Al-Khwarizmi Engineering!!! Journal Al-Khwarizmi Engineering Journal, Vol. 6, No. 1, PP 80 - 87 (2010) Modeling and Simulation of Sensorless Speed Control of a Buck Converter Controlled Dc Motor Bassim M. H. Jassim * Tagreed M. Ali ** Department of Eelectrical Engineering/ College of Engineering/ University of Baghdad * Email: bassimmhj@yahoo.com ** Email: tagmali@yahoo.com (Received 24 March 2009: accepted 20 October 2009) Abstract This paper investigate a sensorless speed control of a separately excited dc motor fed from a buck type dc-dc converter. The control system is designed in digital technique by using a two dimension look-up table. The performance of the drive system was evaluated by digital simulation using Simulink toolbox of Matlab. Keywords: DC motor, speed control, buck converter. 1. Introduction In speed control of the dc motor, high frequency output voltage ripple is achieved using dc chopper where the average voltage across the motor terminals can be controlled by using the duty ratio of power switching device [Sen]. Different control methods have been used to regulate the motor speed like PI controller [Gurbuz] and fuzzy logic control [Tipsuwanporn]. In much application the use of speed sensors like tachogenerator or shaft encoder will add a significant cost and weight to the drive system. In this work, high chopping frequency is achieved using a MOSFET as a switching device and a smooth dc output voltage and current are generated using a buck type dc-dc converter with sensorless speed control technique to reduce the cost and weight of the drive system. The control method is simple and reliable and does not need exact system parameters measurement when implemented practically. The buck converter circuit design is presented in section II, while section III explains the proposed control technique with a two dimension look-up table which is used in speed control of induction machines [Jeftenic]. The complete system is modeled in section IV, and then simulated using Simulink toolbox of Matlab in section V. Finally section VI presents the simulation results and conclusion for the proposed control system for both step change in reference speed and motor load. 2. Buck Converter Design The buck converter circuit diagram is shown in Fig.1, where the steady state output voltage depends linearly on the duty ratio D where: Va =D.Vs 0  D  1 …(1) The buck converter modes of operation are explained in details by [Mohan]. The converter switching frequency is 20 KHz, and the input voltage is 240V. Fig.1. Buck Converter Circuit Diagram. Bassim M. H. Jassim!!!! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 80 -87 (2010) 81 2.1. Inductor design The inductor value depends on the admissible current ripple iL which is given by the following relation [Mohan]: L iL 1  (Vs – Va ). fs D …(2) The continuous conduction mode of the converter is ensured by making the minimum output current equal to the motor no load current which is about 2A for the used motor in this work. Therefore AiL 4 is the maximum admissible value. Solving Eq. (2) for L yields: iL TsDVaVs L    .).( …(3) Where: fs Ts 1  Substituting Eq.(1) by Eq.(3) gives: iL TsDDVs L    .)1( …(4) Clearly the maximum value of the right hand side of Eq. (4) occurs at 5.0D ; thus the value of the inductor becomes: iL TsVs L   4 . …(5) Taking AiL 2 to ensure more smoothness, the value of the inductor will be 1.5 mH . 2.2. Capacitor Design The output voltage ripple can be minimized by making the corner frequency fc of the output LC filter as fsfc  ; also a rule of thumb of /300 f A minimum at KHz20 is more realistic when electrolytic capacitors are used[Chyrysis] and a ccordingly for the A20 rated armature current, the capacitor selected to be two of f4700 connected in parallel is to reduce the equivalent series resistance of the capacitor. 3. The Proposed Control Concept The well known equation of the dc motor is: RaIaEgVa . …(6) Where: nKaEg . …(7) Using the last two equations with Eq.(1), yields: Vs RaIanKa D ..   …(8) Then: ),( IanfD  …(9) The proposed algorithm assumes that the reference speed is equal to the actual speed, so if there is a two dimension look-up table in which the first field represents motor speed, the second field represents the armature current and the third one represents the duty ratio; then the required duty ratio can be calculated for a given reference speed and motor load which is estimated by the armature current. The schematic of the drive and control system is shown in Fig.2. For operating points not included in the table, cubic spline interpolation and extrapolation is used to calculate the required duty ratio. The two dimension look-up table can be formed in two ways. The first method uses simple measurements for small number of operating points while in the second method, the steady state dc motor equivalent circuit is used to calculate the required armature voltage and then the duty ratio for a given reference speed and motor load. Fig.2. Buck Converter Controlled dc Motor Fig.3 shows the calculated function ),( IanreffD  , from which the required duty ratio is calculated for a given reference speed and armature current, therefore, the speed can be controlled using only the armature current signal. A current limiter is used to protect the system from the large starting and transient currents, which can damage the converter and possibly the motor. Bassim M. H. Jassim!!!! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 80 -87 (2010) 82 4. System Modeling and Simulation This section includes the modeling of the dc motor and the buck converter, and then the overall system is simulated using Simulink toolbox of Matlab. 4.1. DC motor Modeling A separately excited dc motor is modeled by the equations below [Tipsuwanporn]: t ia LaiaRaegva    .. …(10) Where: nKaeg .. The torque balance equation is: t n JnBTlt    .. …(11) Where: iaKat . 4.2. Buck Converter Modeling The buck converter is modeled using the equations [Chrin]: )..( 1 voRliLvsd Lt iL    …(12) )( 1 ioiL Ct vc    …(13) )(Re ioiLsrvcvo  …(14) Where: 1d When the switch is on. 0d When the switch is off. Using the equations (10-14) with the look-up table, Fig.4 shows the overall system simulation while Fig.5 and Fig.6 are the simulation of the dc motor and the buck converter respectively using Simulink toolbox of Matlab. 1000 1200 1400 1600 1800 2000 0 10 20 30 0.2 0.3 0.4 0.5 0.6 0.7 Motor Speed,[rpm] Fig.3 The duty ratio vs. the armature current and motor speed Armature Current,[Amp.] D ut y R at io Fig.3. The Duty Ratio Vs. the Armature Current and Motor Speed Bassim M. H. Jassim!!!! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 80 -87 (2010) 83 5. Simulation Results and Conclusion Based on the system model, the motor parmeters, and the converter parameters shown in the appendix, Simulink is used to simulate the system under consideration. Simulation results are shown in Fig.7 and Fig.8 for step response for speed change from 1000 rpm to 1800 rpm ( 104.7 rad/sec to 188.5 rad/sec) and from 1800 rpm to 1000 rpm at rated motor load, and for step change in motor load from 7 N.m to 11 Nm and from 11 Nm to 7Nm at rated speed respectively. These figures clarify the soft start of the motor and the operation of the current limit as well as the satisfactory transient response. The results demonstrate the effectiveness of the proposed control scheme. One can conclude that the steady state accuracy depends mainly on the look-up table forming. The experimental method for producing a look-up table will lead to more accurate results than that of the method of calculation used in this work since it takes into account some effects, like the parasitic elements not considered in the model. Practical implementation of this proposed control method doesn’t require exact motor parameters measurement and lookup table can be changed easily without any hardware modification to take into account the mechanical status of the motor which is changed after a long period of operation. Referance Speed Armature Current current limitter 25 Subsystem3 DC Motor In 1 In 2 Out1 Out2 Subsystem1 Buck Converter In 1 In 2 In 3 Out1 Step 2 Step 1 Scope 3 Scope 1 Saturation Repeating Sequence 20 Khz Relay 1 Relay Low pass filter 1 0.005 s+1 Lookup Table (n-D) 2-D T (u)u1 u2 Logical Operator AND Input Voltage 240 Motor Load Torque Arm ature Voltage Speed in rad/s ec Armatue Current Duty Ratio Fig. 4. Simulink of a Sensorless Buck Converter Controlled dc Motor. Bassim M. H. Jassim!!!! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 80 -87 (2010) 84 Ra Ia Kaphi B n (rad /sec)1/J Kaphi 1/La Armature current Armature voltage Out22 Out 1 1 Integrator 2 1 s Integrator 1 s -K - Gain 9 -K - -K - Gain 6 1 Gain 4 -K - -K - In 2 2 In 1 1 Fig. 5. Simulink of a Separately Excited dc Motor. RL Vo= Armature Voltage IL Input Voltage Duty Ratio Armatue Current Out 1 1 Resr -K - Product Integrator 3 1 s Integrator 1 1 s -K - 1/L -K - 1/C -K - In 3 3 In 2 2 In 1 1 Fig. 6. Simulink of Buck Converter. Bassim M. H. Jassim!!!! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 80 -87 (2010) 85 0 5 10 15 20 25 30 -50 0 50 100 150 200 Time in Sec Fig.8. Transient Response due to Step Change in Load. Speed in rad/Sec Current in Amp. Speed & armature current 0 5 10 15 20 25 30 -50 0 50 100 150 200 Time in Sec. Fig.7. Transient Response due to Step Change in Speed. Current in Ampere Speed in rad/Sec Speed & arrmature current Bassim M. H. Jassim!!!! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 80 -87 (2010) 86 Notation eg Motor generated voltage (or back emf). fs Converter switching frequency. ia Motor armature current. iL Converter inductor current. io Converter output current. n Motor speed. nref Motor reference speed. t Developed torque. va Motor armature voltage. vc Converter capacitor voltage. vo Converter output voltage. A Ampere B Friction coefficient. C Converter capacitance. D Duty ratio Eg Average motor generated voltage. Ia Average armature current. J Moment of inertia. Ka Back emf and torque constant. L Converter inductance. La Motor armature circuit inductance. Ra Motor armature circuit resistance. srRe Capacitor equivalent series resistance. Rl Converter inductor internal resistance. Tl Load torque. Va Average motor armature voltage. Vc Average capacitor voltage. Vo Average converter output voltage. Vs Converter input voltage. iL Inductor current ripple. Appendix The dc motor used has the following specifications: DC motor, 110V, 2.5 hp, 1800rpm, AIa 20  1Ra , ,46mHLa  mKgJ  093.0 2 for the motor and its connected load, .sec/..008.0 radmNB  for the motor and its coupled load., radVKa sec/.55.0 , which is the back emf and torque constant. The buck converter specifications are: Input voltage VVs 240 . Output voltage VaVo  is adjustable according to required speed and load. Output current IaIo  . mHL 5.1 , with internal resistance Rl 0.017  , C two capacitors connected in parallel each of 4700 .f with srRe 0.25  , switching frequency .20KHzfs  6. References [1] Chrip, p. and Bunlaksananusorn, C,”Large signl average modeling and simulation of dc- dc converters with simulunk,” IEEE- Power Conversion Conference-Nagoya, 2007. [2] Chyrysis, C. George, High frequency switching power supplies, 2nd ed., McGraw- Hill, 1989. [3] Gurbuz Fatma and Eyup Akpinar,”Stablity analysis of a closed loop control for a pulse width modulated dc motor drive,” Turk J Elect. Engin., Vol.10, No.3, 2002. [4] Jeftenic, B.I., Bebic, M.Z., and Nitrovic, N.N.,” A simplified speed sensorless control for variable frequency induction motor drives,” IEEE Transaction on Energy Conversion, Vol.14, No.3, Sept. 1999. [5] Mohan, N., Undland, T.M., and Robbin, W.P., Power electronics: converters application and design, 3rd ed., Wiley& Sons, 2003. [6] Sen, P.C., Principles of electric machines and power electronics, 2nd ed., John Wiley & Sons, 1997. [7] Tipsuwanporn, V., Numsomran, A., and Klinsmitth, N.,” Separately excited dc motor with fuzzy self organizing,” International conference on control, automation and systems. Oct.,2007. )2010( 87-80 ، صفحة1، العدد 6مجلة الخوارزمي الھندسیة المجلد باسم محمد جاسم 87 نمذجة ومحاكاة محرك تیار مستمر مسیطر علیھ بواسطة مغیر تیار مستمر خافض للفولتیھ وبدون متحسس سرعھ **تغرید محمد علي *باسم محمد حسن جاسم جامعة بغداد/ كلیة الھندسھ/ قسم الھندسھ الكھربائیھ bassimmhj@yahoo.com:البرید االلكتروني * tagmali@yahoo.com:البرید االلكتروني ** الخالصة Buck)(رك تیار مستمر منفصل االثاره بواسطة محول تیار مستمر خافض للفولتیھ من نوع تحقق ھذه الورقھ البحثیھ في امكانیة السیطره على سرعة مح ثم تم تقییم مواصفات النظام من خالل محاكاة النظام باستخدام وبدون استخدام متحسس سرعھ وباستخدام تقنیھ رقمیھ من خالل استخدام جدوال ثنائي االبعاد Simulink toolbox).