Model-Free Predictive Current Control for Interior ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 2, FEBRUARY 2014

667

Model-Free Predictive Current Control for Interior Permanent-Magnet Synchronous Motor Drives Based on Current Difference Detection Technique Cheng-Kai Lin, Tian-Hua Liu, Senior Member, IEEE, Jen-te Yu, Li-Chen Fu, Fellow, IEEE, and Chieh-Fu Hsiao

Abstract—A model-free predictive current control (PCC) of interior permanent-magnet synchronous motor (IPMSM) drive systems based on a current difference detection technique is proposed. The model-based PCC (MBPCC) of IPMSM requires knowledge of parameters such as resistance, q-axis inductance, and extended back EMF. This paper develops a new model-free approach that alleviates the need for excessive prior knowledge about the system and only utilizes the stator currents as well as the current differences corresponding to different switching states of the inverter. Despite the salient difference of the proposed approach, it adopts a measure similar to that in the MBPCC approach to obtain the next switching state of the inverter by minimizing a cost function. It is noteworthy that the proposed method is easy to implement due to its simplicity and free of any multiplication operation. For comparison purposes, a digital signal processor, TMS320LF2407, is used to execute the two aforementioned current control techniques. Several experimental results show that the proposed method can significantly improve the current-tracking performance. Index Terms—Current difference detection, interior permanentmagnet synchronous motor (IPMSM), predictive current control (PCC).

I. I NTRODUCTION

C

URRENT control techniques play an important role in power electronics, particularly in the six-switch threephase inverters which are widely applied in ac machine drives. Among them, interior permanent-magnet synchronous motors (IPMSMs) have been extensively used in the last decades due to their high power density, high torque-ampere ratio, and high efficiency. To achieve fast and accurate current tracking, some current control techniques have been developed, such as hysteresis current control [1], pulsewidth modulation (PWM) control [2], and predictive current control (PCC) [3]–[6]. For an IPMSM, the most important aim of current control is to

Manuscript received May 15, 2012; revised August 7, 2012, October 10, 2012, and January 8, 2013; accepted February 13, 2013. Date of publication March 15, 2013; date of current version August 9, 2013. This work was supported by the National Science Council of Taiwan and National Taiwan University under Grant NSC 99-2221-E-011-151-MY3, Grant NSC 100-2221E-002-082-MY3, Grant NSC 101-2218-E-019-008-MY2, and Grant NTUCESRP -102R7617. C.-K. Lin is with National Taiwan Ocean University, Keelung 20224, Taiwan (e-mail: [email protected]). T.-H. Liu and C.-F. Hsiao are with the National Taiwan University of Science and Technology, Taipei City 106, Taiwan (e-mail: [email protected]). J.-t. Yu and L.-C. Fu are with National Taiwan University, Taipei City 106, Taiwan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2013.2253065

ensure that the stator currents effectively track their references in both transient and steady-state responses as closely as possible. Among the three aforementioned controls, the PCC is special because it is very effective in controlling the currents of ac motors [3], [4], as well as inverters and converters, such as three-phase grid-connected inverters [5]–[7], three-phase grid-connected converter [8], seven-level cascaded inverters [9], three-phase voltage-source inverters [10]–[13], and matrix converters [14], [15]. In addition, other predictive control techniques, such as model predictive direct torque control [16], [17], model predictive speed control [18], predictive functional control [19], predictive direct power control [20], predictive torque control [21], [22], and predictive sliding mode control [23], have also been reported in literature. The model-based PCC (MBPCC) presented in [11] can effectively control the currents of a three-phase balanced load, which is connected to an inverter. The idea is very appealing and is easy to realize using a digital signal processor (DSP). This method is based on a discrete-time model of the three-phase balanced load to predict the load currents. Since it is model based, the back EMFs, load voltages, and load parameters must be known. The performance is affected by estimation errors and uncertainties of these parameters. To deal with parameter uncertainties, a parameter identification method, which requires a lot of computations, was proposed in [24]. The MBPCC [11], [25] did not require PWM control but was still able to effectively determine the switching state of the inverter. In fact, the MBPCC algorithm can predict the future behavior of the load and can provide a switching state for the next sampling time so as to achieve the desired currenttracking performance. Unlike the hysteresis current control, which is based on the error between the present current command and the corresponding sampled one, the MBPCC takes into consideration the errors between the current command and all possible future currents to be generated by the inverter [11], where the errors are used in a cost function. Recently, several authors have developed different predictive techniques for permanent-magnet synchronous motors (PMSMs) and IPMSMs [19], [26]–[32]. For example, in [19], a predictive function control was designed to control the speed of PMSM. The response was improved using a second-order linear state observer. However, the method required a lot of effort to tune the observer gains under different speed conditions. Naouar et al. proposed a field programmable gate array-based PCC for a synchronous machine [26], [27]. In the method, the

0278-0046 © 2013 IEEE

668


state variables were expressed in the d − q reference frame. As a result, the rotor position and the motor speed are required in order to execute the current prediction algorithm. Pacas et al. presented a predictive direct torque control to achieve a fast torque response for the PMSM drive system [28], utilizing the torque ripple and the stator flux. It still has the drawback of undesired torque ripples. To circumvent this problem, a new torque predictive control was proposed by Zhu et al. [29], which effectively reduced the torque ripples. However, their method was complex to realize, resulting in a long execution time. To solve the problem, a modified method which takes computation delay into consideration was reported in [30]. A comparison between two-configuration predictive control, PWM predictive control, and direct predictive control was discussed in [31]. According to that study, the current ripple of the direct predictive control is severe compared to the other two predictive controls. To cope with system disturbances and uncertainties, a robust high-bandwidth discrete-time PCC scheme for a direct-drive PMSM was proposed in [32]. The results were good; however, the whole computation load of the PCC scheme was heavy for a DSP, including executions of the space vector PWM, adaptive current observer, adaptive laws, and PCC. Most PCC schemes, however, are model based. Take ac machines connected to inverters as an example. The system parameters and the back EMFs should be exactly known. In reality, their values cannot be obtained precisely as the accurate back EMF of the IPMSM is difficult to detect, especially when the motor is operated at low speeds. In addition, the algorithms of the aforementioned PCCs are very complicated when the disturbances [5], time delay compensations [11], [12], [33], and parameter uncertainties [32], [34] are taken into account. Many predictive control techniques have been successfully applied to the PMSMs in the past. Unfortunately, only a few papers have discussed the application of PCC to the IPMSMs [35], [36]. This motivates us to propose a new PCC for IPMSMs. First, for comparison purposes, the MBPCC is utilized using an extended back EMF estimation method proposed here. Next, based on a current difference detection technique to calculate the current difference of each switching state, a model-free PCC (MFPCC) is presented to improve the performance of current tracking and relive the knowledge of parameters required by MBPCC. Here, we assume that the sampling period is short enough, and hence, the next current difference can be estimated using the stored one. A current difference update mechanism is proposed to reduce the prediction error. In the proposed MFPCC, only addition and subtraction operations are used. Similar to the MBPCC [11], [12], the next switching state that minimizes a cost function can be determined at the present sampling time and then to directly trigger the inverter in the next sampling interval. The major contribution of this paper is that the new method does not require any information on resistance, inductance, voltage, and back EMF, i.e., it is an MFPCC. A few papers have discussed the model-free predictive control. For example, Beerten et al. proposed a model-free predictive direct torque control [37]. It, however, only focused on the predictive torque and flux control. In this paper, the MFPCC will be further investigated. To our knowledge, the concept

presented in this paper is original, and the results obtained here exhibit appealing advantages compared to the existing works in the literatures. The implementation of the proposed method is fairly easy, which is realized by a DSP. Experimental results will be given to demonstrate the feasibility and effectiveness of the new method. The rest of this paper is organized as follows. In Section II, the MBPCC is discussed. Section III presents the new MFPCC and its details. The effect of parameter variations is studied and discussed in Section IV in terms of numerical simulations. Experimental results are shown in Section V to validate the new MFPCC, and the comparison between this new approach and MBPCC is also made. Finally, a conclusion is given in Section VI. II. MBPCC Consider a balanced, three-phase, and wye-connected IPMSM. The stator voltage equations can be expressed as follows [38]: d (Laa ia + Lab ib + Lac ic + λm cos θre ) (1) dt d 2 vb = rs ib + Lba ia +Lbb ib +Lbc ic +λm cos θre − π dt 3

va = rs ia +

vc = rs ic +

d dt

(2) 2 Lca ia +Lcb ib +Lcc ic +λm cos θre + π 3 (3)

where va , vb , and vc are the stator voltages of the IPMSM; ia , ib , and ic are the stator currents; θre is the rotor position; rs is the stator resistance; λm is the flux linkage from the rotor; and Laa , Lab , Lac , Lba , Lbb , Lbc , Lca , Lcb , and Lcc denote the self-inductances and mutual-inductances, respectively, containing rotor position information. The inductances can be defined as Laa = Lls + LA − LB cos(2θre ) 2 Lbb = Lls + LA − LB cos 2θre + π 3 2 Lcc = Lls + LA − LB cos 2θre − π 3 1 2 Lab = Lba = − LA − LB cos 2θre − π 2 3 1 2 Lac = Lca = − LA − LB cos 2θre + π 2 3 1 Lbc = Lcb = − LA − LB cos(2θre ) 2

(4) (5) (6) (7) (8) (9)

where Lls represents the leakage inductance, LA represents the component of the inductance, which is unrelated to the rotor position, and LB stands for the amplitude of the cosine component of the inductance, whose argument contains the rotor position. It is true that the inductance value LB appearing in (4)–(9) is large. However, this is the fundamental characteristic of the

LIN et al.: MFPCC FOR IPMSM DRIVES BASED ON CURRENT DIFFERENCE DETECTION TECHNIQUE

669

IPMSM, which has an obvious position-related difference. The definitions of LA and LB are given as [39] LA = (Ns /2)2 πrlε1 μ0 LB = (Ns /2)2 πrlε2 μ0 /2

(10) (11)

where r is the radius, which is from the center of the rotor to the inside circumference of the stator, l is the axial length, Ns is number of turns of winding in each phase, μ0 is permeability of the air, and ε1 and ε2 are the coefficients related to the air gap length. The equivalent three-phase stator-voltage equations of the IPMSM, which include the extended back EMFs, are used for current prediction in this paper. Substituting (4)–(9) into (1)–(3), together with some mathematical manipulations, the three-phase stator-voltage equations (1)–(3) can be rearranged as follows [38]: d (λm cos θre ) dt d 2 1 + ib − LA − LB cos 2θre − π dt 2 3 3 1 d + Lls + (LA + LB ) − LA dt 2 2 3 − LB − LB cos(2θre ) ia 2 2 d 1 ic + rs ia + − LA − LB cos 2θre + π dt 2 3 (12) d 2 vb = λm cos θre − π dt 3 d 1 + − LA + 2LB cos(2θre ) ia dt 2 3 d 1 + − LA − LB + 2LB cos(2θre ) dt 2 2 √ + 3LB sin(2θre ) ib + rs ib d 2 1 ic + − LA − LB cos 2θre + π dt 2 3 3 d + (13) Lls + (LA + LB ) ib dt 2 d 1 vc = − LA + 2LB cos(2θre ) ia dt 2 3 d + Lls + (LA + LB ) ic dt 2 d 2 1 ib + − LA − LB cos 2θre − π dt 2 3 2 d + λm cos θre + π dt 3 d 3 1 + − LA − LB + 2LB cos(2θre ) dt 2 2 √ − 3LB sin(2θre ) ic + rs ic . (14)

va =

Next, the equivalent q-axis inductance Lq is defined as Lq = Lls +

3(LA + LB ) . 2

(15)

Fig. 1. Configuration of the voltage-source inverter-fed IPMSM.

The approximation of Lq as a constant is very rough. In reality, Lq is saturated when the three-phase stator currents increase to certain level. However, the relationship between them is very complicated. To simplify the situation, Lq is considered as a constant in this paper. As a result, the MBPCC does not perform well due to the parameter’s varying problem. Generally speaking, the mathematical models of the threephase stator-voltage equations are very complicated [11], [21], [40]. In addition, the MBPCC may not be applicable due to the coupling effect of the inductances. However, it is possible to decouple and simplify the three-phase stator-voltage equations [38]. The decoupling processes are complicated and thus are omitted here as they are beyond the scope of this paper, and only the results are shown. The reader is referred to [38] for the details. Given (12)–(15), the equivalent three-phase statorvoltage equation, according to [38], can be expressed as vx = rs ix + Lq

dix + ex , dt

x ∈ {a, b, c}

(16)

where the subscript “x” denotes the phase and ex is the extended back EMF [38]. The stationary a − b − c frame is used in this paper, which can explain the proposed MFPCC method in a simpler way. The d − q modeling, on the other hand, needs coordinate transformation which consumes certain computation resources. It is well known that not every kind of three-phase load can be modeled in the d − q frame, e.g., an unbalanced three-phase load. According to (16), the coordinate transformation does not change the fact that the value of Lq is a constant; as a result, (16) can be used to estimate the extended back EMF and to predict the stator current. The IPMSM is driven by a voltagesource six-switch three-phase inverter. The configuration of the drive system is shown in Fig. 1, where Vdc is the dclink voltage. To avoid short circuit of the dc-link, the inverter only allows eight switching states, listed in Table I, resulting in six active-voltage vectors and two identical zero-voltage vectors as shown in Fig. 2. Table I shows the information of the output voltages at different voltage vectors. In the ideal case, it is difficult to distinguish the output voltages V0 and V7 without using the voltage sensor. In reality, the two zero-voltage vectors may result in different output voltages and different switching frequencies due to the nonlinearity nature of the inverter. Choosing one from the two, either V0 or V7 , we can reduce the difficulty in implementing the MBPCC [11], [12]. There are seven switching states that need to be considered,

670


TABLE I SWITCHING STATES OF SSTP INVERTER

sampling interval. Considering the delay compensation in (17), one can derive the predicted stator current in the (k + 2)th sampling interval as rs Ts p Ts p (vx (k+1)−ex (k+1)) ix (k+1)+ ix (k + 2) = 1− Lq Lq (18) where iP x (k + 1) is the predicted current obtained from (17), vx (k + 1) is a candidate stator voltage applied in the (k + 1)th sampling interval, and ex (k + 1) is the extended back EMF in the (k + 1)th sampling interval. Since it is impossible to measure the future extended back EMF ex (k + 1) in the (k)th sampling interval, an estimation method has been proposed in [33]. Supposing that the sampling interval Ts is short enough, the following equation can be derived: ex (k) ≈ ex (k−1) = vx (k−1)−

Fig. 2. Voltage vectors of the inverter.

Fig. 3. Block diagram of the IPMSM drive system with the MBPCC.

leading to seven candidate voltage vectors that can be used to predict the future stator current. Fig. 3 shows a block diagram of the MBPCC. For simplicity, we attach a number to an input signal in Fig. 3 to represent multiple inputs. As one can observe, the measured a- and b-phase currents and the related voltages are used to estimate the extended back EMFs. To get the three-phase stator voltages without using voltage sensors, a look-up table of the stator voltages with respect to the switching states is used, as depicted in Table I. According to the discrete-time form of (16), the predicted stator current can be expressed as [12] rs Ts Ts ix (k) + (vx (k)−ex (k)), x ∈ {a, b, c} ipx (k + 1) = 1− Lq Lq (17) where Ts is the sampling interval, the superscript “p” denotes the predicted value, vx (k) is the stator voltage applied in the (k)th sampling interval, ex (k) is the extended back EMF in the (k)th sampling interval, ix (k) is the measured stator current in the front part of the (k)th sampling interval, and iP x (k + 1) is the predicted value of the stator current in the (k + 1)th

rs Ts +Lq Lq ix (k)+ ix (k−1). Ts Ts (19)

From (19), we can also obtain ex (k + 1) ≈ ex (k) according to [33]. Due to the crudeness of extended back EMF estimation, it is possible for such a technique to cause a larger current ripple. It is true that one can use a simple observer to estimate the extended back EMF. However, the observer cannot work well when the motor is at standstill or in a low-speed operation range due to the small value of the extended back EMF. An observer does require certain amount of computation time. Normally, an observer would give inaccurate estimation during the transient period, even its steady-state error is zero. In addition, an observer has an embedded gain tuning/scheduling issue to deal with if the motor is operated in a wide speed range. Although (19) is imperfect, at present time, it is the method that we adopt to estimate the future extended back EMF. The predicted stator current can now be expressed as rs Ts p Ts (vx (k+1)−ex (k−1)) . ix (k+1)+ ipx (k+2) = 1− Lq Lq (20) As can be seen from (20), ipx (k + 2) consists of three parts. The first part is the predicted current ipx (k + 1), the second part is the next stator voltage vx (k + 1), and the third part is the extended back EMF ex (k − 1). The candidate voltages are shown in Table I. Since there are seven possible switching states, we can obtain seven values for the predicted stator current ipx (k + 2). To determine the (k + 1)th switching state in the (k)th sampling interval, a simple mechanism that minimizes a cost function, consisting of predicted current errors, is used here. The (k + 1)th stator current commands can be approximated as the (k)th ones, provided the sampling interval is short enough. The cost function can be defined as g(k) = |i∗a (k) − ipa (k + 2)| + |i∗b (k) − ipb (k + 2)| + |i∗c (k) − ipc (k + 2)|

(21)

where the symbol “∗” denotes the reference command. The (k)th stator current commands can be obtained from the d − q axis current commands through the d − q to a − b − c coordinate transformation. After that, the next switching state can


671

be determined in the (k)th sampling interval by choosing a voltage vector that minimizes (21). Then, the predicted stator current can be calculated via substitution of the seven possible voltage vectors into (20). The cost function (21) is assessed by the predicted current errors, and the switching state of the corresponding voltage vector that minimizes it will be applied in the next sampling interval. The six switches of the inverter, namely, Sa1 , Sa0 , Sb1 , Sb0 , Sc1 , and Sc0 , are utilized to drive an IPMSM according to the applied switching state.

III. MFPCC Ideally, the MBPCC [11], [12] can predict the future stator current of the IPMSM to achieve a fast current-tracking response with satisfactory performance. Obviously, the accuracy of the predicted stator current, according to (20), depends on the stator resistance, q-axis inductance, stator voltage, and extended back EMF. Compared to the MBPCC [11], [12], the hysteresis current control [1] is insensitive to parameter variations of the motor because its switching state only uses the current commands and the measured currents. To achieve fast current tracking, small current ripples, and insensitivity to the parameter variations, a model-free method, based on current difference detection technique, is proposed here. This method does not require any knowledge of the parameters of the motor. The current difference detection technique is based on the assumption that the stator current during each switching interval is linear [39]. As a result, the stator current difference within each switching interval can be precisely calculated. In fact, the stator current needs to be detected twice during each sampling interval. The stator current difference is computed by a simple subtraction operation. A more detailed explanation about the current difference detection technique is discussed in [39]. Since the inverter generates eight different switching states, the calculated stator current differences can be classified into eight different kinds accordingly. Moreover, the stored previous current differences are updated by the new ones in the present sampling interval. In [11] and [12], the stator voltages are obtained from Table I. According to their approaches, the zero voltages V0 and V7 are indiscriminative. They can cause the common-mode voltage and increase the switching frequency of the inverter. To solve these problems, we consider eight switching states, among which S0 and S7 are different in the proposed method. Consequently, the effects resulting from using only one zero voltage can be reduced [41]–[43]. To illustrate the proposed method, a detailed description is provided as follows (refer to Fig. 4). First, in the (k)th sampling interval, the first and second measured currents are denoted as ix (k, 1) and ix (k, 2), respectively, and ix represents ia , ib , or ic . In order to obtain the correct current difference signal and to avoid the current spikes while measuring the stator current, the first current detection ix (k, 1) is finished before the (k)th switching state is performed, and the second current detection ix (k, 2) is delayed by a fixed time period after the (k)th switching state is performed. The details of the measured a-phase stator current and the related current sampling signal are shown in Fig. 5.

Fig. 4. Schematic diagram of the stator current prediction.

Fig. 5. Measured a-phase stator current and the related current sampling signal.

As can be seen in Fig. 4, the starting point of a typical switching interval is lagging behind that of the corresponding sampling interval by a fixed amount of time. It indicates that the stator current at the end of the (k)th switching interval will be measured in the (k + 1)th sampling interval. As a result, the current difference corresponding to the (k)th switching interval cannot be calculated in the (k)th sampling interval. In other words, the current difference corresponding to the previous switching state can be calculated in the present sampling interval. Now, define the stator current difference under the (k − 1)th switching state as Δix |S(k−1) = ix (k, 1)|S(k−1) − ix (k − 1, 2)|S(k−1)

(22)

where ix (k, 1)|S(k−1) and ix (k − 1, 2)|S(k−1) denote the stator currents under the switching state S(k − 1) whose argument (k − 1) refers to the (k − 1)th switching interval. In the present work, it is necessary to compute the current difference by detecting current twice in one sampling interval. The reason is that the accuracy of the current difference is very important. We believe that detecting current only once in each sampling interval to realize the MFPCC is potentially feasible and worthy of further investigation in the future. At the next sampling instant, one has Δix |S(k) = ix (k + 1, 1)|S(k) − ix (k, 2)|S(k) .

(23)

672


Similarly, the following equation holds: Δix |S(k+1) = ix (k+2, 1)|S(k+1) − ix (k+1, 2)|S(k+1) . (24) Combining (23) and (24), one can obtain the future current ix (k + 2, 1) under the switching state S(k + 1) at the end of the next switching interval as ix (k + 2, 1)|S(k+1) = ix (k, 2)|S(k) + Δix |S(k) + Δix |S(k+1) + ix (k + 1, 2)|S(k+1) − ix (k + 1, 1)|S(k) .

(25)

To simplify (25), a new future stator current ix (k + 2)|S(k+1) can be defined as ix (k + 2)|S(k+1) = ix (k + 2, 1)|S(k+1) − ix (k + 1, 2)|S(k+1) + ix (k + 1, 1)|S(k) .

(26)

With (26), (25) can be rearranged as ix (k+2)|S(k+1)= ix (k, 2)|S(k)+Δix |S(k)+Δix |S(k+1) . (27) It can be observed from (27) that the future stator current ix (k + 2)|S(k+1) consists of three terms. The first term ix (k, 2)|S(k) can be measured at the beginning of the (k)th sampling interval, the second term Δix |S(k) is the current difference under switching state S(k), and the third term Δix |S(k+1) is the current difference under switching state S(k + 1). According to Fig. 4, the current differences Δix |S(k) and Δix |S(k+1) will be calculated in the (k + 1)th and (k + 2)th sampling intervals, respectively. Therefore, their estimated values could be used to predict the current ix (k + 2)|S(k+1) . Since the switching interval of the inverter is very short, the previous calculated current differences can be stored and can be used to approximate the future values of the current differences Δix |S(k) and Δix |S(k+1) . The aforementioned approximation is reasonable if the switching interval is short enough. As a result, the current differences Δix |S(k) and Δix |S(k+1) can be expressed as follows: Δix |S(k) ≈ Δix,pre |Si =S(k) , Δix |S(k+1) ≈ Δix,pre |Sj =S(k+1) ,

i ∈ {0, 1, . . . , 7} j ∈ {0, 1, . . . , 7}

(28) (29)

where Si is equal to the switching state S(k) and Sj can be any one of the candidate switching states listed in Table I. The subscript “pre” refers to the previous value. From (25)–(29), one concludes that the predicted stator current in the front part of the (k + 2)th sampling interval can be calculated as follows: ipx (k+2)|Sj = ix (k, 2)|S(k) +Δix,pre |S(k) +Δix,pre |Sj (30) where the superscript “p” denotes the predicted value. In contrast to (20), one can observe that the stator resistance, q-axis inductance, stator voltage, and extended back EMF are not required in (30). In the same way, the prediction can be extended to the end of the (k + 1)th switching interval. The details are shown in Fig. 4. As can be seen from (30), the accuracy of the current predictions only depends on the measured currents and the current differences. To achieve good approximations for Δix |S(k) and

Fig. 6.

Diagram of the time sequence for implementation of the MFPCC.

Δix |S(k+1) , the previously stored current differences should be updated by the new calculated ones. The updating frequencies of the corresponding current differences are not the same, which may result in certain degrees of current prediction inaccuracy under some switching states. However, since the sampling frequency of the DSP used to realize the proposed method is very high, up to 10 kHz, the effect of different updating frequencies is very limited. Similar to (21), the cost function can be defined as g(k)|Sj = i∗a (k) − ipa (k + 2)|Sj + i∗b (k) − ipb (k + 2)|Sj + i∗c (k) − ipc (k + 2)|Sj . (31) The (k + 1)th switching state can be determined in the (k)th sampling interval by choosing the one that minimizes (31) for j = 0, . . . , 7. Fig. 6 shows the sequence of the seven successive tasks executed in each sampling interval of the DSP with detailed descriptions. The flowchart of the proposed MFPCC algorithm is shown in Fig. 7, in which gold is a variable to store the minimum value of the cost function and Sm is a variable to save the switching state that minimizes (31). For j = 0, . . . , 7 in (30), the eight predicted stator currents under eight candidate switching states can be calculated through the for-loop shown in Fig. 7. After the for-loop, the variable Sm will be used to output the next switching state in the next sampling interval. It is clear, according to Figs. 6 and 7, that the proposed method is based on the current difference detection technique, which is obviously different from the MBPCC [11], [12]. Improved performance in terms of current tracking can be expected from the proposed MFPCC strategy, since it is totally insensitive to the motor parameters as well as to the back EMF. Also, the proposed method does not require the model of the IPMSM; it can be applied to other ac motors, such as synchronous reluctance motors or induction motors. The performance of the proposed MFPCC depends on the sampling interval of the DSP. In fact, a better current tracking can be obtained by reducing the sampling interval of the DSP. The implementation of the proposed method is relatively easy, compared to the MBPCC, as neither the back EMF estimation


673

current differences is very limited. In practice, it only affects the result of current prediction of the first few switching intervals. All initially stored current differences of the eight switching states are set to zero, and the motor’s speed is zero at the initial time. After the speed command is set, the speed error is generated. The three-phase current commands are then created by the outer loop controller. Following that, the three-phase real currents are generated to track the current commands. The system can then be started. IV. S IMULATION R ESULTS OF PARAMETER VARIATIONS To gain some insight into the effect of the parameter variations on the current prediction, two parameter-sensitive expressions, based on (17) and (18), for the MBPCC with delay compensation are provided as follows [44]: Ts rs Ts ∂ipx (k + 2) Ts rs Ts = − 2 1− ∂Lq Lq L2q Lq Lq × (vx (k) − ex (k)) −

Ts L2q

× (vx (k + 1) − ex (k + 1)) rs Ts rs Ts +2 1− ix (k) L2q Lq 2 Ts ∂ipx (k + 2) Ts =2 rs − ix (k) ∂rs L2q Lq −

Fig. 7.

Flowchart of the proposed MFPCC.

nor the parameter identification is required. The trigger signals of the inverter are directly determined by the outputs of the DSP. By this way, the proposed scheme does not require any PWM techniques to generate the switching signals. In the implementation, the initial current differences of the eight switching states are set to zero since we do not have the past current differences at the beginning. As a result, the initial accuracy of the current prediction, according to (30), may not be good enough. After execution of the algorithm depicted in Fig. 7, the next switching state can be chosen even if the predicted currents are inaccurate. However, the current differences are updated as long as the related switching state is applied. Therefore, after a few sampling intervals, the accuracy of current prediction becomes much better. Because the switching frequency is 10 kHz, the influence from the initial

Ts2 (vx (k) − ex (k)) . L2q

(32)

(33)

A thorough analysis of (32) and (33) is too difficult due to their nonlinearity nature. To resolve this difficulty, some simulations of the IPMSM drive system equipped with the MBPCC and the MFPCC are carried out using MATLAB/Simulink. To provide a fair comparison, the real extended back EMF is used as feedback in the simulations for the MBPCC to predict the stator current. Ideally, the current-tracking performance of the MBPCC with delay compensation should be about the same as that of the MFPCC if the parameters and the extended back EMF used in the former are exactly known. In the simulations, the parameters and the extended back EMF of the MBPCC are varied to show their effects on the current predictions, whereas the parameters of IPMSM are kept constant. The mean absolute error of the three-phase stator currents, which is defined in (35), is used to quantify the current-tracking performance. Fig. 8 shows some simulation results for MBPCC, where the IPMSM is operated at different speeds subject to parameter variations. First of all, under normal condition when the IPMSM is operated in a wide range of speed, including at the critical one, the figure shows that MBPCC results in satisfactory performances. Next, as can be seen from the figure, the performance of MBPCC is affected by its parameter variations. As for Fig. 9, it shows current errors of the MBPCC under normal condition as well as under variations of extended back EMF. Again, its performance is affected when the extended back EMF is varied. In general, the extended back EMF, in

674


Fig. 8. Current errors of MBPCC at different speeds and different parameter variations.

Fig. 9. Current errors of MBPCC at different speeds and variations of extended back EMF.

practice, is not measurable, whereas the practical stator resistance and q-axis inductance may be varying. As a result, their estimation becomes inevitable for MBPCC, which naturally leads to certain degree of estimation errors, and thus affects the performance unfortunately. To realize an estimation of the extended back EMF in actual implementation, here we choose (19) in our experiments, although as a matter of fact, it is not the only method to approach this problem. Nevertheless, the hereby proposed MFPCC is, in fact, measurable signal based and hence is free of the aforementioned inherent problem. Fig. 10 shows the current errors resulting from the parameter variations in the MBPCC when the IPMSM is operated at 500 r/min under an external load of 2 N · m. Such parameter variations refer to the changes of the values of the q-axis inductance, stator resistance, or extended back EMF in MBPCC, and the individual variation ranges from −80% to 80%. Here, we test with mild case where two out of the three mentioned parameters are kept at their nominal values while the third one is varied as described. Note that there are two cases where the current errors for MBPCC are evaluated, namely, with and without the delay compensation [11], and both results are shown in Fig. 10. It is apparent that the current-tracking performance with delay compensation is more sensitive to parameter variations than the one without compensation. On the other hand, unlike MBPCC, MFPCC does not depend on these parameters, and hence, its error, defined in (35), will be fixed (represented as a single point in Fig. 10) regardless of the prescribed parameter variations. The delay problem mentioned in [12] only occurs in real DSP systems and not in the computer’s simulation due to the latter’s powerful central processing unit. This explains why the performances of the MBPCC with and without delay compensation make no difference under normal conditions.

Fig. 10. Current errors resulting from parameter variations in MBPCC. (a) q-axis inductance. (b) Resistance. (c) Extended back EMF. TABLE II PARAMETERS OF AN IPMSM

According to the simulations, we can see that the MBPCC is sensitive to the variations of the parameters and the extended back EMF. V. E XPERIMENTAL R ESULTS Several experiments of the proposed MFPCC are carried out to show the current-tracking performance in comparison with the MBPCC. Both the proposed MFPCC and the MBPCC [12] are used in the inner current-loop control to determine the switching states and then drive the IPMSM. These two different current control algorithms are executed by a Texas Instruments DSP, TMS320LF2407. The nominal values of the parameters of a three-phase four-pole IPMSM, made by Shin-Ding, are shown in Table II. The block diagram of the proposed MFPCC scheme is shown in Fig. 11. The outputs of the inverter provide


675

DSP is around 100 μs for both PCC schemes. In this paper, the computation times of the MBPCC and the MFPCC algorithms are around 60 and 45 μs, respectively. The IPMSM is connected to a dynamometer via its axis. The d-axis current command is maintained at zero in all experiments. The three-phase stator current commands can be obtained from the d- and q-axis current commands through the d − q to a − b − c coordinate transformation. To further measure the performance of current tracking quantitatively, we define two mean absolute errors as follows: Fig. 11. Block diagram of the IPMSM drive system with the proposed MFPCC.

MiX =

N 1 |eiX (k)| N k=1 N

Miabc

1 ∗ |iX (k) − iX (k)| , X ∈ {a, b, c, d, q} (34) = N k=1 (Mia + Mib + Mic ) (35) = 3

where N denotes the total number of sampling points. Also, in order to quantitatively examine the effect on the current ripples resulting from the two PCC schemes, a performance index of current ripple is defined as N 1 JiR =

(i∗R (k) − iR (k))2 , R ∈ {a, d, q}. (36) N k=1

Fig. 12. Implemented circuit of the IPMSM drive system.

three-phase adjustable voltages to drive the IPMSM. The motor is equipped with a 4000 pulses/revolution incremental encoder. The triggering signals of the inverter are determined by the DSP programmed in assembly language. The inverter includes six insulated-gate bipolar transistors (IGBTs) and is 6MBI50L-060 type, made by Fuji Electric. Its specifications are as follows: 50-A continuous rating current, 100-A maximum peak current, and 600-V continuous rating voltage. The implemented circuit of the drive system is shown in Fig. 12. The hardware circuit consists of five parts. Part A is a power supply. Part B includes two Hall-effect current sensors, an interfacing circuit, and two 16-b A/D converters. Part C is the DSP board. Part D is the IGBT module. Part E includes some driving circuits and an encoder circuit. The a-phase and b-phase currents of the IPMSM are measured by the Hall-effect current sensors which are LA55-P type, made by LEM. The bandwidth of the current sensors is about 100 kHz. The DSP reads the outputs of the current sensors via A/D converters with conversion time equal to 5 μs. The DSP reads the two sampled currents at two sampling points and then computes the current difference. The speed and position of the IPMSM can be obtained after the pulses from the encoder are read. The dclink voltage is 200 V. The current prediction with time delay compensation of the MBPCC is implemented using (20). Also, the cost function is calculated via (21) to obtain an optimal switching state to be applied in the next switching interval. The block diagram of the MBPCC scheme is shown in Fig. 3. The maximum frequency of the output clock of the DSP (TMS320LF2407) is 30 MHz. The sampling interval of the

The results are listed in Table III, according to the aforementioned definitions. The table shows that the mean absolute errors and the current ripples of the MFPCC are smaller than that of the MBPCC. Moreover, by using the MFPCC, the total harmonic distortion of the a-phase stator current is reduced from 6.9% to 3.2% when the IPMSM is operated at 6 A q-axis and 0 A d-axis commands. In addition, the current ripple in Table III can be expressed as a percentage of the current command and is shown in Fig. 13. As one can observe, the current ripple from the MFPCC is obviously reduced, ranging from 6% to 10% for Jiq and from 5% to 20% for Jid under different current commands, as compared to that from the MBPCC. The current responses of the two PCC schemes under a square-wave q-axis command are shown in Fig. 14, where eid , eiq , and eia denote the d-axis current error, the q-axis current error, and the a-phase stator current error, respectively. Both schemes force the currents to follow their commands. It can be seen from Fig. 14(b) that the performance of the proposed method is superior in terms of having smaller current ripples, compared to Fig. 14(a) from the MBPCC. The transient current responses of the two PCC schemes are shown in Fig. 15(a) and (b). The q-axis current command is changed from 0 to 8 A within 0.2 ms. The measured q-axis current tracks its command precisely. In Fig. 15(a), the rising time of MBPCC is around 2.21 ms, compared to 2.09 ms of MFPCC as shown in Fig. 15(b). Therefore, one can conclude that the proposed MFPCC provides faster current response and smaller current ripples than the MBPCC. To show the dynamic responses of the two PCC schemes reacting to a step change of the q-axis current command, a test is performed where the current command jumps from 2 to 8 A.

676


TABLE III COMPARISONOF TRACKING ERRORSAT DIFFERENT CURRENT COMMANDS

Fig. 13. Current ripple percentages under different current commands.

Fig. 15. Experimental results of the two PCC schemes under a step q-axis current command from 0 to 8 A with zero d-axis current command. (a) MBPCC. (b) Proposed MFPCC.

Fig. 14. Experimental results of the two PCC schemes under a square-wave q-axis current command ranging from −8 to 8 A with zero d-axis current command. (a) MBPCC. (b) Proposed MFPCC.

The results are shown in Figs. 16 and 17, where ωrm denotes the speed of the IPMSM. Both schemes can track the current commands well. Figs. 16(b) and 17(b) show the corresponding currents in the α − β reference frame and the d − q reference frame. There are two circles at the left part of Figs. 16(b) and 17(b). The smaller one corresponds to the steady-state response of the q-axis current under 2-A command, and the larger one is corresponding to 8-A command. The line between the two circles represents the transition response of the current change, stepping from 2 to 8 A. Fig. 17(a) and (b) shows the responses for both steady-state and transient parts. According to the measured results, the proposed method outperforms the MBPCC in terms of current tracking.


Fig. 16. Experimental results of the MBPCC scheme under a step q-axis current command from 2 to 8 A with zero d-axis current command. (a) Currents and speed responses. (b) Current trajectory in the α − β stationary coordinates (left) and current error in the d − q coordinates (right).

Fig. 17. Experimental results of the proposed MFPCC scheme under a step q-axis current command from 2 to 8 A with zero d-axis current command. (a) Currents and speed responses. (b) Current trajectory in the stationary α − β coordinates (left) and current error in the d − q coordinates (right).

677

Fig. 18. Stator current response of the IPMSM operated at around 200 r/min, with the q-axis current command being 2 A and the d-axis current command being 0 A. (a) MBPCC. (b) Proposed MFPCC.

Fig. 18 depicts the measurement of the stator current while the motor is operated at about 200 r/min using the two PCC schemes, in which the q-axis current command is 8 A and the d-axis current command is 0 A. Fig. 18(a) shows the measured waveforms of the method. Fig. 18(b) demonstrates that the proposed MFPCC provides satisfactory current tracking with small current ripples. Similar results can be observed in Fig. 19, where the IPMSM is operated at about 1000 r/min. In this paper, a PI speed controller is used for the outer loop (speed) control of the drive system to generate the q-axis current command according to the speed tracking error. As a result, a closed-loop control of the drive system, including the inner loop (current) control and the outer loop (speed) control, is achieved. Figs. 20 and 21 illustrate the current responses and the speed response while the IPMSM is smoothly started from 0 to 500 r/min using the two PCC schemes, respectively. The speed can be effectively controlled at 500 r/min. Compared to Fig. 20, an improved current-tracking performance can be observed from Fig. 21. Using (34)–(36), the current errors and current ripples of the two PCC schemes shown in Figs. 14–21 are quantified and listed in Table IV, which shows that the currenttracking performance of the MFPCC is quite promising compared to that of the MBPCC. According to the experimental results, it can be seen that both the transient and steady-state responses from the MFPCC are superior. It achieves good current tracking even if the q-axis current command undergoes a step change. In addition, the proposed method is easier to implement than the MBPCC because the former does not require back EMF estimation. The experimental results reveal that the effect of delay compensation is not obvious, which may seem unexpected when compared with [12]. The current-tracking

678


Fig. 19. Stator current response of the IPMSM operated at around 1000 r/min, with the q-axis current command being 8 A and the d-axis current command being 0 A. (a) MBPCC. (b) Proposed MFPCC.

Fig. 20. Experimental results of the IPMSM testing from 0 to 500 r/min using the MBPCC scheme. (a) Currents and speed responses. (b) Current and reference trajectories in the α − β coordinates (left) and current error in the d − q coordinates (right).

performance is influenced by the saturation effect of Lq , the skin effect of rs , the drift of the stator voltage, the quantization error of the A/D converter, and the estimation error of the

Fig. 21. Experimental results of the IPMSM testing from 0 to 500 r/min using the proposed MFPCC scheme. (a) Currents and speed responses. (b) Current and reference trajectories in the α − β coordinates (left) and current error in the d − q coordinates (right).

extended back EMF. Moreover, the motor used in this paper is an IPMSM, which is a highly nonlinear and coupled load. Since the real back EMF of IPMSM is difficult to estimate due to the coupling effects of inductances if the method proposed in [12] is used, we estimate the extended back EMF instead of using its real value in the MBPCC based on a simplified mathematical model [38]. We expect that the estimation error of the extended back EMF of the IPMSM would be greater than that (estimation error of real back EMF) of a three-phase decoupled load used in [12] because of the mathematical simplification applied to IPMSM. It is noteworthy and fair to state that the performance of the MBPCC with the delay compensation for other types of motors might be better than that for IPMSM whenever the real back EMF needs to be estimated. This can also be seen from (17) and (20) in which the estimation error of the extended back EMF obviously affects the accuracy of the predicted current and, in turn, affects the performance of delay compensation. In addition, from the simulation results, one can see that the MBPCC with delay compensation is, to certain extent, sensitive to the parameter variations, and this observation is expected according to (32) and (33). Note that the predicted stator current of (20) is based on the predicted value of (17). Since the latter involves some parameters, their variations will degrade its accuracy, which will deteriorate the accuracy of (20) further. Consequently, (20) becomes more sensitive to parameter variations in the experiments. Putting them together should account why the results of the MBPCC for predicting the stator current of the IPMSM in this paper may not be consistent with the literature [12].


679

TABLE IV COMPARISONOF AVERAGE CURRENT-TRACKING ERRORS OBTAINED FROM THE EXPERIMENTAL RESULTS OF F IGS . 14–21

Based on the simulations, it is expected that different back EMF estimation methods in the MBPCC may result in different current predictions when implemented. To reduce the difficulty of back EMF estimation in terms of the method’s easiness and needed development time as far as the actual implementation is concerned, we choose to use the one presented in [11], which is popular, to estimate the extended back EMF, although there exist other options. However, this issue is not discussed further as it is out of the scope of this paper. More studies will be done by the authors in the future. Normally, one would expect that a control technique which uses less information cannot outperform another one that utilizes much more information. Given the experimental results, the MFPCC obviously has better performance than the MBPCC. There are four possible reasons. First, the q-axis inductance can be saturated as the stator currents increase. Second, the stator resistance rs is not constant, but rather, it varies due to the increasing temperature and skin-effect. Third, the stator voltage used in (19) is obtained from Table I, which is based on the assumption that the dc-bus voltage is known and is always constant, rather than from the voltage sensors. Fourth, recall that the IPMSM is connected to a dynamometer via its axis. The latter is an external disturbance to the motor and is not included in the motor’s electrical model, which naturally results in error of current prediction. Fifth, the estimation method of the extended back EMF is based on [11], which may result in some current prediction errors. Therefore, the performance of MFPCC, which uses online instant information, is expected to be better than that of the MBPCC which uses parameters measured offline and stator voltages from Table I. VI. C ONCLUSION In this paper, a new MFPCC for the IPMSM and its implementation have been presented based on detection of current differences. This method does not require any information on

the motor parameters, the back EMF, and the stator voltage, and only stator currents and their differences need to be available. Since only current measurement is required, the new approach can be easily applied to other ac motors. In addition, its computational load is relatively low, and it is insensitive to parameter variations. The experimental results of both transient and steady-state current-tracking responses are satisfactory and validate the effectiveness of the proposed PCC method.

ACKNOWLEDGMENT The authors would like to thank the reviewers for their constructive suggestions which greatly improved this paper.

R EFERENCES [1] J. A. Suul, K. Ljøkelsøy, T. Midtsund, and T. Undeland, “Synchronous reference frame hysteresis current control for grid converter applications,” IEEE Trans. Ind. Electron., vol. 47, no. 5, pp. 2183–2194, Sep./Oct. 2011. [2] K. M. Cho, W. S. Oh, Y. T. Kim, and H. J. Kim, “A new switching strategy for pulse width modulation (PWM) power converters,” IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 330–337, Feb. 2007. [3] J. Guzinski and H. Abu-Rub, “Speed sensorless induction motor drive with predictive current controller,” IEEE Trans. Ind. Electron., vol. 60, no. 2, pp. 699–709, Jan. 2013. [4] R. Vargas, J. Rodriguez, U. Ammann, and P. W. Wheeler, “Predictive current control of an induction machine fed by a matrix converter with reactive power control,” IEEE Trans. Ind. Electron., vol. 55, no. 12, pp. 4362–4371, Dec. 2008. [5] K.-J. Lee, B.-G. Park, R.-Y. Kim, and D.-S. Hyun, “Robust predictive current control based on a disturbance estimator in a three-phase gridconnected inverter,” IEEE Trans. Power Electron., vol. 27, no. 1, pp. 276– 283, Jan. 2012. [6] J. M. Espi, J. Castello, R. Garcia-Gil, G. Garcera, and E. Figueres, “An adaptive robust predictive current control for three-phase grid-connected inverters,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3537–3546, Aug. 2011. [7] J. M. E. Huerta, J. Castelló-Moreno, J. R. Fischer, and R. García-Gil, “A synchronous reference frame robust predictive current control for threephase grid-connected inverters,” IEEE Trans. Ind. Electron., vol. 57, no. 3, pp. 954–962, Mar. 2010.

680


[8] Z. Song, C. Xia, and T. Liu, “Predictive current control of three-phase grid-connected converters with constant switching frequency for wind energy systems,” IEEE Trans. Ind. Electron., vol. 60, no. 6, pp. 2451– 2464, Jun. 2013. [9] C.-C. Hua, C.-W. Wu, and C.-W. Chuang, “A digital predictive current control with improved sampled inductor current for cascaded inverters,” IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1718–1726, May 2009. [10] Q. Zeng and L. Chang, “An advanced SVPWM-based predictive current control for three-phase inverters in distributed generation systems,” IEEE Trans. Ind. Electron., vol. 55, no. 3, pp. 1235–1246, Mar. 2008. [11] J. Rodríguez, J. Pontt, C. A. Silva, P. Correa, P. Lezana, P. Cortes, and U. Ammann, “Predictive current control of a voltage source inverter,” IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 495–503, Feb. 2007. [12] P. Cortés, J. Rodríguez, C. A. Silva, and A. Flores, “Delay compensation in model predictive current control of a three-phase inverter,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 1323–1325, Feb. 2012. [13] H. Abu-Rub, J. Guzinski, Z. Krzeminski, and H. A. Toliyat, “Predictive current control of voltage-source inverters,” IEEE Trans. Ind. Electron., vol. 51, no. 3, pp. 585–593, Jun. 2004. [14] F. Villarroel, J. R. Espinoza, C. A. Rojas, J. Rodriguez, M. Rivera, and D. Sbarbaro, “Multiobjective switching state selector for finite-states model predictive control based on fuzzy decision making in a matrix converter,” IEEE Trans. Ind. Electron., vol. 60, no. 2, pp. 589–599, Feb. 2013. [15] M. Rivera, A. Wilson, C. A. Rojas, J. Rodríguez, J. R. Espinoza, P. W. Wheeler, and L. Empringham, “A comparative assessment of model predictive current control and space vector modulation in a direct matrix converter,” IEEE Trans. Ind. Electron., vol. 60, no. 2, pp. 578–588, Feb. 2013. [16] T. Geyer, “Computationally efficient model predictive direct torque control,” IEEE Trans. Power Electron., vol. 26, no. 10, pp. 2804–2816, Oct. 2011. [17] T. Geyer, G. Papafotiou, and M. Morari, “Model predictive direct torque control—Part I: Concept, algorithm, and analysis,” IEEE Trans. Ind. Electron., vol. 56, no. 6, pp. 1894–1905, Jun. 2009. [18] S. D. Cairano, D. Yanakiev, A. Bemporad, I. V. Kolmanovsky, and D. Hrovat, “Model predictive idle speed control: Design, analysis, and experimental evaluation,” IEEE Trans. Control Syst. Technol., vol. 20, no. 1, pp. 84–97, Jan. 2012. [19] H. Liu and S. Li, “Speed control for PMSM servo system using predictive functional control and extended state observer,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 1171–1183, Feb. 2012. [20] A. Bouafia, J.-P. Gaubert, and F. Krim, “Predictive direct power control of three-phase pulsewidth modulation (PWM) rectifier using space-vector modulation (SVM),” IEEE Trans. Power Electron., vol. 25, no. 1, pp. 228– 236, Jan. 2010. [21] H. Miranda, P. Cortés, J. I. Yuz, and J. Rodríguez, “Predictive torque control of induction machines based on state-space models,” IEEE Trans. Ind. Electron., vol. 56, no. 6, pp. 1916–1924, Jun. 2009. [22] C. A. Rojas, J. Rodríguez, F. Villarroel, J. R. Espinoza, C. A. Silva, and M. Trincado, “Predictive torque and flux control without weighting factors,” IEEE Trans. Ind. Electron., vol. 60, no. 2, pp. 681–690, Feb. 2013. [23] M. Curkovic, K. Jezernik, and R. Horvat, “FPGA-based predictive sliding mode controller of a three-phase inverter,” IEEE Trans. Ind. Electron., vol. 60, no. 2, pp. 637–644, Feb. 2013. [24] J. Weigold and M. Braun, “Predictive current control using identification of current ripple,” IEEE Trans. Ind. Electron., vol. 55, no. 12, pp. 4346– 4353, Dec. 2008. [25] M. J. Duran, J. Prieto, F. Barrero, and S. Toral, “Predictive current control of dual three-phase drives using restrained search techniques,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3253–3263, Aug. 2011. [26] M. W. Naouar, A. A. Naassani, E. Monmasson, and I. Slama Belkhodja, “FPGA-based predictive current control for synchronous machine speed drive,” IEEE Trans. Power Electron., vol. 23, no. 4, pp. 2115–2126, Jul. 2008. [27] M.-W. Naouar, E. Monmasson, A. A. Naassani, I. Slama-Belkhodja, and N. Patin, “FPGA-based current controls for ac machine drives— A review,” IEEE Trans. Ind. Electron., vol. 54, no. 4, pp. 1907–1925, Aug. 2007. [28] M. Pacas and J. Weber, “Predictive direct torque control for the PM synchronous machine,” IEEE Trans. Ind. Electron., vol. 52, no. 5, pp. 1350– 1356, Oct. 2005. [29] H. Zhu, X. Xiao, and Y. Li, “Torque ripple reduction of the torque predictive control scheme for permanent-magnet synchronous motors,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 871–877, Feb. 2012.

