This article has been accepted for publication in a future issue of this journal, but has not been

fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2020.2984433, IEEE
Transactions on Industrial Electronics
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

An Improved Model Predictive Current

Control for PMSM Drives Based on Current
Track Circle
Xiaodong Sun, Senior Member, IEEE, Minkai Wu, Gang Lei, Member, IEEE,
Youguang Guo, Senior Member, IEEE, and Jianguo Zhu, Senior Member, IEEE

Abstract—Model predictive current control (MPCC) is a motors (PMSMs) are considered as new power source applied
high-performance control strategy for permanent magnet in EVs to replace the internal combustion engine [6] and [7].
synchronous motor (PMSM) drives, with the features of The EVs motor should have a large starting torque and a wide
quick response and simple computation. However, the range of speed regulation ability to meet the required power and
conventional MPCC results in high torque and current torque of starting, acceleration, driving, deceleration and
ripples. This paper proposes an improved MPCC scheme
for PMSM drives. In the proposed scheme, the back
braking. In addition, the motor also needs high controllability,
electromotive force is estimated from the previous stator steady precision and dynamic performance. Therefore, an
voltage and current, and it is used to predict the stator efficient and advanced control strategy is necessary to improve
current for the next period. To further improve the steady the drive performance of PMSMs.
state and dynamic performance, the proposed MPCC
selects the optimal voltage vector based on a current track B. Related Research
circle instead of a cost function. Compared with the There are various kinds of control methods for PMSM
calculation of cost function, the prediction of the current drives, such as the field-oriented control (FOC) and direct
track circle is simple and quick. The proposed MPCC is torque control (DTC) [8], [9]. Although the FOC can achieve
compared with conventional MPCC and a duty-circle based good steady-state performance and quick response with a wide
MPCC (DCMPCC) by simulation and experiment in the speed range, it has difficulty in adapting the complicated
aspect of converter output voltage and sensitivity analysis.
Results prove the superiority of the proposed MPCC and its
vehicle motor conditions [10]. FOC consists of an internal
effectiveness in reducing the torque and current ripples of current loop and an external speed loop which need fine tuning
PMSM drives. work. The stationary reference frame needs to transform to the
Index terms- Permanent magnet synchronous motor, rotating reference frame. In general, internal current loop and
model predictive current control, current track circle, cost external speed loop are PI control modules [11]. In the DTC
function scheme, the current loop and pulse width modulation (PWM)
block are not needed. And the final voltage vector is obtained
I. INTRODUCTION from the pre-switch table on the basis of the torque and flux
error signs. Compared to the FOC [12] and [13], the DTC has
A. Motivation
quicker dynamic response with simple structure. However, the
Recently the environment is getting more and more DTC generates high torque and flux ripples and high switching
concerned due to the use of fossil fuels without restraint. The frequency causes the hardware power loss [14] and [15]. The
most prominent application is the tradition fuel vehicles, and it conventional FOC and DTC have been combined with sliding
is time to upgrade and update. Electrical vehicles (EVs) have mode control to overcome the drawbacks.
less emission and higher energy conversion efficiency [1]-[5]. With the increasing demands of electric drive system and
With the advantages of high efficiency, high power density, recent advancements in the digital signal processing area,
small size and light weight, the permanent-magnet synchronous model predictive control (MPC) comes into reality as an
efficient control scheme [16]. The PMSM, converter and
Manuscript received August 09, 2019; revised January 6, 2020; controller compose the electric drive system to build model.
accepted March 12, 2020. This work was supported by the National MPC predicts the next period behavior of controlled variables,
Natural Science Foundation of China under Project 51875261, the
Natural Science Foundation of Jiangsu Province of China under which are current, torque and stator flux. Different from DTC
Projects BK20180046 and BK20170071, the “Qinglan project” of pre-switch, the MPC selects the optimal voltage vector by
Jiangsu Province, the Key Project of Natural Science Foundation of minimizing the error between the reference value and predictive
Jiangsu Higher Education Institutions under Project 17KJA460005, and value. A finite-control-set model predictive control (FCS-MPC)
the Six Categories Talent Peak of Jiangsu Province under Project
2015-XNYQC-003. (Corresponding author: Gang Lei.) in [17] is applied. Hence, MPC is more precise and more
X. Sun and M. Wu are with the Automotive Engineering Research efficient than DTC. A predictive speed controller (PSC) based
Institute, Jiangsu University, Zhenjiang 212013, China (email: on MPC was proposed in [18]. A dynamic performance with
xdsun@ujs.edu.cn, ujswmk@163.com). direct PSC has been achieved with short prediction horizon and
G. Lei and Y. Guo are with the School of Electrical and Data
Engineering, University of Technology Sydney, NSW 2007, Australia less computational requirements. Model predictive torque
(e-mail: Gang.Lei@uts.edu.au, Youguang.Guo-1@uts.edu.au). control (MPTC) is an improved MPC which pays attention to
J. Zhu is with the School of Electrical and Information Engineering, high-performance torque control [19]. Usually, torque and
University of Sydney, NSW, 2006, Australia (e-mail: stator flux are chosen as the control variables in the cost
jianguo.zhu@sydney.edu.au).
function. As for the torque ripple and current harmonics, MPTC
demonstrates better performance than DTC [20]. Because of the

