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1. IntroductionAdjustablespeed motor drives are widely used in various applications, such as manufacturing automation systems and residential heating, ventilation, and air conditioning (HVAC) equipments. In the past, DC motors were extensively used in these applications. However, the commutators and brushes of DC motors would reduce the reliability of the drive systems. The permanent magnet AC motors (PMACMs) have emerged as viable candidates for highperformance servo drive applications to solve the maintenance problems of the DC motors. The PMACMs are classified on the basis of the wave shape of the induced backEMFs, i.e. sinusoidal and trapezoidal [3]. The sinusoidal type is known as PM synchronous motor (PMSM), and the trapezoidal type is brushless DC motor (BLDCM). The BLDCMs have 15% more power density than PMSMs, due to the higher ratio of the rms value to the peak value of the flux density [4]. Besides, since only two phases are excited at any instant of the BLDCM control, the commutation control of the BLDCMs is much simpler than the PMSMs, which require continuous and instantaneous absolute rotor position. Therefore BLDCMs are becoming more attractive for many industrial applications, such as compressors, electrical vehicles, and DVD players etc. Because BLDCMs use permanent magnets for excitation, rotor position sensors are needed to perform electrical commutation. Usually, three Halleffect sensors are used as rotor position sensors for a BLDCM. However, the rotor position sensors present several disadvantages from the standpoint of total system cost, size, and reliability. For this reason, many research working on controlling the motor speed of BLDCMs without rotor position sensors have been reported in the literatures [5][47], which can be generally classified into three types. The first method is directly or indirectly measure positiondependent variables, such as backEMFs and thirdharmonic voltages [8][17]. Though this method is easily to be implemented to provide rotor position information, directly access to the power converter or machine terminals is usually necessary and may introduce noise. Since the backEMF is very small at low speed and is zero at standstill, the direct measurement method can not work at lowspeed operations. In addition, auxiliary hardware circuits are required for the indirect measurement method. The second method is to derive the rotor position and speed information with a mathematic motor model by measuring the phase voltages and currents. This is so called observerbased method [18][37]. Since the motor model is adopted to calculate the flux vectors, this method is generally heavily dependent on the model parameters. Some online adaptive tuning methods have been proposed to compensate the parameter uncertainty. However, more computational efforts are required for the adaptation, which implies that a more powerful microprocessor is necessary. The third sensorless method is to utilize the rotor saliency or magnetic saturation. The rotor position information is extracted by exciting a highfrequency signal to the motor. Several signal injection patterns and modified pulsewidthmodulation (PWM) techniques have been reported [38][47]. Since this method is independent of the rotor speed and motor parameters, this method can be used at low speeds and standstill. However, the highfrequency signal injections may cause some undesirable effects to the drives, such as torque pulsations. Although there are many sensorless approaches in the literature, few of them can be both applied to the PMSMs and BLDCMs [21][24]. Since the flux distribution in a BLDCM is trapezoidal, therefore, the wellknown dq rotor reference frames model developed for the PMSM is not applicable, and some properties of the twoaxis stationary reference frame can not be used either. The research objectives of this dissertation is thus in threefolds. The first one is to develop an effective and practical sensorless control technique for the BLDCMs to reduce the hardware complexity and cost, and to increase the mechanical robustness and reliability compared to the previous existing methods. A modified backEMF measurement based sensorless approach is presented. With considering the realization constraints, the proposed algorithm has been successfully realized with integratedcircuit (IC) architecture for many lowcost applications [15]. The second objective of this research is to develop a general rotor position and speed estimation algorithm for PMACM drive system over a wide speed control range. In this