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Third Harmonic Injection Based Nonlinear Control of IPMSM Drive for Wide Speed Range Operation Md. Mizanur Rahman* and M. Nasir Uddin** * Department of Electrical and Computer Engineering North South University, Bangladesh E-mail:
[email protected]
Abstract– This paper presents a nonlinear controller incorporating third harmonic injection for wide speed range operation of interior permanent magnet synchronous motor (IPMSM) drive. Due to magnetic saturation, constant motor parameters lead to an unsatisfactory performance for the controller. Therefore, taking parameter variations into account an adaptive backstepping based nonlinear controller is developed for an IPMSM drive. Furthermore, a sinusoidal third harmonic injection (THI) technique is integrated to increase the DC bus utilization which facilitates a higher speed operating range. The field control permits extended speed range utilizing the reluctance torque. Stability of the control law state variables are demonstrated through Lyapunov stability criterion and global asymptotic stability is assured through the application of criterion supported by Barbalat’s lemma. Feasibility of the proposed drive is tested in both simulation and experiment for laboratory 3.7kW IPMSM drive. A performance comparison of the proposed harmonic injection based nonlinear controller is shown with classical vector control and nonlinear controller without THI and parameter estimation. Index Terms— Interior permanent magnet synchronous motor, adaptive backstepping based control, third harmonic injection, parameter estimation, speed control. NOMENCLATURE ݒௗ , ݒ Stator voltages; d-and q- axis components. ݅ௗ , ݅ Stator currents; d-and q- axis components. ܮௗ , ܮ Stator inductances; d-and q- axis components. ܴ௦ Stator per phase resistance. Ȍ Rotor magnetic-flux linkage. ߰௦ Stator flux linkage. P Motor pole pairs number. ߱ Actual rotor speed. ߱ Electrical speed of the rotor (߱=P߱ ) ܶ , ܶ Motor electromagnetic developed and load torque.
Rotor inertia constant. ܤ Friction damping coefficient. I.
INTRODUCTION
The interior permanent magnet synchronous motor (IPMSM) has been becoming a popular choice for ac drives
** Department of Electrical Engineering Lakehead University, Thunder Bay, Canada E-mail:
[email protected]
as it offers high efficiency, low turbulence with reliability, high power density and small air gap [1,2]. Effective control of high performance drives is affected due to nonlinear behavior of winding currents and magnetic saturation of the rotor core [3]. System performance degrades with the classical PI controllers having constant gains [4-6]. To overcome the drawbacks of conventional controller’s researcher have newly developed adaptive backstepping controllers where system nonlinearities and uncertainties have been incorporated in the design stage which tend to vary with operating conditions [7,8]. To linearize torque equation, ݅ௗ is considered zero by most of the researchers which simplifies supervision technique but resulting higher resistive losses and poor efficiency at light loads [9]. Moreover, with ݅ௗ =0 control techniques, motor air-gap flux cannot be controlled which restricts the motor speed to rated speed as the reluctance torque components are neglected. Maximum torque per ampere (MTPA) and field weakening (FW) techniques are utilized to control the flux for wide speed range operation [10-12]. But both MTPA and FW schemes are parameter dependent and hence, the performance is affected by the variations of d- and q-axis inductance unless these parameters are estimated online. Therefore, a control technique is required for variable speed drives where speed should follow a specified reference trajectory, regardless of load disturbances, parameter variations and model uncertainties. In [12] FW control strategy of IPMSM is proposed to achieve constant output power but the motor parameters remain constant. Authors in [13] reported MTPA and FW algorithms to expand the operating speeds but the controller does not ensure the drive stability. To avoid phase currents baseband distortion, linear modulation region is preferred by the researchers for pulse width modulation based control schemes where 86.67% inverter supply potential is utilized for motor line-line potential [14]. Keeping control schemes in linear modulation region, inverter DC bus utilization can be increased by 15.47% incorporating third harmonic injection (THI) which reduces the magnitude of the phase voltages [15]. When rotor flux is aligned with controller reference frame, incorporating sinusoidal THI speed as well as torque oscillations can be reduced [16]. Therefore, a nonlinear speed controller coupled with THI for less speed oscillations and reduction in motor current harmonics with increased inverter supply utilization is presented in this paper. Existing nonlinear controllers did not
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consider the variation of all motor parameters such as temperature fluctuations that alters the effective drive performance [17]. Therefore, in this paper the robustness of the controller is achieved by online estimation of stator resistance, load torque and d-q axis inductances through Lyapunov stability theory. The global asymptotic stability is assured through the application of criterion supported by Barbalat’s lemma. The field control incorporates the MTPA below the rated speed and FW above the rated speed. Furthermore, sinusoidal THI technique is incorporated to increase the DC bus voltage utilization and to minimize the speed oscillations. The effectiveness of the proposed drive is verified by real-time test on a DSP board DS1104 for a laboratory 3.7kW IPMSM. Results obtained from both simulation and real-time environment confirms that the proposed THI based nonlinear control scheme offers robustness, higher speed operating range with less speed oscillations, stator current reduction and lowest torque ripples as compared to the classical vector control (VC) scheme and system without sinusoidal THI and parameter estimation. II.