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different units of torque and stator flux, the cost function MPCC (DCMPCC).
focuses on weighting factor of stator flux which requests some D. Paper organization
tuning works and keeps the MPTC unique. Meanwhile, an The remainder of this paper is organized as follows.
improved model predictive current control (MPCC) based on Section Ⅱ presents the model of PMSM and conventional
the incremental model for PMSM drive was proposed in [21] to MPCC. The proposed MPCC is given in Section Ⅲ. Section Ⅳ
solve the parameter dependence problem. Two MPCC methods describes the simulation results. Section Ⅴ presents the
with a duty-cycle-control were proposed to achieve optimal experimental results and discussions, followed by the
vector selection and vector duration in [22]. In [23], an MPCC conclusion.
with phase-shifted pulse width modulation (PS-PWM) was
presented to improve the steady-state control performance. II. PMSM MODEL AND CONVENTIONAL MPCC
Furthermore, a model-free predictive current control (PCC) of The continuous-time model of PMSM in the α-β-axis
interior permanent-magnet synchronous motor (IPMSM) drive stationary reference rotor frame can be written as [19]
systems based on a current difference detection technique was
d s di d x di
proposed in [24]. Its computational load is relatively low and it us = Rs is + = Rs is + Ls s + = Rs is + Ls s + Ex (1)
is insensitive to parameter variations. In order to reduce the dt dt dt dt
computation burden and eliminate the weighting factor in ψ x =  f + id ( Ld − Lq ) e je (2)
conventional model predictive torque control (MPTC), this
3
paper proposed an improved MPTC algorithm without the use Te = pn ( x  is ) (3)
of weighting factor [25]. Nevertheless, the conventional MPCC 2
usually employs only one voltage vector during one control where us, is, ψs, ψx, and Ex= [Eα Eβ]T represent the stator voltage
period which is unable to obtain satisfactory performance vector, stator current vector, stator flux vector, active flux
because the current error does not reach the smallest. Being vector and back EMF, respectively. id and iq denote the d-axis
similar to DTC, the improved MPCC employs this principle and q-axis current in the synchronous frame. Rs, Ld, Lq, ψf, and
that applies one active vector and one zero vector during one θe are the stator resistance, d-axis and q-axis inductance,
control period to produce small current variations. Therefore, permanent magnet flux, and electrical rotor position,
MPCC can achieve higher steady-state performance and respectively. Te is the electromagnetic torque, and pn is the
quicker response to a greater extent. A DFCB-MPTC was number of pole pairs.
proposed in [26] to compensate the lumped disturbance by the The equation of mechanical motion is expressed as
analysis of FCS-MPTC with mismatched parameters and active d m
disturbance ability of traditional PI controller. A continuous J = Te − Tl − Bm (4)
dt
voltage vector model-free predictive current control method where J is the rotational inertia, B is the damping coefficient,
was proposed for surface-mounted PMSMs to reduce the ωm is the mechanical angular velocity, and Tl is the load torque.
current ripples of FCS-MPC in [27]. Reference [28] proposed a
constant switching frequency multiple-vector based FCS- 
MPCC scheme to reduce computation burden, low-order sector2 sector6
harmonic currents, and variable switching frequencies. A
generalized multiple-vector-based MPC for PMSM drives, U*
s

