Dead-time Voltage Error orrection with Parallel Disturbance Observers or High Perormance V/ ontrol Tetsuma Hoshino, Jun-ichi Itoh Department o Electrical Engineering Nagaoka University o Technology Nagaoka, Japan Takayuki Kaneko Electronics Technology Laboratory Fuji Electric Advanced Technology o., Ltd. Tokyo, Japan Abstract This paper proposes a dead-time compensation method with a parallel disturbance observer and a current controller in the d-q rotational rame or V/ control. The parallel disturbance observers consist o a ast response disturbance observer and a slow response disturbance observer to separate the back electromotive orce (EMF) rom the estimated disturbance voltage. As a result, the dead-time error voltage is corrected using the proposed method. The proposed method is validated based on the simulation and experimental results. This method can improve the current distortion to less than /9 that o the conventional method. Keywords-component; induction motor, V/ control, dead-time, disturbance observer I. INTRODUTION Recently, inverter systems have been applied to adjustable speed drive systems with induction motors in various ields or the economic utilization o energy. The V/ (motor voltage/output requency) control method or an induction motor is more suitable to general applications than a speed sensor-less vector control method, because the V/ controller is very simple, and robust or variation o the motor parameters. All voltage source type inverters require dead-time, which causes output voltage errors and has a signiicant eect on the low-voltage output range, such as at low speed. Thereore, dead-time compensation techniques are very important to realize a low cost motor drive system. Thus many dead-time correction methods are proposed [-6]. In particular the most popular voltage error compensation method is eed orward compensation o the output voltage command according to the direction o the load current. This is very simple; however, it does not work well or the low speed range, because o diiculties in detection o the load current polarity [7]. Moreover, the precise dead-time compensation method, which based on dead-time error voltage measured toward the load current value in o-line, has been proposed [8]. However, this method is also diicult to compensate the dead-time error voltage because the dead-time voltage error values is inluenced by the temperature and dispersion o a switching device. On the other hand, dead-time compensation methods using a disturbance observer have been previously proposed [9-]. In these reports, the disturbance observer is used or the sensorless vector control system o a permanents magnet motor in a rotational rame or a three-phase rame. However, V/ control o the induction motor is not considered. The dead-time compensation methods using a disturbance observer have some advantages as shown in next. Easier parameter setting than the other method. Possible to compensate orward drop voltage o a switching device, simultaneously. Possible to compensation in on-line at all times. This paper proposes a dead-time compensation method with a parallel disturbance observer and a current controller in the d-q rotational rame or V/ control. This work is aimed at providing a simple and robust control system instead o speed sensor-less vector control. The voltage error on the d- and q- axes current caused by the dead-time is suppressed by an auto current regulator (AR) in the d-axis and the disturbance observers in the q-axis. The parallel disturbance observers consist o a ast response disturbance observer and a slow response disturbance observer to separate the back electromotive orce (EMF) rom the estimated disturbance voltage. As a result, the dead-time error voltage is corrected using the proposed method. The proposed method is validated based on the simulation and experimental results. This method can improve the current distortion to less than /9 that o the conventional method. II. PRINIPLES OF DISTURBANE OBSERVERS FOR DEAD-TIME ERROR VOLTAGE ORRETION A. Problems o dead-time and conventional conpensation Fig. shows behavior o the voltage error during the deadtime period. Switch o time, it is so called dead-time, is added to gate pulses o u p and u n in order to avoid the short circuit between an upper arm and a lower arm. To obtain dead-time period, the turned-on timing o the gate pulse u p and u n are delayed during T d as shown in Fig. (b). 97-68/7/$5. 7 IEEE