approach, the flux linkage increments are calculated to derive the rotor position. Without integrating the flux linkage increments, the integration drift or offset problems can be avoided with this approach. The detailed realization issues of the sensorless algorithm will be introduced by using a commercial Texas Instrument digital signal processor (DSP) with fixedpoint arithmetic (TMS320LF2407A). The third objective of this study is to develop a control parameter tuning strategy for the highperformance motor drives. The developed PCbased autotuning software can be used for the online tuning of the control parameters of a digital motor drive through the RS232/485 serial interface. The selected control parameters can be offline tuned according to a selected performance index. In a practical servo drive, there exist many nonlinear characteristics and physical constraints such as voltage and current limits, detuning effect of vector control, parameter variations due to temperature variations, quantization error due to limited sampling effect, etc. In order to overcome uncertainties due to these effects, a fuzzylogicbased optimization scheme is developed for a practical digital motor drive. The proposed fuzzy optimization algorithm will be verified on a PCMATLAB environment. 2. Sensorless commutation controlA. BackEMFs measurement and zerocrossing detectionFrom the mathematical modeling of the BLDCM, the sum of three terminal voltages three terminal voltages, v_{a}, v_{b}, and v_{c}_{,} can be derived as follows (1) For analyzing the effectiveness of the backEMF estimation, the commutation from phase ab to phase ac is considered as an example. During the twophase conducting period, two conducting phase currents are opposite and another one is zero, that is i_{b}=i_{a}, i_{c}=0. Therefore, from (1), the backEMF of the nonexcited phase c is (2) By simplifying (2), e_{c }can be estimated as follows (3) For an ideal trapezoidal backEMF, e_{a}(£c_{e})+ e_{b}(£c_{e}) is equal to zero. Hence, the nonexcited phase backEMF can be fully estimated by (3) with only three terminal voltages. For the nonideal or distorted backEMFs [48], however, e_{a}(£c_{e}) is different from e_{b}(£c_{e}), that is (4) Due to this nonzero term, the backEMF estimation algorithm in (3) would produce an electrical angledependent error, and cause a phase shift to the zerocrossing point of the real backEMF. If the shapes of the backEMFs can be known, this error can be compensated in advance. However, for unknown backEMFs, this error would cause inaccurate commutation control. Therefore, some phase compensation strategies have been proposed to improve the accuracy of the estimation [12][14]. Fig. 1 shows the backEMF estimation during the twophase conducting period. ¡@
During the commutation period, three phases are conducted until the decaying current reduces to zero. It should be noted that the estimation algorithm in (3) is only valid by assuming the nonexcited phase current is zero. Hence (3) would become a wrong estimation for backEMFs during the threephase conducting period. In this example, during the commutation from phase ab to phase ac, the terminal voltage vb is equal to half dclink voltage () due to the freewheeling diode clamping effect until phase current ib vanishes as shown in Fig. 1. Hence, if (3) is applied for the estimation, then the estimated backEMF of nonexcited phase a would be derived as follows (5) Obviously, differs from the real backEMF . Since the backEMF estimation can no be achieved during the threephase conducting period with only three terminal voltages, a delayed sampling technique is required to mask the estimation for avoiding wrong zerocrossing detection during this period. Fig. 2 illustrates the typical waveforms of the estimated nonexcited phase backEMF and the corresponding zerocrossing signal during twophase conducting period and threephase conducting periods. It should be noted that the duration of the threephase conducting period would depend on the operating conditions [49]. Hence the delayedsampler should be adjusted according to the different operations. In this paper, an adaptive delay controller is presented to improve the backEMF estimation. Fig. 3 shows the block diagram of the modified backEMF estimation and zerocrossing detection. The threshold value Dth for the delay controller can be adaptively calculated as (6) Since the estimated backEMF signal must contain noises, a hysteresis comparator with the hysteresis band Zh is used for avoiding wrong zerocrossing detection. Besides, a digital filter is also used to filter out the possible noise.