MOTOR MODEL AND NONLINEAR CONTROL
Considering sinusoidal induced EMF with no damper winding on rotor and negligible core losses, state model of an IPMSM drive is derived from synchronous machine can be obtained by as follows [18]: ௗ ௗ௧ ௗ ௗ௧
ଵ
ൌ ሾݒௗ Ǧܴ௦ ݅ௗ ܲ߱ ܮ ݅ ሿ
ଵ
ൌ ሾݒ Ǧܴ௦ ݅ Ǧܲ߱ ܮௗ ݅ௗ Ǧܲ߱ ߰ሿ
ௗఠೝ ௗ௧
ܶ =
ଵ
ൌ ሾܶ Ǧܶ Ǧܤ ߱ ሿ
ଷ ଶ
ሾ߰݅ ሺܮௗ െ ܮ ሻ݅ௗ ݅ ሿ
ܶ =ܶ ܤ ߱ ߱ܬ
(1) (2) (3)
݁ఠ ൌ߱ כǦ߱
ଵ
݁ఠሶ = ሾܤ ߱ ܶ െ
ଷ ଶ
ሺ߰݅ ൫ܮௗ െ ܮ ൯݅ௗ ݅ ሻሿ
(7)
where, ݁ఠሶ = rate of change of speed error (error dynamic). To fulfill the speed tracking objectives, derivative of the ଵ initial Lyapunov function, ܸ ൌ ݁ఠଶ is given by: ଶ
ܸሶ ൌ݁ఠ ݁ఠሶ ൌ
ഘ
ሾܤ ߱ ܶ െ
ଷ ଶ
ሺ߰݅ ൫ܮௗ െ ܮ ൯݅ௗ ݅ ሻሿ(8)
To ensure the stability of (8), ݅ௗ and ݅ is identified as virtual control variable. The stabilizing function ݅ௗ and ݅ are selected such that (8) becomes negative semi-definite. Initially, the reluctance torque is neglected (݅ௗ =0) to ensure the stability of (8) and ݅ is chosen as: ݅ௗ = כ0 and ݅ כൌ
ଶ ଷట
ሺܤ ߱ ܶ ݇ఠ ݁ܬఠ ሻ (9)
where ݇ఠ is closed-loop feedback gain, ݅ௗ כand ݅ כis the command currents, replacing (9) into (8): ܸሶ =-݇ఠ ݁ఠଶ
(10)
Speed tracking requirements of (10) are fulfilled assuming ݇ఠ Ͳ. For proper tracking, corresponding current error variables are defined as: ݁ௗ ൌ݅ௗ כǦ݅ௗ (11) ݁ ൌ݅ כǦ݅ (12) For stabilizing ݅ௗ and ݅ , the derivatives of the error dynamics of (11) and (12) are defined as: ݁ௗሶ =
(5)
A. Controller Design Motor actual speed converges to the command speed and speed tracking is achieved where error dynamics (speed) is specified as:
(6)
where, ݁ఠ = speed error and ߱ = כspeed reference. Then, from (3), and (6) one can get:
(4)
Flux weakening technique involves d- and q-axis current interacting components; reluctance torque as shown by the second term of (4) which provides exact speed control over an extended speed range [9]. Due to nonlinear nature and variations of dynamic operating conditions, motor parameters are not constant. Traditionally, ݅ is controlled to control the motor speed while ݅ௗ is maintained zero to make controller development easier. However, with this assumption motor cannot be operated above rated speed as reluctance torque is zero while the reluctance torque can be utilized to operate the drive at its maximum torque production level. For expanded operating region, MTPA is utilized to determine d-axis current within the rated speed and FW above the rated speed while parameters are estimated online. Control laws for d-q axis command voltages are achieved through the proposed nonlinear controller. Furthermore, pulse width modulation (PWM) technique is used where sinusoidal THI is applied for translated d-q axis command voltages with the scaled third harmonic.