(مایسمى بالـ 1000 1200 1400 1600 1800 2000 0 10 20 30 0.2 0.3 0.4 0.5 0.6 0.7 Motor Speed,[rpm] Fig.3 The duty ratio vs. the armature current and motor speed Armature Current,[Amp.] Duty Ratio £ £ GATE DRIVE Duty Ratio Input Voltage Vs L C MOSFET iL D L iL 1 º D fs D A iL 4 = D L iL Ts D Va Vs L D - = . ). ( fs Ts 1 = iL Ts D D Vs L D - = . ) 1 ( 5 . 0 = D iL Ts Vs L D = 4 . A iL 2 = D mH fc fs fc << / 300 f m A KHz 20 A 20 f m 4700 Ra Ia Eg Va . + = n Ka Eg . F = Vs Ra Ia n Ka D . . + F = ) , ( Ia n f D = M GATE DRIVE LOOK- UP TABLE LPF Reference Speed Armature Current Duty Ratio Input Voltage Vs Armature Voltage Va L C MOSFET ) , ( Ia nref f D = t ia La ia Ra eg va ¶ ¶ + + = . . n Ka eg .. F = t n J n B Tl t ¶ ¶ + + = . . ia Ka t . F = ) . . ( 1 vo Rl iL vs d L t iL - - = ¶ ¶ ) ( 1 io iL C t vc - = ¶ ¶ ) ( Re io iL sr vc vo - + = 1 = d 0 = d Referance Speed Armature Current current limitter 25 Subsystem3 DC Motor In1 In2 Out1 Out2 Subsystem1 Buck Converter In1 In2 In3 Out1 Step2 Step1 Scope3 Scope1 Saturation Repeating Sequence 20Khz Relay1 Relay Low pass filter 1 0.005s+1 Lookup Table (n-D) 2-D T(u) u1 u2 Logical Operator AND Input Voltage 240 Motor Load Torque Armature Voltage Speed in rad/sec Armatue Current Duty Ratio Ra Ia Kaphi B n (rad/sec) 1/J Kaphi 1/La Armature current Armature voltage Out22 Out1 1 Integrator2 1 s Integrator 1 s -K- Gain9 -K- -K- Gain6 1 Gain4 -K- -K- In2 2 In1 1 RL Vo= Armature Voltage IL Input Voltage Duty Ratio Armatue Current Out1 1 Resr -K- Product Integrator3 1 s Integrator1 1 s -K- 1/L -K- 1/C -K- In3 3 In2 2 In1 1 eg fs ia iL io n nref t va vc vo B C D Eg Ia J F Ka L La Ra sr Re Rl Tl Va Vc Vo Vs iL D A Ia 20 = W = 1 Ra , 46 mH La = m Kg J - = 093 . 0 . sec/ . . 008 . 0 rad m N B = rad V Ka sec/ . 55 . 0 = f V Vs 240 = Va Vo = Ia Io = mH L 5 . 1 = = Rl W = C 4700 . f m = sr Re W . 20 KHz fs =  Title  GATE DRIVE LOOK-UP TABLE LPF Reference Speed Armature Current Duty Ratio Input Voltage Vs Armature Voltage Va L C MOSFET Title  GATE DRIVE Duty Ratio Input Voltage Vs L C MOSFET MODELING AND SIMULATION OF SENSORLESS SPEED CONTROL OF A BUCK CONVERTER CONTROLLED DC MOTOR Bassim M. H. Jassim Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 80 -87 (2010) Al-Khwarizmi Engineering Journal Al-Khwarizmi Engineering Journal, Vol. 6, No. 1, PP 80 - 87 (2010) Modeling and Simulation of Sensorless Speed Control of a Buck Converter Controlled Dc Motor Bassim M. H. Jassim * Tagreed M. Ali ** Department of Eelectrical Engineering/ College of Engineering/ University of Baghdad * Email: bassimmhj@yahoo.com ** Email: tagmali@yahoo.com (Received 24 March 2009: accepted 20 October 2009) Abstract This paper investigate a sensorless speed control of a separately excited dc motor fed from a buck type dc-dc converter. The control system is designed in digital technique by using a two dimension look-up table. The performance of the drive system was evaluated by digital simulation using Simulink toolbox of Matlab. Keywords: DC motor, speed control, buck converter. 1. Introduction In speed control of the dc motor, high frequency output voltage ripple is achieved using dc chopper where the average voltage across the motor terminals can be controlled by using the duty ratio of power switching device [Sen]. Different control methods have been used to regulate the motor speed like PI controller [Gurbuz] and fuzzy logic control [Tipsuwanporn]. In much application the use of speed sensors like tachogenerator or shaft encoder will add a significant cost and weight to the drive system. In this work, high chopping frequency is achieved using a MOSFET as a switching device and a smooth dc output voltage and current are generated using a buck type dc-dc converter with sensorless speed control technique to reduce the cost and weight of the drive system. The control method is simple and reliable and does not need exact system parameters measurement when implemented practically. The buck converter circuit design is presented in section II, while section III explains the proposed control technique with a two dimension look-up table which is used in speed control of induction machines [Jeftenic]. The complete system is modeled in section IV, and then simulated using Simulink toolbox of Matlab in section V. Finally section VI presents the simulation results and conclusion for the proposed control system for both step change in reference speed and motor load. 2. Buck Converter Design The buck converter circuit diagram is shown in Fig.1, where the steady state output voltage depends linearly on the duty ratio D where: Va =D.Vs 0 D 1 …(1) The buck converter modes of operation are explained in details by [Mohan]. The converter switching frequency is 20 KHz, and the input voltage is 240V. Fig.1. Buck Converter Circuit Diagram. 