B. Commutation Phase ShifterAfter detecting the zerocrossing signal of the estimated nonexcited phase backEMF, an additional 30degree phase shift is required to perform correct commutation. Conventionally, this phase shift is generated using an analog filter [8]. However, the phase lag resulted by the filter varies with motor speed; hence the accuracy of the sensorless commutation control depends on the rotor speed. In [11], a novel frequencyindependent phase shifter (FIPS) has been proposed as shown in Fig. 4(a). The algorithm of this phase shifter is very simple and useful for sensorless commutation control. Since the count values of c_{p}(k) and c_{n}(k) depend on the rotating speed, and the value of scaling factor g is less than one, a long bitlength divider is required at low speed operation to compute gc_{p}(k) and gc_{n}(k), i.e. the commutation instants, precisely. However, the computation effort of the long bitlength divider is quite large for the realtime applications. In this paper, a digital simplifiedtype FIPS, which only needs a simple multiplier instead of a long bitlength computation unit, is presented as shown in Fig. 4(b) to reduce the computation effort of the original FIPS. To describe the basic operation of the proposed digital phase shifter, an ideal periodic input signal is considered. Fig. 5 illustrates the operational waveforms of the proposed phase shifter. Assume that the input x(k) in Fig. 4(b) is the zerocrossing signal z(k) of the nonexcited phase backEMF, and the output y(k) is the corresponding commutation signal h(k). h^{*}(k) is the desired commutation signal. Also, g_{d} is set as twotimes of the increasing increment g_{i} to make the phase shift equal to 30 degrees from z(k). k_{zn} denotes the time when the nth zerocrossing of input signal z(k) occurs, and k_{cn} denotes the time when the nth commutation occurs. In order to analyze the effectiveness and robustness of the proposed phase shifter, two kinds of input signals are considered: i) the frequency of the input signal is accelerating and no measurement noise (error due to acceleration); ii) the input signal is periodic and includes measurement noises (error due to noise). First, consider the case (i) and assume the acceleration rate is . Fig. 6(a) shows the typical waveform of an accelerating input signal is depicted. The phase shift error due to acceleration can be calculated as follows (7)
From (7), it can be seen that the phase shift error due to acceleration is a function of g, , and . A higher rotating speed will produce a lower phase shift error based on (7), which implies that better performance can be achieved at higher speed. Since is faster than , the phase shift error is lower than as shown in Fig. 6(a). It should be noted that the phase shift error will not be accumulated. Hence the accurate commutation signal can be estimated at the instant k_{c}_{3.} Next, the case (ii) is considered. Fig. 6(b) illustrates a periodic input signal with the frequency , and two kinds of noises are inserted. One wrong zerocrossing signal with time interval m_{1} is generated at k_{z}_{1 }for simulating the error due to freewheeling diodeclamping effect, and the other wrong zerocrossing signal with time interval m_{2} is generated at k_{z}_{4} for simulating the measurement error due to flatness around zero. The phase shift error due to the noises can be described by (8) where denotes the desired commutation instant. From (8), it can be seen that the phase shift error due to input noises is a function of , g, m_{1}, and m_{2}. It should be noted that the phase shift error increases with increasing rotor speed, which implies that the input noises have significant effect at highspeed operation. Also, note that when , the phase shift error becomes zero, that is, the effect of noises can be cancelled by the integral action of the proposed phase shifter. Besides, phaseadvanced control, i.e. , can also reduce the phase shift errors. Similar analysis can be done for the next zerocrossing instant k_{z}_{6}, the phase shift error due to the noises can be derived as (9) A phase shift error _{ }would occur at k_{c}_{2}, but would be vanished at next commutation instant k_{c}_{3.