which unifies the prior MPC methods in one frame with much
lower complexity and computational burden proposed in [29].
sector3 U4(100)
These works made contribution to the computational U0(000)

complexity of duty-cycle-based MPCC indeed. U3(011) U7(111) 

sector4

C. Contribution
This paper proposes an improve MPCC which selects the
optimal voltage vector based on a current track circle instead of sector1 sector5
a cost function. The back electromotive force (EMF) is
Fig. 1. Space voltage vector of a two-level voltage source inverter.
estimated based on the previous value of stator voltage and
Considering the output form of power inverters, the
current. Furthermore, the sensitivity of motor parameter
predictive control strategies applied in the field of PMSM
variations is verified. The main contributions of this paper are
control are mostly based on the limited possible switching states,
listed as follows.
and the motor model is derived to predict the system behavior
1) The proposed MPCC establishes a new reference
when various switching states are switched. As for the output
frame based on a current track circle. The current locus
of the predictive control algorithm, that is to say, the selection
and initial points are shown in the established
of switch state is always based on the control target. By defining
reference frame. Only one zero voltage must be
a cost function composed of cost variables and comparing the
predicted as to reduce the torque ripple and current
future state value calculated based on the prediction model, the
harmonics instead of all the voltage vectors.
control output is obtained by minimizing the cost function value.
2) The proposed MPCC selects the optimal voltage
Therefore, the predictive control strategy can be summarized
vector based on a current track circle instead of a cost
into three parts, the definition of the cost function established
function to reduce the computational burden compared
according to the control objective, discrete modeling of the
to the conventional MPCC and the duty-cycle-based

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motor control system and the output sequence of the system The optimal duration of the best nonzero vector uopt is also
model which may be calculated based on the inverter state called duty circle and the cost function is established to
prediction model. Fig. 1 shows the voltage vectors of a two - guarantee the accuracy of selected voltage vector. The cost
level voltage source inverter in a stationary reference frame α- function is shown as follows:
β. uopt topt
2

The conventional MPCC relies on the minimization of a F1 = u − *

s (7)
cost function to select the voltage vector. In other words, the Ts
cost function is on behalf of evaluation objectives to select the By solving the derivation of F1 in allusion to topt, the
optimal voltage vector for the next sampling time. The winding optimal vector duration is obtained as:
current equation is discretized based on sampling time Ts. Using us*  uopt
discrete time model, the future state set of winding current can topt = 2
Ts (8)
be predicted according to the actual current measured at uopt
sampling time k in the prediction algorithm. The scheme of It is evident that the selection of optimal voltage vector and
conventional MPCC is shown in Fig. 2. duration are much simpler.
i* ( k + 1)  i* ( k ) Inverter
Current error SA
minimization SB ia , ib , ic III. THE PROPOSED MPCC
Winding current cost function F IGBT PMSM

predictive model F = i* ( k + 1) − i P ( k + 1)
SC 3 This study proposes a novel MPCC algorithm to simplify
8
the control complexity and computational burden, which is
i (k ) iP
U 0−7 ( k + 1) based on a current track circle. The cost function is not needed
because the current trajectory is corresponding with different
Fig. 2. Conventional MPCC control scheme. voltage vector directions.
The model predictive current control aims to stabilize the
current signal and minimize the error between the predicted A. EMF Estimation
current value and the reference current value by calculating the From (1), the current equation of PMSM can be obtained
cost function. The cost function can be expressed as follows: as follows:
F = i* ( k + 1) − iP ( k + 1) + i* ( k + 1) − iP ( k + 1) (5) dis 1
= ( us − Rs is − Ex ) (9)
where iα and iβ are the real and imaginary components of the dt Ls
stator current in the stator reference frame, respectively. The The derivative of current is discretized by using the
values with superscript * and p represent reference and forward Euler formula.
predicted values. dis is (k + 1) − is (k )
 *+ iq*
 (10)
PI * Reference us* Vector uopt S a ,b , c dt Ts
e je is
-
 id* voltage vector selection/ Pulse
signal
PMSM
0 calculation duration topt Ts
is (k + 1) = is (k ) + (us (k ) − Rs is (k ) − Ex (k )) (11)
Ex ( k ) us ( k ) Ls
EMF is (k )
estimation where Ts is the sampling time.
is (k + 1)
Current Due to the technology limitations, the back Ex(k) cannot be
prediction
directly measured. Fortunately, Ex(k) can be calculated by (1)
d e
dt
Resolver and (2), but it is strictly related to the accuracy of electrical
Fig. 3. DCMPCC control scheme. parameters. Due to the variation of operating environment, the
In the duty-cycle-based MPCC (DCMPCC), as proposed motor parameters have a large difference between the original
MPCC Ⅱ in [22], the reference voltage vector us* is calculated parameters. Therefore, it is necessary to estimate the EMF
as follows: directly using as few parameters as possible. During several
i* − i (k + 1) control periods, the motor speed changes, which may be
us* = Rs is (k + 1) + Ls s s + Ex (k ) (6)
Ts considered as that the speeds are approximate at k moment and
(k+1)th moment. The Ex(k) is concerned with the rotor speed ω,
As usual, the reference voltage vector us* will be
so Ex in several period can be assumed the same. According to
compounded by two nonzero voltage vectors and one zero with
the above analysis, the EMF at (k-1)th moment using the past
high switching frequency. In order to reduce the computational
values of stator voltage and current is:
complexity and switching frequency, the DCMPCC only uses
L
one nonzero voltage and one zero vector. The scheme of Ex (k − 1) = us (k − 1) − Rs is (k ) − s (is (k ) − is (k − 1)) (12)
DCMPCC is shown in Fig. 3. On the basis of the location of us*, Ts
it is time to select the optimal vector which is closest to the us*. 1
Ex (k ) = ( Ex (k − 1) + Ex (k − 2) + Ex (k − 3) + E x (k − 4)) (13)
As shown in Fig. 1, the distance between u6 and us* is the 4
shortest in all other nonzero voltages. Therefore, u6 is selected The similar EMF can be obtained at (k-2)th, (k-3)th and (k-
as the optimal voltage vector. In other words, as soon as the 4)th moment by the analogical method, respectively.
location of us* is ensured, the best nonzero voltage vector can In simple terms, the predictive current in (11) can be
be obtained, which is more efficient than the conventional deduced by the past value of estimated EMF in (12). The
MPCC. availability has been proved by the presented experimental
results in [21]. However, the variations of inductance have