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݁ሶ ൌ
ଵ
[ܴ௦ ݅ௗ െ ܲ߱ ܮ ݅ െ ݒௗ ](13)
ଶሺ ିഘ ሻ ଷట
ሺܶ െ ܶ െ ܤ ߱ ሻ
ଵ
(ܴ௦ ݅ ܲ߱ ܮௗ ݅ௗ
ܲ߱ ߰ െ ݒ )
(14)
Stator inductances are affected by changing air-gap flux in the rotor core and temperature variation affects the stator resistance. Thus, ܮௗ ǡ ܮ and ܴ௦ should be estimated online. Precise tracking can be achieved by load torque estimation as to adapt changing operating conditions. Therefore, parameters are estimated adaptively as: ݁ ൌ ܮௗ െ ܮௗ ݁ொ ൌ ܮ െ ܮ ݁ ൌ ܶ െ ܶ ݁ோ ൌ ܴ௦ െ ܴ௦
(15) (16) (17) (18)
where, ܮௗ , ܮ are the estimated d- and q- axis inductances; ܶ , ܴ௦ are the estimated load torque and estimated stator resistance. New Lyapunov function including the speed, currents and estimated quantities can be defined as: ଵ
ܸଵ ൌ ሺ݁ఠଶ ݁ௗ ଶ ݁ ଶ ଶ
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ଵ ଶ ݁ ఊభ
ଵ ଶ ݁ ఊమ ொ
ଵ ଶ ݁ ఊయ
ଵ ଶ ݁ ሻ(19) ఊర ோ
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߱ כ
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+ -
݅ௗ כ
݁ఠ
Reference current generator
ݒௗ כ Reference d and q voltage generator
݅ כ
ݒ כ
dq
abc
߱
ܴƶ ܴ௦ ܮௗ
ܮ
ܶ
Sinusoidal
ݒכ
ݒ כ
Third harmonic injection
ݒ כ
PWM inverter
݅
abc
Parameter estimator
݅ ݅
݅ௗ
dq
Ʌ୰
݅ d/dt
IPMSM
Encoder
Fig.1: Sinusoidal third harmonic injection based nonlinear control of IPMSM drive for wide speed range operation.
(a)
(19) cannot be less than zero; it is lower bounded. (b) (27) is negative semi-definite and less than or equal to zero. ଵ ଵ ଵ Vլ 1=݁ఠ ݁ఠሶ +݁ௗ ·ௗ +݁ · ݁ · ݁ொ ·ொ ݁ · (c) (27) is a continuous function of time as it is a ఊభ ఊమ ఊయ ଵ bounded function. ݁ · ఊర ோ ோ ݁߱ ଷ ଷ = ഘ ሾെ݁ െ ݇ఠ ݁ܬఠ ߰݁ ሺܮௗ െ ܮ ሻ݁ௗ ݅ ሿ+ [ܴ௦ ݅ௗ െ ଶ ଶ լ Then: V1 ĺ0 as ൝ ݁݀ ൡĺ0. Consequently, control laws are ଶሺ ିഘ ሻ ݁ݍ ܲ߱ ܮ ݅ െ ݒௗ ]+݁ [ ሺܶ െ ܶ െ ܤ ߱ ሻ ଷట validated and global asymptotic stability of the proposed ଵ ଵ ଵ (ܴ ݅ ܲ߱ ܮௗ ݅ௗ ܲ߱ ߰ െ ݒ )] ݁ · ݁ொ ·ொ ௦ ఊభ ఊమ system is verified. ଵ ଵ ݁ · ݁ோ ·ோ (20) ఊయ ఊర III. MTPA AND FW ALGORITHM To establish the global asymptotic stability of (20), In order to control flux below rated speed d-axis current stabilizing control voltages ݒௗ and ݒ are chosen as: is calculated in terms of ݅ based on MTPA technique where The derivative of the Lyapunov’s function in (19) is as follows:
ଷ ݒௗ ൌ ܴ௦ ݅ௗ െ ܲ߱ ܮ ݅ ܭௗ ݁ௗ ܮௗ ܮௗ ሺܮௗ െ ܮ ሻ݅ ݁ఠ (21) ଶ
ݒ ൌ
ଶ ሺିഘ ሻ ଷ
ሾ
ଷట
ଶ
ሺ߰݅ ൫ܮௗ െ ܮ ൯݅ௗ ݅ ሻ െ ܶ െ ܤ ߱ ሿ+
ଷ ܴ௦ ݅ ܲ߱ ܮௗ ݅ௗ ܲ߱ ߰ ܭ ݁ ܮ ߰݁ఠ ܮ
where, ݇ఠ , ݇ௗ and ݇ are closed-loop feedback constants and ߛଵ , ߛଶ , ߛଷ and ߛସ are adaptive gains. Substituting (21) and (22) into (20), parameters are predicted online based on adaptive backstepping can be defined as:
·ோ =ߛସ ሾ
ഘ
ଶ ሺ ିഘ ሻ
·ொ = -ߛଶ [
ଶ ଷഘ ଶ
(23)
ሿ
ଷഘ
· = -ߛଵ [-
ሿ
ଷట
(24) െ
ሺ ିഘ ሻ
ట ሺ ିഘ ሻ ట
െ
ఠೝ
ఠೝ
]
(25)
ሿ
(26)
Based on command voltages as defined in (21) & (22) and update laws from (23) to (26), the Lyapunov derivative in (20) can be shown to be negative semi-definite with bounded state variable as: Vլ 1=-݇ఠ ݁ఠଶ -ܭௗ ݁ௗ ଶ -ܭ ݁ ଶ 0