} C. Commutation Phase CompensationIn order to produce maximum torque at lowspeed operation for BLDCMs, the phase currents are required to be aligned in phase with the backEMF waveforms, i.e. phase shift between zerocrossing of the nonexcited phase backEMF and real commutation signal is 30 degrees [50]. However, a commutation phase error may exist due to the phaselag of lowpass filtering, noises, transient operations, and nonideal effect of the estimated backEMF. In this paper, the proposed digital phase shifter provides a phase compensation capability for adjusting excitation angles for the sensorless commutation control of BLDCMs. The phase compensation can be easily implemented by fixing the decreasing slew rate g_{d}, and changing the increasing slew rate g_{i} with the following equation: (9) where q_{f} is the phase lag due to the lowpass filtering of the terminal voltages, and is the desired advanced angle. D. Rotor Speed EstimationThe accuracy of speed estimation is very crucial for closedloop speed control. Since the commutation signal h(k) can be estimated with the presented algorithm, the time interval T_{c} between two commutations can be easily calculated as shown in Fig. 7. Hence the rotating speed can be estimated as follows [8],[13]: (10) where is the estimated rotating speed from commutation signals, P denotes the number of rotor poles, and f_{e} is the electrical rotating frequency. However, this method can only update the estimated speed when commutation occurs, and works poorly at lowspeed operations because of no information between two commutations. In order to improve the speed estimation at lowspeed operation, this paper proposes a novel speed estimation technique, which can estimate the instantaneous speed at each sampling instant of speed control loop. Fig. 7 also presents a concatenation waveform of the ideal nonexcited phase backEMF signal e(k). The rotating speed can be also estimated from the peak value e_{p} of the backEMF as follows: (11) where K_{E} is the backEMF constant of a BLDCM. The estimation algorithm in (11) suffers from a similar problem as (10), because the peak value e_{p} can be only actually known at each commutation instant. However, e_{p} can be predicted from the sampled backEMF signal e(k) with sampling period T_{s} between two commutations. When the sampling instant is between two commutations, i.e. k_{c1}<k<k_{c2}, the speed estimation algorithm is derived as follows: (12) where is equal to , because no commutation occurs during this period. From the observation of (12) the estimated speed can be updated at each sampling instant of the speed control loop by differentiating the nonexcited phase backEMF.
E. Simulation AnalysesFig. 8 shows the comparison of the ramp speed responses with different acceleration rates. It is clear that the sensorless commutation phase error due to acceleration increases with increasing acceleration rates. Fig. 9 shows the comparison of the closedloop sensorless control performance at lowspeed operations with two different speed estimation techniques. It is clear that the control performance with estimated speed from commutation signals is worse than the one with estimated speed from backEMF voltages, especially for the disturbance rejection ability. Therefore, the proposed rotor speed estimation algorithm can extend the sensorless speed control range to lower speeds compared to the conventional method [8],[13]. From the simulation analyses, accurate sensorless commutation control can be achieved for the BLDCM drive at lowspeed and highspeed steadystate operations as well as transient operations. Therefore, this approach can be effectively used for many lowcost applications. However, for verylow speed operations (below 100 rpm), this sensorless approach is problematic due to a low signaltonoise ratio (SNR) in voltage signals, which are the major variables for estimating the commutation signal and rotor speed. Besides, the proposed sensorless approach can be only applied to the BLDCMs with trapezoidal backEMFs. Therefore, a more general and robust sensorless control algorithm will be developed in the following section.