The voltage error during the dead-time depends on the direction o a lowing current. When the output current direction o the leg is positive which is deined rom the leg to load, the current in the leg lows through the ree wheeling diode (FWD) o the lower arm during the dead-time period. Thus, the output voltage is decreased by the dead-time period. On the other hands, when the output current direction is negative, the current in the leg lows through the FWD o the upper arm. Thus, the output voltage increases. The value o the voltage error depends on the dead-time period and dc-link voltage as shown in Fig.. Finally, the voltage error is decided by (). Δ V s V dc T d sign( i u ) () where, s : switching requency, V dc : dc-link voltage, T d : dead-time period, i u : output current o the leg, sign(x):sign unction. I x> then sign(x), i x< then sign(x), i x then sign(x). It should be noted that the magnitude o the voltage error does not depends on the amplitude o the output voltage and the output current. Thereore, when the output voltage is small such as a low speed operation, the aect o the dead-time is strongly appeared because the ratio o the voltage error to the output voltage becomes large. B. Dead-time correction method using disturbance observers Fig. shows the equivalent circuit, in which a secondary leakage inductance is converted to a primary side, o an induction motor on d-q rotating rame. This paper proposes a dead-time compensation method with a disturbance observer. The voltage error o the dead-time is estimated by the output current and the motor parameters. The relation between the motor voltage v and current i is obtained by (). V dc u p u n i u> i u < u* ON OFF u p u n i u> i u< Vdc/ -V dc/ V dc/ -Vdc/ Figure. Equivalent circuit o induction motor. ON T d OFF Voltage error Voltage error (b) Relationship between reerence (a) An inverter leg. pulse and voltage error Figure. Relations between reerence pulse and voltage error. OFF T d ON R + pl v d ωlσ vq R σ ω L R + pl σ R σ ω R + p L m p ω ω m ω p i d iq ω + ω m φ d R + p φq L m where, R is the primary resistance, R is the secondary resistance, p is dierential operator p d / dt, L m is the magnetizing inductance, L σ is the equivalent leakage inductance, ω is the primary angular requency, ω m is the secondary angular requency, i d is d-axis components o the primary current on the d-q rame, i q is q-axis components o the primary current on d-q rame, v d is d-axis components o the primary voltage, v q is q-axis components o the primary voltage, φ d is d-axis components o secondary lux, and φ q is q-axis components o secondary lux. From equation (), when the d-axis corresponds to the vector or the secondary lux φ and the q-axis component φ q is equal to zero, the q-axis voltage v q is calculated using (3). () L m: magnetizing inductance, ΔV: disturbance voltage, T, T s: aster and slower time-constant o each disturbance observer, K AR: gain o the auto current regulator. Figure 3. Block diagram o an induction-motor drive system using dead-time error correction using disturbance observers. v q ( R + R + pl σ ) i q ωl σ id + ωmφ d. (3) In the equation (3), the st term o the right side change according to the electrical time constant T e L σ / (R +R ) because the q-axis current respond at the electrical time constant. In contrast, the 3 rd term o the right side changes slower than the st term, because the secondary angular requency responds at the mechanical time constant. Then, the nd term means the cross-term. The voltage error can be considered as the voltage disturbance or the q-axis current. In case o the low speed operation, ω and ω m in (3) become the small to other terms. Thus, i those small terms can be neglected, then the voltage error can be estimated using a voltage disturbance observer as shown in (4).
ˆ + st ( R + R + slσ ) I q Δ V (4) where, suix means controller parameter, T is time constant o the observer, s is Laplace operator, and I q is Laplace transer o i q. Fig. 3 shows a block diagram or the proposed compensation method using V/ control. The eedback ilter using the T (ast response disturbance observer) estimates the back EMF in addition to the disturbance voltage. To estimate only the voltage error rom dead-time in the middle- or highspeed range, the eedback ilter o the T s (slow response disturbance observer) is used to cancel the back EMF. On the other hand, the AR on the d-axis corrects the dead-time voltage error on d-axis and maintains the rated excitation current o the motor. Table. Analysis conditions. Parameters Values Parameters Values Primary resistance R.78Ω Fast response disturbance observer time constant T msec Secondary resistance R.44Ω Slow response disturbance observer time constant T s 5msec Leakage inductance L σ.mh III. ANALYSES OF THE PROPOSED SYSTEM One o advantages o a V/ control method is that a V/ control method is not sensitive or motor parameters in contrast to a speed sensor-less vector control. However the proposed voltage disturbance observers need some motor parameters. We are araid that the proposed observer spoils the advantage o the conventional V/ method. Thereore, the parameter sensitivity o the proposed method is discussed based on transer unctions o the proposed system shown in Fig. 3, in this section. A. Transer unctions o the proposed system Beore analysis o the proposed system, two low-pass ilters written in connected in parallel, as shown in Fig. 3, is assembled as Magnitude [db] (a)disturbance to output voltage transmission characteristics s( Ts T ) ( Ts + T ) + s TsT (5). G( + st + sts + s From q-axis control part in Fig.3, the transer unctions to the output voltage V q rom the voltage error ΔV or rom the command voltage V q * in the Laplace plane are leaded as (6), (7). Vq G( ΔV R + ste + G( R + ste Vq * V q R + + ste G( R + ste where RR +R, R R +R, G( is the transer unction shown in (5) B. Analyses o parameters mismatches using Bode diagrams Fig. 4(a),(b) shows Bode diagrams or (6) and (7), respectively. The solid lines