[30] H.-T. Moon and M.-J. Youn, “Predictive current control for PMSM with consideration of calculation delay,” Electron. Lett., vol. 37, no. 24, pp. 1488–1489, Nov. 2001. [31] F. Morel, X. Lin-Shi, J.-M. Rétif, B. Allard, and C. Buttay, “A comparative study of predictive current control schemes for a permanent-magnet synchronous machine drive,” IEEE Trans. Ind. Electron., vol. 56, no. 7, pp. 2715–2728, Jul. 2009. [32] Y. A.-R. I. Mohamed and E. F. El-Saadany, “Robust high bandwidth discrete-time predictive current control with predictive internal model—A unified approach for voltage-source PWM converters,” IEEE Trans. Power Electron., vol. 23, no. 1, pp. 126–136, Jan. 2008. [33] P. Cortés, J. Rodriguez, D. E. Quevedo, and C. A. Silva, “Predictive current control strategy with imposed load current spectrum,” IEEE Trans. Power Electron., vol. 23, no. 2, pp. 612–618, Mar. 2008. [34] S.-J. Jeong and S.-H. Song, “Improvement of predictive current control performance using online parameter estimation in phase controlled rectifier,” IEEE Trans. Power Electron., vol. 22, no. 5, pp. 1820–1825, Sep. 2007. [35] M. Kadota, S. Lerdudomsak, S. Doki, and S. Okuma, “A novel current control system of IPMSM operating at high speed based on model predictive control,” in Proc. Power Conver. Conf., Apr. 2–5, 2007, pp. 1315–1319. [36] D.-H. Yim, B.-G. Park, R.-Y. Kim, and D.-S. Hyun, “A predictive current control associated to EKF for high performance IPMSM drives,” in Proc. IEEE Appl. Power Electron. Conf. Expo., Mar. 6–11, 2011, pp. 1010–1016. [37] J. Beerten, J. Verveckken, and J. Driesen, “Predictive direct torque control for flux and torque ripple reduction,” IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 404–412, Jan. 2010. [38] C.-K. Lin, T.-H. Liu, and C.-H. Lo, “Sensorless interior permanent magnet synchronous motor drive system with a wide adjustable speed range,” IET Electr. Power Appl., vol. 3, no. 2, pp. 133–146, Mar. 2009. [39] J.-L. Shi, T.-H. Liu, and Y.-C. Chang, “Position control of an interior permanent-magnet synchronous motor without using a shaft position sensor,” IEEE Trans. Ind. Electron., vol. 54, no. 4, pp. 1989–2000, Jun. 2007. [40] E. Fuentes and R. Kennel, “Sensorless predictive torque control of the PMSM using a reduced order extended Kalman filter,” in Proc. Sensorless Control Elect. Drives, Sep. 2011, pp. 123–128. [41] A. M. Hava and E. Ün, “Performance analysis of reduced common-mode voltage PWM methods and comparison with standard PWM methods for three-phase voltage-source inverters,” IEEE Trans. Power Electron., vol. 24, no. 1, pp. 241–252, Jan. 2009. [42] A. M. Hava and E. Ün, “A high-performance PWM algorithm for common-mode voltage reduction in three-phase voltage source inverters,” IEEE Trans. Power Electron., vol. 26, no. 7, pp. 1998–2008, Jul. 2011. [43] H.-D. Lee and S.-K. Sul, “Common-mode voltage reduction method modifying the distribution of zero-voltage vector in PWM converter/inverter system,” IEEE Trans. Ind. Electron., vol. 37, no. 6, pp. 1732–1738, Nov./Dec. 2001. [44] J. Rodriguez and P. Cortes, Predictive Control of Power Converters and Electrical Drives. Hoboken, NJ, USA: Wiley, 2012.

Cheng-Kai Lin was born in Taipei, Taiwan, on July 11, 1980. He received the B.S. degree from the Department of Electrical Engineering, Ming Chi University of Technology, Taipei, in 2002 and the M.S. and Ph.D. degrees in electrical engineering from the National Taiwan University of Science and Technology, Taipei, in 2004 and 2009, respectively. From October 2009 to August 2012, he was a Postdoctoral Researcher with the Department of Electrical Engineering, National Taiwan University, Taipei. He is currently an Assistant Professor with the Department of Electrical Engineering, National Taiwan Ocean University, Keelung, Taiwan. His research interests include motor drive control, power electronic applications, and control applications.


Tian-Hua Liu (S’85–M’89–SM’99) was born in Tao Yuan, Taiwan, on November 26, 1953. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from the National Taiwan University of Science and Technology, Taipei, Taiwan, in 1980, 1982, and 1989, respectively. From August 1984 to July 1989, he was an Instructor with the Department of Electrical Engineering, National Taiwan University of Science and Technology. He was a Visiting Scholar with the Wisconsin Electric Machines and Power Electronics Consortium, University of Wisconsin, Madison, WI, USA, from September 1990 to August 1991 and with the Center of Power Electronics Systems, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA, from July 1999 to January 2000. From August 1989 to January 1996, he was an Associate Professor with the Department of Electrical Engineering, National Taiwan University of Science and Technology, where he has been a Professor since February 1996. He served as Department Chair from 2006 to 2009. His research interests include motor controls, power electronics, and microprocessor-based control systems.

Jen-te Yu was born in 1961. He received the M.S. degree in aerospace engineering from Wichita State University, Wichita, KS, USA, and the M.S. degree in electrical engineering from Georgia Institute of Technology, Atlanta, GA, USA. He is currently working toward the Ph.D. degree in the Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan. He has several publications in the areas of adaptive control, nonlinear control, output feedback control, optimal control, and networked control.

681

Li-Chen Fu (F’04) received the B.S. degree from the National Taiwan University, Taipei, Taiwan, in 1981 and the Ph.D. degree from the University of California, Berkeley, CA, USA, in 1987. Since 1987, he has been with the National Taiwan University, where he was awarded the Lifetime Distinguished Professorship and Irving T. Ho Chair Professorship in 2007. He served as the university’s Secretary General from 2005 to 2008. He has been extremely active and highly regarded in his technical field. In terms of editorial work, he served as an Associate Editor of the prestigious control journal Automatica from 1996 to 1999. In 1999, he started a new international control journal Asian Journal of Control, of which he is the Editor in Chief. His areas of research interest include robotics, visual detection and tracking, and control theory and applications. Dr. Fu served as the Program Chair of the 2003 IEEE International Conference on Robotics and Automation as well as the Program Chair of the 2004 IEEE Conference on Control Applications. Due to his profound academic reputation, he has been the President and the Vice-President for Publication of the Asian Control Association since 2006 and 2012, respectively. He has received much recognition for his outstanding performance in research and education during his 26-year technical career. He was elected as a Distinguished Lecturer for the IEEE Robotics and Automation Society in 2004–2005 and 2007 and for the IEEE Control Systems Society from 2013 to 2015.

Chieh-Fu Hsiao was born in Taipei, Taiwan, on July 20, 1989. He received the B.S. degree from Chung Yuan Christian University, Tao Yuan, Taiwan, in 2011. He is currently working toward the M.S. degree in the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei. His research interests include motor control and power electronics.