3. Rotor Position Estimation AlgorithmFor a PMACM, the induced backEMF voltages are functions of the rotor position, and are proportional to the angular speed. Hence, the threephase backEMF voltages can be expressed as (13) where e_{1}, e_{2}, and e_{3} are normalized trapezoidal or sinusoidal fluxdistribution functions. From (13), it can be seen that if the backEMF constant K_{E} is assumed constant, the rotor position can be estimated from the backEMF voltages and the rotor speed. However, if only the relationship between the rotor position and the backEMF voltages is used, the position estimation scheme may not operate accurately at low speeds due to the low signaltonoise ratio of the backEMF voltages. Besides, only the nonexcited phase backEMF voltage can be directly measured for the BLDCMs as discussed in the previous chapter. Hence, in order to improve the accuracy of the rotor position estimation, the relationship between the rotor position and the flux linkage of the permanent magnets is also utilized in the rotor position estimation algorithm. The total flux linkages in the motor can be obtained by integrating the threephase voltages and currents as follows (14) From (13) and (14), the flux linkages are functions of phase currents and the rotor position. Therefore, the rotor position can be deduced from the estimated flux linkage. However, the integration computation in (14) suffers from the integration drift due to motor parameter variations and measurement errors. This drift induces a significant problem in the estimation of the flux linkages, especially at low speeds [18][27]. In order to overcome the drawbacks of the drift problem, a novel rotor position estimation algorithm is proposed by utilizing flux linkage increments. Substituting (13) into (14), the flux linkage equations can be rewritten as (15) For digital implementation, if the sampling frequency is high enough, the rotor position increment within one sample interval can be estimated from (15) as follows (16) where £Gi_{a}, £Gi_{b}, and £Gi_{c} are the phase current increments, and £G£p_{a}, £G£p_{b}, and £G£p_{c} are the flux linkage increments within one sampling interval of each phase. Ideally, each phase should produce identical rotor position increment, that is (17) where is the estimated rotor position increment. By using a weighted average method [24] to estimate the rotor position increment, (16) can be rewritten as follows: (18) By summing each row in (18), the general rotor position estimation algorithm can be derived as (19) With the presented method in (19), the integration computation is moved from the flux linkage estimation to the rotor position estimation. Besides, the internal closedloop correction mechanism can correct the estimated rotor position at each sampling instant to stabilize the position integration as shown in Fig. 10. This is one important feature of this algorithm. Furthermore, this internal correction loop can also improve the robustness of the rotor position estimation with respect to the parameter variations and measurement noises. Fig. 11(a) shows the sensorless speed control performance of the sensorless BLDCM drive over a wide speed range. From the point of view of the practical application, the proposed sensorless approach has good performance over a wide speed control range even during the speed reversal as shown in this figure. Besides, the sensorless estimation algorithm is also applied to a PMSM with sinusoidal backEMFs to verify the generality of this approach. Fig. 11(b) shows the similar simulation result of the sensorless speed control performance. The performance is consistent with the BLDCM shown in Fig. 11(a).
4. Fuzzy Optimization AlgorithmIn order to specify the relationship between the servo control parameters and servo performance, a performance evaluation method is presented. Two objective functions are defined for evaluating the speed dynamic response as follows (20) (21) where J_{TR}(N) and J_{CE}(N) denote the objective functions of the speed transient response and the corresponding control effort at the N cycle, respectively. The desired rise time £Gt_{r} of speed response can be determined when the rotor speed is greater than . With small gains, the control effort is small and the speed response is very slow. By increasing the velocity loop gains, the transient speed error may decrease to a minimum value with increasing the control effort. After defining these objective functions, the design problem for highperformance servo drives becomes as a multiobjective optimization problem, which implies to minimize all these four objective functions simultaneously. Since there are some tradeoffs between these objective functions, the multiobjective problem is difficult to be solved. In order to solve this problem, a weightedsum method [51] is presented for representing the relative importance of each objective function. By properly combining the weighted objective functions, a convex objective function can be formulated for determining the optimal values of servo control parameters as follows (22) where , and W_{V}=[w_{TR},w_{CE}] is a weighting vector, which is used to specify the performance specifications. Hence the optimization problem can be reformulated as follows: subject to (23) where is the control parameter vector. and are the maximum and minimum vectors of K. The combined objective function for evaluating velocity control performance can be rewritten as (24) where w_{CE} can be arbitrarily assigned. Since the combined objective functions are convex functions, the gradient method can be