݅ௗ = כ
(22)
ଶ
· = - ߛଷ ሾെ
initially torque equation is expressed as a function of current angle [21]. Then, Taylor series is used for simplification and final MTPA relation is given by:
(27)
Three criterion of Barbalat’s lemma principle is used to establish asymptotic stability of the controller [19-20], and then applied to the (27). Validity of the conditions are checked as:
ሺ ି ሻ ଶ ݅ ట
(28)
Above the rated speed, ݅ௗ is calculated based on FW technique where stator terminal voltage (ܸ ) is maintained constant at rated value (ܸ ). With ݅ௗ =0 control, ܸ increases with an increase of motor speed. Therefore, above rated speed saturation occurs that results in instability of the drive system where ܸ approaches to ܸ . Thus, magnet flux is weakened by ݅ௗ maintaining ܸ as constant. Initially, peak stator phase voltage is expressed assuming steady-state condition and then simplified by Taylor series expansion. Simplified relation is given by: ଵ
ᇲ
ఠೝ
݅ௗ = כെ (߰ െ
మ ఠ ೝ ᇲ ଶ
)
(29)
For expanded operating speed range, d-axis current is defined as together by (28) and (29). IV.
THIRD HARMONIC INJECTION
Peak of the reference phase voltages can be reduced by injecting third harmonics where fundamental line to line potential is not affected [14]. Thus, the speed as well as torque oscillations are reduced in the linear modulation
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range. Initially, unknown amplitude (Į) based fundamental sine wave with a third harmonics is considered as: F(ș)=sin(ș)+Įsin(3ș)
(30)
Instantaneous magnitude of fundamental waveform is defined by the summation of d- and q-axis voltages as: మ ξሺ௩ ା௩మ ሻ
V=
(31)
ଵǤହ
Thus, instantaneous third harmonic value can be calculated as:
ܸ = ሺሺ͵Ʌሻሻ
(32)
Finally, scaled phase voltages by sinusoidal THI can be expressed as: ܸǡ்ுூ = (ܸ ܸ )*1.1547
(33)
ܸǡ்ுூ = (ܸ ܸ )*1.1547
(34)
ܸǡ்ுூ =(ܸ ܸ )*1.1547
(35)
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deviation of speed for the proposed drive in Fig. 6(a) but it converges within minimum time to the command speed while torque ripple is confined to a small bandwidth without any abrupt peak as compared to the conventional VC scheme which contains higher torque ripples at steady state as shown in Fig. 6(b). Speed and load is suddenly increased to verify the effectiveness of the proposed drive which is shown in Fig. 7. At t=2 s, speed is increased (140 to 250 rad/s) and load is suddenly increased at t=3s from 10 to 12 Nm. It is seen from Fig. 7 that the motor can follow the command speed with a little overshoot at t= 2 s but no steady-state error. If parameters are not estimated and sinusoidal THI is not incorporated in the proposed system, then motor vibrates at higher command speed of 240 rad/s at 50% rated load as shown in Fig. 8. (a)
Using these equations (33)-(35), line-line potential is increased to DC supply voltage where maximum linear amplitude modulation becomes 1.555. V.