2.1. Inductor design The inductor value depends on the admissible current ripple which is given by the following relation [Mohan]: (Vs – Va ). …(2) The continuous conduction mode of the converter is ensured by making the minimum output current equal to the motor no load current which is about 2A for the used motor in this work. Therefore is the maximum admissible value. Solving Eq. (2) for yields: …(3) Where: Substituting Eq.(1) by Eq.(3) gives: …(4) Clearly the maximum value of the right hand side of Eq. (4) occurs at ; thus the value of the inductor becomes: …(5) Taking to ensure more smoothness, the value of the inductor will be 1.5 . 2.2. Capacitor Design The output voltage ripple can be minimized by making the corner frequency of the output LC filter as ; also a rule of thumb of EMBED Equation.3 minimum at is more realistic when electrolytic capacitors are used[Chyrysis] and a ccordingly for the rated armature current, the capacitor selected to be two of connected in parallel is to reduce the equivalent series resistance of the capacitor. 3. The Proposed Control Concept The well known equation of the dc motor is: …(6) Where: …(7) Using the last two equations with Eq.(1), yields: …(8) Then: …(9) The proposed algorithm assumes that the reference speed is equal to the actual speed, so if there is a two dimension look-up table in which the first field represents motor speed, the second field represents the armature current and the third one represents the duty ratio; then the required duty ratio can be calculated for a given reference speed and motor load which is estimated by the armature current. The schematic of the drive and control system is shown in Fig.2. For operating points not included in the table, cubic spline interpolation and extrapolation is used to calculate the required duty ratio. The two dimension look-up table can be formed in two ways. The first method uses simple measurements for small number of operating points while in the second method, the steady state dc motor equivalent circuit is used to calculate the required armature voltage and then the duty ratio for a given reference speed and motor load. Fig.2. Buck Converter Controlled dc Motor Fig.3 shows the calculated function , from which the required duty ratio is calculated for a given reference speed and armature current, therefore, the speed can be controlled using only the armature current signal. A current limiter is used to protect the system from the large starting and transient currents, which can damage the converter and possibly the motor. 4. System Modeling and Simulation This section includes the modeling of the dc motor and the buck converter, and then the overall system is simulated using Simulink toolbox of Matlab. 4.1. DC motor Modeling A separately excited dc motor is modeled by the equations below [Tipsuwanporn]: …(10) Where: The torque balance equation is: …(11) Where: 4.2. Buck Converter Modeling The buck converter is modeled using the equations [Chrin]: …(12) …(13) …(14) Where: When the switch is on. When the switch is off. Using the equations (10-14) with the look-up table, Fig.4 shows the overall system simulation while Fig.5 and Fig.6 are the simulation of the dc motor and the buck converter respectively using Simulink toolbox of Matlab. 