applied to find the optimal control parameters for minimizing the objective functions [52]. The update equations for each control parameter are (25) (26) where N denotes the current iteration number, and h_{vp}, and h_{vi} are the stepsizes for the optimization equations. In general, small stepsizes may lead to an inefficient search process. On the other hand, large stepsizes allow the search process to approach the minimum efficiently. However, large stepsizes may not guarantee the descent direction for optimization and may cause oscillation around the local minimum point. Several methods have been proposed to adaptively adjust the stepsizes during the optimization process [53]. For example, the steepest descent algorithm can be applied to choose the optimal stepsize for the maximum decreasing amount of the objective function at each increment. However, this method needs to calculate the objective values with many different step sizes and may slow the overall optimization process. In this study, a fuzzy stepsize tuning strategy is proposed to adaptively update the step sizes for achieving both fast convergent rate and precise optimum results of the optimization process. Since fuzzylogic can simply transfer the expertknowledge into an algorithm by using linguistic descriptions, the proposed strategy can best extract the expert¡¦s knowledge. Fig. 12 shows the detailed block diagram of the fuzzy stepsize tuner for optimization algorithms. The inputs of the fuzzy stepsize tuners are the combined servo loop objective function J_{V}(N), and the change of the combined objective functions DJ_{V}(N)= J_{V}(N) J_{V}(N1). The output variables are the step sizes for updating velocity control parameters. Fig. 13 shows the block diagram of the proposed fuzzy optimization scheme for the speed controller. This scheme is composed of a twolevel hierarchical architecture. The higher level is the proposed fuzzy optimization algorithm, which executes in a batch processing mode with lower priority, and the lower level is the servo control system, which operates in a realtime processing mode with higher priority. By using the hierarchical structure in realizing the fuzzylogic based optimization techniques for digital servo drives, the benefits of computational efficiency and learning capabilities of intelligent control strategy can be combined [54].
5. Experiment ResultsThe ratings and parameters of the BLDCM are listed in Table 1. Fig. 14 shows the speed control performance with a wide speed control range (100 to 3000 rpm). From this figure, the proposed sensorless algorithm has a widespeed regulation capability and good transient response under fullspeed operations. Fig. 15 shows the steadystate response at 60 rpm with the novel sensorless algorithm under the 0.75 p.u. load condition. The minimum controllable speed is successfully improved with comparison to the backEMF measurement method. Fig. 16 shows the sensorless startup performance from standstill to 300 rpm. A constant currentcontrolled startup strategy is proposed in this study. Stable and smooth startup performance can be achieved with the proposed algorithm. Fig. 17 shows the fullspeed sensorless control performance. Fig. 18 shows the torquespeed characteristics of the proposed sensorless BLDCM drive. The controllable speed ratio is 50:1, and the speed regulation performance is 0.6%.
TABLE 1. Ratings and Parameters of BLDCM Drive.
6. ConclusionsThis work has presented the design and analysis of a sensorless drive for the BLDCM. The proposed sensorless drive is implemented in a realtime motor drive system, and is shown through extensive simulations and experiments to be robust to system parameters and disturbances while providing accurate rotor position estimation. The feature of this sensorless control scheme can be summarized as follows. First, the scheme does not rely on the motor having salient poles, and it does not involve physical modification such as placement of search coils. Second, the scheme is computationally less intensive than many other schemes proposed. The most important feature is that it does not require the knowledge of the mechanical load or the moment of inertia. Only three motor electrical parameters are required for the estimation: the stator resistance, the stator inductance and the backEMF constant. The parameter variations in the sensorless algorithm can be successfully corrected with the internal closedloop. The general property of this sensorless approach has also been demonstrated with simulations for a sinusoidaltype PMSM. Various implementation issues are discussed, including the acquisition of PWM current in a pulse width modulated inverter system and the quantization effect of the digital implementation. Intensive experimental results were given to demonstrate the sensorless control performance. Accurate rotor position and speed estimation, robustness to parameter uncertainty, and good disturbance rejection, can be obtained. In summary, the results of this study suggest that the developed sensorless strategy is a viable alternative for electric drive applications that require the high efficiency, high performance, and robust sensorless BLDCM drives. The sensorless drive design, experimental results and implementation issues addressed in this study will provide valuable information for any future sensorless drive designs. On the other hand, the presented fuzzed optimization technique for control parameter tuning is proved the potential for intelligent servo drives.





Last update: 2004/12/06 
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