SIMULATION RESULTS
Simulation investigation of the proposed IPMSM drive system is carried out using MATLAB/Simulink software utilizing motor parameters shown in Appendix. The values of ݇ఠ , ݇ௗ , ݇ , ߛଵ , ߛଶ , ߛଷ and ߛସ are selected to get the best control performance which verifies ݁ఠ , ݁ௗ and ݁ converge to zero. Speed and d-q axis current responses of the proposed drive for a command speed of 183 rad/s and 19.1 Nm load (rated condition) is shown in Fig. 2(a). At rated condition, speed trajectory follows the command speed smoothly without any steady state error and d-axis current is negative which indicates that the proposed drive can utilize the reluctance torque. The speed, d- and q- axis current error dynamics are gradually merged to zero, as shown in Figs. 2(b) and 2(c), respectively that ensures the global stability of the proposed drive. The balanced operation of the drive system is established through the line currents demonstrated in Fig. 2(d). The estimated load torque and stator resistance presented in Fig. 3 differs from nominal values as parameters are estimated online with changing operating conditions. The estimated d-and q-axis inductances in Fig. 4 also differ from nominal value given in the appendix. Simulated speed and developed torque responses of the proposed sinusoidal THI based nonlinear drive for step increase of command speed from 183 to 275 rad/s at rated load is shown in Fig. 5. It is found that the proposed drive performs better dynamic performance confining torque ripples to small bandwidth while speed follows the command speed that is 1.5 times of the rated speed with negligible speed oscillation. The ability to withstand sudden load disturbance is verified and shown in Fig. 6. The load is suddenly increased from 15 Nm to 19.1 Nm at t=2.5 s. Although there is a small
(b)
(c)
(d)
Fig. 2: Simulated responses of the proposed sinusoidal THI based nonlinear control of IPMSM drive: (a) speed, d- and q- axis currents, (b) speed error, (c) d- and q- axis current error, and d) balanced three phase line currents.
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(b)
Fig. 3: Estimated and actual load torque and stator resistance at rated conditions.
Fig. 6: Simulated speed and developed torque responses at rated speed for step change in load (15 to 19 Nm): (a) proposed drive, and (b) VC scheme.
Fig. 4: Estimated and actual d- and q- axis inductances of the proposed drive at rated conditions.
Fig. 7: Simulated speed response of the proposed drive for step increase of command speed (140-250 rad/s) and with a step increase of load (10-12 Nm).
Fig. 5: Simulated speed and developed torque responses of the proposed drive for increase in command speed (183 to 275 rad/s) at rated load.
(a)
Fig. 8: Simulated speed response without parameter estimation and without THI for a command speed of 240 rad/s at 50% rated load.
Fig. 9 shows the performance of the proposed drive for 25% reduction in q-axis inductance (Lq) as magnetic saturation alters the effective drive performance. It is seen from Fig. 9 that the proposed drive can track the command speed without steady state error that verifies the parameter variation handling capability of the drive. Phase currents are reduced by sinusoidal triplen injection as compared to without THI for same voltages as shown in Fig. 10 that demonstrates the effectiveness of the system.
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Fig. 9: Simulated speed and d-q axis current responses of the proposed drive with 25% decrease of ܮ (ܮ ĺ0.75ܮ ) at rated conditioons.
The starting speed and d-q axiss current responses of the proposed sinusoidal THI based non nlinear control of IPMSM drive at a command speed of 183 rad/s under no load condition is shown in Figs. 12 (a)) and 12(b), respectively. Speed and currents per division mag gnitude is indicated on the oscilloscope. Experimental speed response shows that the onverged quickly to the speed of the proposed drive co command speed with negligible steeady state error. As the daxis current is negative as show wn in Fig. 12(b), it can contribute to utilize the reluctance to orque of the motor. Speed response for an increase in load (1 15 to 19.1 Nm) at a step change in command speed (90 to 18 83 rad/s) is shown in Fig. 13. It is seen that at load applied conditions c speed suddenly drops, but the proposed drive can quickly q recover the speed that demonstrates the robustness of the t proposed drive.
Fig. 10: Simulated balanced three phase current responnse comparison of the proposed drive with and without 3rd harmonic injection at rated conditions.
d Fig. 11: Experimental setup of the proposed drive.
VI.