in Fig. 4 indicate an ideal (6) (7) (b) Output voltage command to output voltage transmission characteristics Figure 4. Frequency response o parallel connected disturbance observer system. condition, where R R and L σ L σ. In addition, the dashed lines indicate various conditions, where either R or L σ is equal to R or L σ multiplied or divided by ten. The other parameters used to calculate the Bode diagrams are given in Table.. In Fig. 4(a), lower magnitude indicates higher disturbance rejection perormance. In Figure 4(b), [db] o magnitude means that controller outputs the same voltage to command voltage v q *. Then, parameter error sensitivities o each R and L σ are considered. ) Ideal conditon ( R R, L σ L σ ) Equation (8) is the transer unction rom the voltage error ΔV to the output voltage V q based on (6) in case o the ideal condition in which the controller parameter agree with the motor parameter. It should be noted that the requency response is same to a notch ilters one at this ideal condition,. The center requency o the notch is obtained by (9).
Imaginary Vq + ΔV + s (a)placement o six roots. (b) Trackings o the most vibratile root No.5. Figure 5. Placement and tracking o roots. O indicates no parameter variations, Δ indicates +%, and indicates %. The solid line, dash-dot line and dashed lines represents the K AR current regulator gain, and the T and T s observer time-constant variations, respectively. π T s T s( T ) + s TTs ( T + Ts ) + s TTs (8) As a result, the disturbance rejection gain in Fig. 4(a) is [db] in a very low requency region. It means that error voltage in the very low requency region such as a low speed region can not be corrected. Thereore slow response disturbance observer time constant T s have to be decided according to operation region o the system. Depending on the applications, the slow response disturbance observer may not use in the very low speed region. ) Aection o the parameter R In a middle and low requency region, the disturbance voltage is suppressed by the proposed method, very well. Thus a speed control range o the system should be designed in this region. On the other hand, the perormance o the disturbance voltage suppression is varied by the parameter R. I R is smaller than the R, then the perormance will be worse. In contrast, i the R is bigger than the R, the perormance will be better. Thereore, the control parameter R should be set to a little larger than the actual motor parameter R. 3) Aection o the parameter L σ The aection o the parameter L σ only appears in the high requency region. However, the behavior is similar to the aection o the parameter R. That is, smaller L σ improves the perormance o the disturbance voltage suppression. In addition, bigger L σ degrades the perormance. Thereore, the control parameter L σ should be set to a little smaller than the actual motor parameter L σ. It should be note that the aection o the parameter L σc is not too bigger than R. Finally, we summarize the considerations about the parameter mismatch. The parameter mismatch o R aects considerably in the middle requency region. The parameter mismatch o L σ aects in the high requency region. (9) The gain o the controller rom reerence voltage V q * to output voltage V q is strongly aected by the parameter mismatch o R. The aection o the L σ is smaller than aection o the R. Thereore R must be determined with consideration or the error in R. However, the proposed system is not as sensitive as the speed sensor-less vector control system.. Stability analyses using roots trackings The stability o the proposed system is analyzed using roots placement and tracking in the complex plane. The conditions or analyses use parameters o a general purpose 75 W induction motor under constant-speed in addition to those given in Table. Fig. 5(a) shows the roots placement under the condition that T ms, T s ms, K AR.5 and ω ω m.65 PU. This system has six roots because it is a sixth dimensional system. The placement o roots No.-4 in Fig. 3 indicates suicient stability, because those roots are dispersed on the real axis in an area that is negatively distant rom the imaginary axis. However, the remaining roots, Nos. 5 and 6, are located nearest to the imaginary axis. Thereore, the stability o the proposed system can be discussed based on root No. 5. Fig. 5(b) shows the root-no.5 trackings o variations in K AR, T, and T s. Each o the parameters is varied ±% rom each o these values. To stabilize the system, the roots should be located in the area negatively distant rom the imaginary axis, in addition to minimizing the imaginary part. Thus, T and T s are set to slower values, and K AR is set to a higher value in order to realize stabilization o the system. It should be noted that a slow T avoids the error voltage correction, and a slow T s deteriorates the acceleration perormance due to the back EMF. In contrast, K AR should be set as high as possible or stabilization with the consideration about a delay time o the eedback loop. As a result, the parameters should be designed according to the next terms. T is set as aster as possible or controller. T s is set to aster than the mechanical time-constant. Ater that, K AR is adjusted or the stability o the system.
* i d * v d * K AR V/ controller -e i d conversion v q * v q ** 3 v u * v v * v w * VSI Inverter IM i u i w s θ Disturbance observer in Fig. 3. i d i q 3 Figure 7. Experimental system. (a) D-axis AR gain set to K AR.5 Table. Experimental conditions. Parameters Values Parameters Values Rated power 75W Rated current 3.6A Poles 4 Rated exciting current.a Rated voltage V Primary resistance R.78Ω Rated requency 5Hz Secondary resistance R.44Ω Rated speed 4r/min Leakage inductance L σ.mh Switching requency khz Dead-time period 3μsec D-axis AR gain. Fast response disturbance observer time constant T Slow response disturbance observer time constant T s msec msec (b) D-axis AR gain set to K AR. Figure 6. Damping result with parameter tuning. Fig. 6 shows the d- and q-axis current, and the q-axis compensating voltage or veriication o the stabilization with K AR. Each parameter has the same values as those used or the analyses except K AR. Note that the load condition is changed rom no load to rated load at. sec, and rom rated load to no load at 4. sec, as shown in Fig. 6. As shown in Fig. 6(a), the vibration in the current occurs because damping is not enough. In contrast, the vibration is converged by adjusting AR gain K AR in Fig. 6(b). Thereore, the valid o the stabilization method is conirmed by the simulation. IV. EXPERIMENTAL RESULT Fig. 7 shows a control block diagram o an experimental system using the proposed V/ control. The experimental system is composed o a general induction motor and an inverter. The output voltage o the inverter is controlled on d and q rotating rame. The voltage command v q * is obtained on q-axis. In additions d-axis has the current regulator to maintain the exciting current and the stabilization. Then, the proposed method is applied to the experimental system shown in Fig.7 so that the perormance o the disturbance voltage rejection is inspected. Table gives the experimental conditions o the controller and the motor. Note that slow response disturbance observer does not work in the low speed region according to the result in the section III-B. A. omparison o THD between the conventional method and the proposed method Fig. 8 shows the u-phase, d-axis and q-axis current waveorms under conditions where the output requency is Hz with no load. It should be noted that the conventional compensation method shown in Fig. 8(a) uses the voltage error eed-orward based on the current direction. The rated excitation current is maintained by the disturbance observers used in the proposed method as shown in Fig. 8(b). The total harmonic distortion (THD) o the current shown in Fig. 8(b) is.98%, with a 7.93 point reduction rom the result as shown in Fig. 8(a). Fig. 8(c) shows each harmonic components o u-phase current. The proposed method corrects the nd, 5 th, and 7 th harmonic component because o the decreasing o current stagnation at zero-crossing point. B. omparison o steady state torque between the conventional method and the proposed method Fig. 9 shows the steady state torque curves. The output requency is set to the rated slip o.67 Hz, and then decreases in speed. The starting torque (at r/min) with the proposed method is 9%, which is six times the torque with the conventional method. Using the proposed method, the current stagnation at zero-crossing point o the conventional method is decreased, so that the current waveorm is improved. It should be note that the torque curve o the proposed method exceeding the ideal line is caused by the over compensation or the voltage drop which depend on the primary resistance R.
