing the current flowing in the motor 1 , i . e ., a value that is smaller than the q - axis current instruction value and calculated according to the torque instruction value , to the subtraction circuit 38 as a q - axis current instruction value ( s 12 ). as a result , the current flowing in the motor 1 decreases , the electric power of each phase winding decreases , and the calorific value reduces as well . the brushless motor control apparatus 3 is also suitable for an electronic power steering ( eps ) apparatus of vehicles . fig6 is an outline block diagram of an electronic power steering apparatus 101 to which the brushless motor control apparatus 3 is applied . a steering wheel 110 is coupled to a steering shaft 112 a and the lower end of this steering shaft 112 a is coupled to a torque sensor 111 for detecting a movement of the steering wheel 110 by a driver . the upper end of a pinion shaft 112 b is coupled to the torque sensor 111 . a pinion ( not illustrated ) is provided on the lower end of the pinion shaft 112 b , and this pinion is engaged with a rack bar 118 in a steering gear box 116 . moreover , one end of each tie rod 120 is coupled to each end of the rack bar 118 , respectively . the other end of the each tie rod 120 is coupled to a steering wheel 124 through a knuckle arm 122 . furthermore , an electric motor 115 that is the three - phase brushless motor is attached to the pinion shaft 112 b through gears ( not illustrated ). a method of attaching the electric motor 115 to the rack bar 118 coaxially may be adopted . a steering control unit 130 is equipped with a known cpu 131 , ram 132 , rom 133 , an i / o 134 serving as an input and output interface , and a bus line 135 connecting these components . the cpu 131 performs control with a program and data stored in the rom 133 and the ram 132 . the rom 133 has a program storage area 133 a and a data storage area 133 b . the program storage area 133 a stores an eps control program 133 p . the data storage area 133 b stores data necessary for operations of the eps control program 133 p . through execution of the eps control program stored in rom 133 by the cpu 131 , the steering control unit 130 calculates a drive torque that corresponds to the torque detected by the torque sensor 111 and should be produced by the electric motor 115 , and makes a motor driver 114 apply a voltage for producing the calculated drive torque to the electric motor 115 . at this time , a resolver 109 detects a rotation angle of the electric motor 115 and a current sensor 108 detects a current flowing in the electric motor 115 , whereby the apparatus checks whether the motor is rotating that corresponds to the drive torque and calculates a voltage to be applied to the electric motor 115 according to the result . that is , this electronic power steering apparatus detects a current flowing in the electric motor 115 with the current sensor 108 , subsequently calculates a voltage to be applied to the electric motor 115 and performs control for driving the electric motor 115 in the construction shown in fig1 and fig2 . in this electronic power steering apparatus 101 , the vehicle may travel with the steering wheel 110 maintained at a fixed angle . this corresponds to the motor lock state described above . the rotation state of the electric motor 115 changes quickly depending on operation states of the steering wheel 110 or driving conditions . that is , by applying the brushless motor control apparatus , appropriate overheat protection that is responsive to operation states of the steering wheel 110 can be realized with excessive or too little overheat protections being avoided . it is to be understood that these embodiments are only illustrative of the application of this invention and this invention is not limited to them , but that changes and modifications may be made based on knowledge of the those skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims .