鄭光耀、鄒應嶼  交通大學電力電子晶片設計與DSP控制實驗室


 目  錄 


1. Introduction

2. Sensorless commutation control

3. Rotor Position Estimation Algorithm

4. Fuzzy Optimization Algorithm

5. Experiment Results

6. Conclusions



無刷直流馬達無感測控制方法之研究與DSP實現技術之發展短評:本研究提出以定子磁通估測為基礎的無刷直流馬達轉子估測方法及結合反抗電動估測法進行自動動相角之調整,方法新穎,在學術上具有成就,且採用單晶片數位訊號處理器,整合自動控制,信號估計,馬達控制,無感測控制方法,完成控制韌體的實現,並以一顆1 HP的無刷直流馬達進行驗證實驗,性能優越,明顯具有實用價值,故特予推薦,給予獎勵。



Note: 本文僅為部分摘要原稿發表於第18屆 宏祣s騰知識經濟論文獎,並榮獲『優秀論文獎』。  

1. Introduction

Adjustable-speed 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 high-performance 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 back-EMFs, 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 Hall-effect 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 position-dependent variables, such as back-EMFs and third-harmonic 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 back-EMF is very small at low speed and is zero at standstill, the direct measurement method can not work at low-speed 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 observer-based 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 on-line 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 high-frequency signal to the motor. Several signal injection patterns and modified pulse-width-modulation (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 high-frequency 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 well-known d-q rotor reference frames model developed for the PMSM is not applicable, and some properties of the two-axis stationary reference frame can not be used either.

The research objectives of this dissertation is thus in three-folds. 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 back-EMF measurement based sensorless approach is presented. With considering the realization constraints, the proposed algorithm has been successfully realized with integrated-circuit (IC) architecture for many low-cost 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 fixed-point arithmetic (TMS320LF2407A). The third objective of this study is to develop a control parameter tuning strategy for the high-performance motor drives. The developed PC-based auto-tuning software can be used for the on-line tuning of the control parameters of a digital motor drive through the RS-232/485 serial interface. The selected control parameters can be off-line 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 fuzzy-logic-based optimization scheme is developed for a practical digital motor drive. The proposed fuzzy optimization algorithm will be verified on a PC-MATLAB environment.

2. Sensorless commutation control

A. Back-EMFs measurement and zero-crossing detection

From the mathematical modeling of the BLDCM, the sum of three terminal voltages three terminal voltages, va, vb, and vc, can be derived as follows


For analyzing the effectiveness of the back-EMF estimation, the commutation from phase a-b to phase a-c is considered as an example. During the two-phase conducting period, two conducting phase currents are opposite and another one is zero, that is ib=-ia, ic=0. Therefore, from (1), the back-EMF of the non-excited phase c is


By simplifying (2), ec can be estimated as follows


For an ideal trapezoidal back-EMF, ea(θe)+ eb(θe) is equal to zero. Hence, the non-excited phase back-EMF can be fully estimated by (3) with only three terminal voltages. For the nonideal or distorted back-EMFs [48], however, ea(θe) is different from -eb(θe), that is  


Due to this nonzero term, the back-EMF estimation algorithm in (3) would produce an electrical angle-dependent error, and cause a phase shift to the zero-crossing point of the real back-EMF. If the shapes of the back-EMFs can be known, this error can be compensated in advance. However, for unknown back-EMFs, 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 back-EMF estimation during the two-phase conducting period.


Fig.1. Back-EMF measurement during two-phase and three-phase 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 non-excited phase current is zero. Hence (3) would become a wrong estimation for back-EMFs during the three-phase conducting period. In this example, during the commutation from phase a-b to phase a-c, the terminal voltage vb is equal to half dc-link voltage () due to the free-wheeling diode clamping effect until phase current ib vanishes as shown in Fig. 1. Hence, if (3) is applied for the estimation, then the estimated back-EMF of non-excited phase a would be derived as follows


Obviously,  differs from the real back-EMF . Since the back-EMF estimation can no be achieved during the three-phase conducting period with only three terminal voltages, a delayed sampling technique is required to mask the estimation for avoiding wrong zero-crossing detection during this period. Fig. 2 illustrates the typical waveforms of the estimated non-excited phase back-EMF and the corresponding zero-crossing signal during two-phase conducting period and three-phase conducting periods. It should be noted that the duration of the three-phase conducting period would depend on the operating conditions [49]. Hence the delayed-sampler should be adjusted according to the different operations. In this paper, an adaptive delay controller is presented to improve the back-EMF estimation. Fig. 3 shows the block diagram of the modified back-EMF estimation and zero-crossing detection. The threshold value Dth for the delay controller can be adaptively calculated as              


Since the estimated back-EMF signal must contain noises, a hysteresis comparator with the hysteresis band Zh is used for avoiding wrong zero-crossing detection. Besides, a digital filter is also used to filter out the possible noise.

Fig. 2. Typical waveforms of non-excited phase back-EMFs and zeror-crossing signals.

Fig. 3. Block diagram of modified back-EMF estimation and zero-crossing detection.

B. Commutation Phase Shifter

After detecting the zero-crossing signal of the estimated non-excited phase back-EMF, an additional 30-degree 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 frequency-independent 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 cp(k) and cn(k) depend on the rotating speed, and the value of scaling factor g is less than one, a long bit-length divider is required at low speed operation to compute gcp(k) and gcn(k), i.e. the commutation instants, precisely. However, the computation effort of the long bit-length divider is quite large for the real-time applications. In this paper, a digital simplified-type FIPS, which only needs a simple multiplier instead of a long bit-length 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 zero-crossing signal z(k) of the non-excited phase back-EMF, and the output y(k) is the corresponding commutation signal h(k). h*(k) is the desired commutation signal. Also, gd is set as two-times of the increasing increment gi to make the phase shift equal to 30 degrees from z(k). kzn denotes the time when the nth zero-crossing of input signal z(k) occurs, and kcn 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  


Fig. 4. Block diagram of digital phase shifters.

Fig. 5. Ideal operational waveforms of the proposed phase shifter.



Fig. 6. Error analyses of the proposed digital phase shifter.

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 kc3. 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 zero-crossing signal with time interval m1 is generated at kz1 for simulating the error due to free-wheeling diode-clamping effect, and the other wrong zero-crossing signal with time interval m2 is generated at kz4 for simulating the measurement error due to flatness around zero. The phase shift error  due to the noises can be described by


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, m1, and m2. It should be noted that the phase shift error  increases with increasing rotor speed, which implies that the input noises have significant effect at high-speed 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, phase-advanced control, i.e. , can also reduce the phase shift errors. Similar analysis can be done for the next zero-crossing instant kz6, the phase shift error  due to the noises can be derived as


A phase shift error  would occur at kc2, but would be vanished at next commutation instant kc3.

C. Commutation Phase Compensation

In order to produce maximum torque at low-speed operation for BLDCMs, the phase currents are required to be aligned in phase with the back-EMF waveforms, i.e. phase shift between zero-crossing of the non-excited phase back-EMF and real commutation signal is 30 degrees [50]. However, a commutation phase error may exist due to the phase-lag of low-pass filtering, noises, transient operations, and nonideal effect of the estimated back-EMF. 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 gd, and changing the increasing slew rate gi with the following equation:


where qf is the phase lag due to the low-pass filtering of the terminal voltages, and  is the desired advanced angle.

D. Rotor Speed Estimation

The accuracy of speed estimation is very crucial for closed-loop speed control. Since the commutation signal h(k) can be estimated with the presented algorithm, the time interval Tc between two commutations can be easily calculated as shown in Fig. 7. Hence the rotating speed can be estimated as follows [8],[13]:


where  is the estimated rotating speed from commutation signals, P denotes the number of rotor poles, and fe is the electrical rotating frequency. However, this method can only update the estimated speed when commutation occurs, and works poorly at low-speed operations because of no information between two commutations. In order to improve the speed estimation at low-speed 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 non-excited phase back-EMF signal e(k). The rotating speed can be also estimated from the peak value ep of the back-EMF as follows:                      


where KE is the back-EMF constant of a BLDCM. The estimation algorithm in (11) suffers from a similar problem as (10), because the peak value ep can be only actually known at each commutation instant. However, ep can be predicted from the sampled back-EMF signal e(k) with sampling period Ts between two commutations. When the sampling instant is between two commutations, i.e. kc1<k<kc2, the speed estimation algorithm is derived as follows:


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 non-excited phase back-EMF.

Fig. 7. Concatenate waveform of ideal non-excited phase back-EMFs.

E. Simulation Analyses

Fig. 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 closed-loop sensorless control performance at low-speed 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 back-EMF 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 low-speed and high-speed steady-state operations as well as transient operations. Therefore, this approach can be effectively used for many low-cost applications. However, for very-low speed operations (below 100 rpm), this sensorless approach is problematic due to a low signal-to-noise 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 back-EMFs. Therefore, a more general and robust sensorless control algorithm will be developed in the following section.

Fig. 8. Simulation result of sensorless ramp-speed control performance with different acceleration rates.



Fig. 9. Simulation result of closed-loop sensorless speed control performance at low-speed operations with different speed estimations: (a) from commutations, (b) from back-EMFs.

3. Rotor Position Estimation Algorithm

For a PMACM, the induced back-EMF voltages are functions of the rotor position, and are proportional to the angular speed. Hence, the three-phase back-EMF voltages can be expressed as        


where e1, e2, and e3 are normalized trapezoidal or sinusoidal flux-distribution functions. From (13), it can be seen that if the back-EMF constant KE is assumed constant, the rotor position can be estimated from the back-EMF voltages and the rotor speed. However, if only the relationship between the rotor position and the back-EMF voltages is used, the position estimation scheme may not operate accurately at low speeds due to the low signal-to-noise ratio of the back-EMF voltages. Besides, only the non-excited phase back-EMF 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 three-phase voltages and currents as follows


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


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                                                                  


where Δia, Δib, and Δic are the phase current increments, and Δφa, Δφb, and Δφc are the flux linkage increments within one sampling interval of each phase. Ideally, each phase should produce identical rotor position increment, that is


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:                                                      


By summing each row in (18), the general rotor position estimation algorithm can be derived as


With the presented method in (19), the integration computation is moved from the flux linkage estimation to the rotor position estimation. Besides, the internal closed-loop 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 back-EMFs 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).

Fig. 10. Block diagram of the internal closed-loop rotor position correction mechanism.



Fig. 11. Simulation result of closed-loop sensorless speed control performance over a wide speed range for: (a) a BLDCM; (b) a PMSM.

4. Fuzzy Optimization Algorithm

In 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



where JTR(N) and JCE(N) denote the objective functions of the speed transient response and the corresponding control effort at the N cycle, respectively. The desired rise time Δtr 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 high-performance servo drives becomes as a multi-objective optimization problem, which implies to minimize all these four objective functions simultaneously. Since there are some tradeoffs between these objective functions, the multi-objective problem is difficult to be solved. In order to solve this problem, a weighted-sum 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                                             


where , and WV=[wTR,wCE] is a weighting vector, which is used to specify the performance specifications. Hence the optimization problem can be re-formulated 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


where wCE 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



where N denotes the current iteration number, and hvp, and hvi are the step-sizes for the optimization equations. In general, small step-sizes may lead to an inefficient search process. On the other hand, large step-sizes allow the search process to approach the minimum efficiently. However, large step-sizes 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 step-sizes during the optimization process [53]. For example, the steepest descent algorithm can be applied to choose the optimal step-size 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 step-size 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 fuzzy-logic can simply transfer the expert-knowledge into an algorithm by using linguistic descriptions, the proposed strategy can best extract the experts knowledge. Fig. 12 shows the detailed block diagram of the fuzzy step-size tuner for optimization algorithms. The inputs of the fuzzy step-size tuners are the combined servo loop objective function JV(N), and the change of the combined objective functions DJV(N)= JV(N)- JV(N-1). 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 two-level 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 real-time processing mode with higher priority. By using the hierarchical structure in realizing the fuzzy-logic based optimization techniques for digital servo drives, the benefits of computational efficiency and learning capabilities of intelligent control strategy can be combined [54].

Fig. 12. Block diagram of the fuzzy step-size tuner.

Fig. 13. Hierarchical fuzzy optimization scheme for the sensorless BLDCM drive.

5. Experiment Results

The 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 wide-speed regulation capability and good transient response under full-speed operations. Fig. 15 shows the steady-state 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 back-EMF measurement method. Fig. 16 shows the sensorless startup performance from standstill to 300 rpm. A constant current-controlled startup strategy is proposed in this study. Stable and smooth startup performance can be achieved with the proposed algorithm. Fig. 17 shows the full-speed sensorless control performance. Fig. 18 shows the torque-speed characteristics of the proposed sensorless BLDCM drive. The controllable speed ratio is 50:1, and the speed regulation performance is 0.6%.

Fig. 14. Experimental result of sensorless speed control performance over a wide speed range with the proposed sensorless commutation control.

Fig. 15. Steady-state response at 60 rpm with the rotor position estimation algorithm.

Fig. 16. Sensorless startup performance from standstill to 300 rpm.

Fig. 17. Full-speed sensorless control performance.

Fig. 18. Torque-speed characteristics of the proposed sensorless algorithm for a BLDCM drive.

TABLE 1. Ratings and Parameters of BLDCM Drive.

3-phase brushless DC motor

Type Y-connection, 4 poles
Rated power 400 W
Rated speed 2400 rpm
Rated voltage 200 V
Rated stator current 3.2 A
Stator resistance 2 W
Stator inductance 8 mH
Torque constante 0.5 N-m/A

6. Conclusions

This work has presented the design and analysis of a sensorless drive for the BLDCM. The proposed sensorless drive is implemented in a real-time 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 back-EMF constant. The parameter variations in the sensorless algorithm can be successfully corrected with the internal closed-loop. The general property of this sensorless approach has also been demonstrated with simulations for a sinusoidal-type 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.


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