EXPERIMENTAL RESU ULTS
A digital-signal processor (DSP) booard is used to implement the proposed THI based nonllinear control of IPMSM drive in real-time for a 3.7kW mootor [24]. Fig. 11 shows the experimental set-up. A personal computer (PC) is used where DSP board is equipped andd supplied by a software development system which providdes the feature of changing command speeds and index ppulses from the keyboard with editing and downloading caapabilities of the software programs. An optical encoder is uused to sense the rotor position and using encoder interface thhe signal is fed to the DSP board. To get better resolution, the encoder output is increased to 4*1024 pulses using 4-fold pullse multiplication process. Encoder pulses are counted by a 24-bit position counter and then numerical differentiation iss used to compute the motor speed from rotor position anggles. Two phase currents are measured by Hall-effect currrent sensors and other phase current is determined by balancced currents with current and frequency range of 0~200 A and 0~250 kHz, respectively. A/D (analog to digital) conveerters are used to fed the current into DSP board. The currrent signals are converted into voltage and amplified by thee interface circuit. Finally, these pulses are fed to the IGBT bassed driver circuit. A dc-machine is used as generator to adjusst the load to the test motor. The real-time model of the prooposed system is loaded to the DSP board. The sampling freqquency of 10 kHz is found suitable for the real-time implementtation.
Speed [25 rad/s/div v]
(a)
(b)
o the proposed sinusoidal THI Fig. 12: Experimental starting responses of based nonlinear IPMSM drive under 183 raad/s and no load conditions: (a) speed, and (b) d-and q- axis currents.
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Fig. 13: Experimental speed response for a step increase in load from (15 to 19 Nm) at a step change in command speed (90 to 183 rad/s).
Fig. 14 demonstrates comparative dynamic performance analysis of the proposed drive with the conventional VC scheme under 50% rated load and command speed of 183 rad/s. It is found that the classical VC scheme has higher torque ripples, whereas proposed drive indirectly controls the torque and maintains the lowest torque ripples. Figs. 15(a) and 15(b) show the speed response of the proposed IPMSM drive for a step increase of command speed (100 to 250 rad/s) at 50% rated load with and without sinusoidal THI, respectively. If sinusoidal THI is incorporated in the drive system shown in Fig. 15 (a), speed oscillations are reduced as compared to system without sinusoidal THI. A reduced motor vibration with the integration of sinusoidal THI is further verified by the steady-state stator current responses with and without sinusoidal THI as shown in Figs. 16(a) and 16(b), respectively. It is clearly seen from phase ‘a’ current response that without sinusoidal THI, there is noticeable distortion in the phase current waveform.
Fig. 15: Experimental speed response of the proposed drive for a step increase in command speed (100 to 250 rad/s) at 50% rated load: (a) with sinusoidal THI, and (b) without sinusoidal THI.
Fig. 16: Experimental phase ‘a’ current response: a) with sinusoidal THI, b) without sinusoidal THI.
VII.
Fig. 14: Torque responses for a command speed of 183 rad/s and 50% rated load: a) classical VC scheme, and b) proposed IPMSM drive.
CONCLUSION
A sinusoidal third harmonic injection based nonlinear control of IPMSM drive for wide speed range operation of IPMSM drive incorporating parameter uncertainties and flux control has been presented in this paper. Adaptive controller has been developed considering all the system nonlinearities
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where stability of the control laws is verified through Lyapunov’s stability criterion supported by Barbalat’s lemma. Finally, sinusoidal third harmonic voltages are injected to enhance the utilization of DC bus voltage. Reduced steady-state speed oscillation conditions was verified both in simulation and real-time for different operating conditions. Performance of the proposed drive has been compared with the system without parameter estimation and without THI. Rapid convergence to command speed, reduction in speed oscillations over the rated speed and a visible reduction in phase current with THI is achieved through the simulation and real-time results. The proposed drive with THI has also demonstrated excellent load disturbance rejection, with fast recovery and without steady state error than that of the without parameter estimation and without THI. Thus, the proposed drive not only provides high dynamic performance but also provides reduction in power losses through the reduction in stator currents. APPENDIX - IPMSM PARAMETERS Label ܲ௧ௗ
Parameter IPMSM rated power
Value with units 3.7 kW
ܸ௧ௗ
Rated rms voltage
183 v 14.2 A
ܫ௧ௗ
Rated current
݂௧ௗ
Rated frequency
87 Hz
߱
Rated rotor speed
183 rad/s
ܲ ܮௗ , ܮ ܴ௦
Pole pair numbers d- and q- axis inductance Stator resistance
3 .00506, .00642 H 0.242 ohm
Rotor inertia constant
0.0133 Kg.m2
ܤ
Damping coefficient
0.001 Nm/rad/s
߰
Magnetic flux constant
.2449 v/rad/s
VIII.
REFERENCES
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