5. Simulation Results and Conclusion Based on the system model, the motor parmeters, and the converter parameters shown in the appendix, Simulink is used to simulate the system under consideration. Simulation results are shown in Fig.7 and Fig.8 for step response for speed change from 1000 rpm to 1800 rpm ( 104.7 rad/sec to 188.5 rad/sec) and from 1800 rpm to 1000 rpm at rated motor load, and for step change in motor load from 7 N.m to 11 Nm and from 11 Nm to 7Nm at rated speed respectively. These figures clarify the soft start of the motor and the operation of the current limit as well as the satisfactory transient response. The results demonstrate the effectiveness of the proposed control scheme. One can conclude that the steady state accuracy depends mainly on the look-up table forming. The experimental method for producing a look-up table will lead to more accurate results than that of the method of calculation used in this work since it takes into account some effects, like the parasitic elements not considered in the model. Practical implementation of this proposed control method doesn’t require exact motor parameters measurement and lookup table can be changed easily without any hardware modification to take into account the mechanical status of the motor which is changed after a long period of operation. Fig. 4. Simulink of a Sensorless Buck Converter Controlled dc Motor. Fig. 5. Simulink of a Separately Excited dc Motor. Fig. 6. Simulink of Buck Converter. Notation Motor generated voltage (or back emf). Converter switching frequency. Motor armature current. Converter inductor current. Converter output current. Motor speed. Motor reference speed. Developed torque. Motor armature voltage. Converter capacitor voltage. Converter output voltage. A Ampere Friction coefficient. Converter capacitance. Duty ratio Average motor generated voltage. Average armature current. Moment of inertia. Back emf and torque constant. Converter inductance. Motor armature circuit inductance. Motor armature circuit resistance. Capacitor equivalent series resistance. Converter inductor internal resistance. Load torque. Average motor armature voltage. Average capacitor voltage. Average converter output voltage. Converter input voltage. Inductor current ripple. Appendix The dc motor used has the following specifications: DC motor, 110V, 2.5 hp, 1800rpm, , 2 for the motor and its connected load, for the motor and its coupled load., , which is the back emf and torque constant. The buck converter specifications are: Input voltage . Output voltage is adjustable according to required speed and load. Output current . , with internal resistance 0.017 , two capacitors connected in parallel each of EMBED Equation.3 with 0.25 , switching frequency 6. References [1] Chrip, p. and Bunlaksananusorn, C,”Large signl average modeling and simulation of dc-dc converters with simulunk,” IEEE- Power Conversion Conference-Nagoya, 2007. [2] Chyrysis, C. George, High frequency switching power supplies, 2nd ed., McGraw-Hill, 1989. [3] Gurbuz Fatma and Eyup Akpinar,”Stablity analysis of a closed loop control for a pulse width modulated dc motor drive,” Turk J Elect. Engin., Vol.10, No.3, 2002. [4] Jeftenic, B.I., Bebic, M.Z., and Nitrovic, N.N.,” A simplified speed sensorless control for variable frequency induction motor drives,” IEEE Transaction on Energy Conversion, Vol.14, No.3, Sept. 1999. [5] Mohan, N., Undland, T.M., and Robbin, W.P., Power electronics: converters application and design, 3rd ed., Wiley& Sons, 2003. [6] Sen, P.C., Principles of electric machines and power electronics, 2nd ed., John Wiley & Sons, 1997. [7] Tipsuwanporn, V., Numsomran, A., and Klinsmitth, N.,” Separately excited dc motor with fuzzy self organizing,” International conference on control, automation and systems. Oct.,2007. نمذجة ومحاكاة محرك تيار مستمر مسيطر عليه بواسطة مغير تيار مستمر خافض للفولتيه وبدون متحسس سرعه باسم محمد حسن جاسم* تغريد محمد علي** قسم الهندسه الكهربائيه/ كلية الهندسه/ جامعة بغداد * البريد الالكتروني:bassimmhj@yahoo.com ** البريد الالكتروني:tagmali@yahoo.com الخلاصة تحقق هذه الورقه البحثيه في امكانية السيطره على سرعة محرك تيار مستمر منفصل الاثاره بواسطة محول تيار مستمر خافض للفولتيه من نوع ((Buck وبدون استخدام متحسس سرعه وباستخدام تقنيه رقميه من خلال استخدام جدولا ثنائي الابعاد ثم تم تقييم مواصفات النظام من خلال محاكاة النظام باستخدام مايسمى بالـ ( .(Simulink toolbox Speed & armature current Fig.3. The Duty Ratio Vs. the Armature Current and Motor Speed � EMBED PBrush ��� Current in Amp. Speed in rad/Sec Fig.8. Transient Response due to Step Change in Load. Time in Sec 200 150 100 50 0 -50 30 25 20 15 10 5 0 Speed & arrmature current Speed in rad/Sec Current in Ampere Fig.7. Transient Response due to Step Change in Speed. 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