Torque [%] Ideal torque (Based on rated slip) (a) Without proposed method Figure 9. Improvement o steady state torque curve with proposed compensation method. (b) With proposed method Figure. haracteristics against step-shape load torque.. Acceleration Braking m m :.pu/div. (c) Harmonic component in i u waveorm Figure 8. urrent waveorms at Hz under no-load condition. (Output requency Hz, no load, 75W induction motor) i d i q, i d :.pu/div.. Dynamic state charactraistics Fig. shows the characteristic responses to the step-shape load torque. The output requency was set to 5 Hz, and the step load was applied at sec. The proposed method works without stall against step-shape load, which means that the proposed method keeps stable in the dynamic state. Fig. shows the acceleration and braking characteristic between zero and the rated speed. The acceleration and braking time is set to.5 sec under the no load condition. The proposed method can generate high starting torque and acceleration torque though the middle and high speed region, i u : A/div. because the slow response disturbance observer cancels back- EMF rom the output o the ast response disturbance observer. In addition to acceleration, the proposed method can generate braking torque at all speed range. i q i u (ms/div.) Figure. haracteristics against acceleration and braking.
D. Veriication o the aection o parameter mismatch Fig. shows the aection o the THD by the variations o parameter mismatches o R or L σ. When the R was smaller than the R, the THD is increased. Likewise, when the R was bigger than the R, the THD is decreased. On the other hands, when the parameter L σ was dierent to the actual L σ, the THD is increased. Those results agree with the conclusion in the section III-B. Thus, the validity o the analyses was conirmed. iu THD [%] V. ONLUSIONS A parallel disturbance observer, used or dead-time error voltage correction, was proposed and veriied. A summary o the outcomes indicated in this study is as ollows: The proposed method can suppress the disturbance voltage except back-emf. The THD o the motor current is improved by less than /9 that or the conventional method. Using the proposed method, the starting torque is improved to 9%, which is six times that or the conventional method. The parameter mismatch does not causes signiicantly perormance degradation. The proposed method is robust against the dynamic loads e.g. step load torque and acceleration. AKNOWLEDGMENT This study was supported by Industrial Technology Grant Program in 5 rom New Energy and Industrial Technology Development Organization (NEDO) o Japan. Figure. THD variations about parameter mismatching. REFERENES [] T. Sukegawa, K. Kamiyama, K. Mizuno, T. Matsui, and T. Okuyama, : Fully digital vector-controlled PWM VSI ed ac drives with an inverter dead-time compensation strategy, IEEE Transaction on Industry. Application., vol. 7, no. 3, pp. 55 559, (May/Jun. 99). [] J. W. hoi and S. K. Sul, : Inverter output voltage synthesis using novel dead time compensation, IEEE Transaction on Power Electronics, vol., no., pp. 7, (Mar. 996). [3] A. R. Munoz and T. A. Lipo, : On-line dead-time compensation technique or open-loop PWM-VSI drive, IEEE Transaction on Power Electronics, vol. 4, no. 4, pp. 683 689, (Jul. 999). [4] S.-G. Jeong and M.-H. Park, The analysis and compensation o deadtime eects in PWM inverters, IEEE Transaction on Industry. Electronics., vol. 38, no., pp. 8 4, Apr. 99. [5] A. Muñoz-Garcia and T. A. Lipo, On-line dead-time compensation technique or open-loop PWM-VSI drive, IEEE Transaction on Power Electronics, vol. 4, no. 4, pp. 683 689, Jul. 999. [6] A. ichowski, J. Nieznanski, Sel-Tuning Dead-Time ompensation Method or Voltage-Source Inverters IEEE Power Electronics Letters, vol. 3, no., June 5 [7] H. Zhao, Q. M. J. Wu, and A. Kawamura, An accurate approach o non-linearity compensation or VSI inverter output voltage, IEEE Transaction on Power Electronics., vol. 9, no. 4, pp. 9 35, Jul. 4 [8] S. Kakizaki, M. Ito, T. Fukumoto, H. Hamane, and Y. Hayashi, Measurment o Parameters and the Automatic Measurement o an Error Voltage by Dead Time o an Induction Motor IEEJ Annual meeting, 4-43, (Mar. 7) [9] H. S. Kim, H. T. Moon, and M. J. Youn, : On-line dead-time compensation method using disturbance observer, IEEE Transaction on Power. Electronics., vol. 8, no. 6, pp. 36 345, (Nov. 3). [] N. Urasaki, T. Senjyu, K. Uezato, T. Funabashi, : An Adaptive Dead- Time ompensation Strategy or Voltage Source Inverter Fed Motor Drives IEEE Transactions on Power Electronics, Vol., No. 5, (Sep. 5).