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caused a fairly large error on the estimated EMF by the (12). In An active voltage vector is equal to itself adding zero vector.
order to improve the stability and fault tolerance against the Therefore, the variations of current track consist of variations
inductance variation, this paper uses the mean value of caused by zero voltage vector and active voltage vectors, which
estimated EMFs during the last four control periods. Even if the are represented by (Δiα0(k+1), Δiβ0(k+1)) and (Δiαx(k+1),
inductance changes more than ±50%, the system is still stable Δiβx(k+1)). As well-known, the six non-zero active voltage
and the estimated EMF is accurate. vectors are decided by the switching states of the inverter.
When the dc-link voltage is constant, the amplitudes of six non-
B. One-step Delay Compensation
zero active voltage vectors are the same except the directions of
The final control of electrical motor drives is realized by them. If ignoring the variation of Ls and Rs, the amplitude of
the hardware and peripheral circuit. Because of the effect of (Δiαx(k+1), Δiβx(k+1)) is also the same, other than the direction
various factors, the controller output cannot be applied of (Δiαx(k+1), Δiβx(k+1)) resembling the applied active voltage
immediately. For example, the required voltage vector obtained vector. In order to reduce the computational burden aroused by
at (k)th moment is not implemented at (k+1)th moment due to the seven current tracks and cost function, a new reference
the delay of the digital signal processors. Especially, the control frame α’-β’ is established in this section. Use the transformation
performance is deteriorated when the number of samples is not equation as the following:
high. Therefore, it is necessary to take action to compensate for i ' (k + 1) = i (k ) − i 0 (k + 1)
the delay using the Heun’s method. The accuracy of predictive  (17)
current value in (11) will be lower than that of current i ' (k + 1) = i (k )+i 0 (k + 1)
prediction with new compensation method. The current where (iα’(k+1), iβ’(k+1) is the current track in the reference
compensation can be demonstrated as follows: frame α’-β’.
T The aim of establishing the frame α’-β’ is to keep the
isc (k + 1) = is (k ) + s (us (k ) − Rs is (k ) − Ex (k )) (14)
Ls current track generated by zero voltage vector in the frame α-β
coinciding with the original point of the frame α’-β’. Therefore,
− Rs (isc (k + 1) − is (k ))Ts
is (k + 1) = isc (k + 1) + (15) the applied active voltage vector is reflected through the current
2 Lq track (iα’(k+1), iβ’(k+1)) at horizontal and vertical coordinates
where isc(k+1) is the current compensation of stator current. (Δiαx(k+1), Δiβx(k+1)) in Fig. 5.
 ' i (k + 1) x
C. Selection of the Optimal Voltage Vector (i ' (k + 1), i ' (k + 1))

This paper proposes an improved MPCC which selects the

optimal voltage vector based on a current track circle instead of i x (k + 1)
a cost function. After having obtained the back EMF from (12)
and (13), the current at the next control period can be predicted (i 0 (k + 1), i 0 (k + 1)) 
by (14) and (15). The proposed MPCC predicts one zero voltage  '
i 0 (k + 1)
vector to achieve switching state for every sample period based
on the direction of the current trajectory in a new reference
(i (k ), i (k ))
frame. The control diagram of the proposed MPCC is shown in i 0 (k + 1)
Fig. 4. (0, 0) 
* + PI
iq* i* S a ,b , c
Vector

- Anti- Park
id* i* PMSM
0 conversion selectation
Fig. 5. Relative location of the new reference frame α’-β’and the stator
i 0 (k + 1) i 0 (k + 1) us ( k ) reference frame α-β.
e
Current is (k )
(i* ' (k + 1), i* ' (k + 1))
EMF
trajectory
prediction
estimation
'
Ex ( k )
sector6
is (k + 1) Current
prediction
d e sector2
Resolver
dt
Fig. 4. Control diagram of the proposed MPCC. i ' Actual current circle
Reference current circle
Different from the conventional MPCC, the proposed Predictive current circle

MPCC cancels the cost function and builds the current track U0(000) U4(100)
circle in the reference frame. The current equation is U3(011) U7(111)
sector4
'
transformed into the following: sector3

 Ts Ts
i (k + 1) = L (u0 (k ) − Rs i (k ) − Ex (k )) + L u (k ) sector1 sector5
 s s
 (16)
T
i (k + 1) = (u (k ) − R i (k ) − E (k )) + u (k )
s Ts
  0 s  x  Fig. 6. Space voltage vector in the reference frame α’-β’.
 Ls Ls
In the reference frame α’-β’, the whole region is also
where iα, uα, eα and iβ, uβ, eβ are the current, voltage and back divided into six sectors (sector1-sector6) shown in Fig. 6. The
EMF in the stationary reference frame and α-β frame, direction of the current track is the same as the applied active
respectively. voltage vector. The concrete position of current track is
The left-hand side of equation defined as variation of determined by the angle θ. According to the variation of current
current track can be changed by the right-hand side of equation. track caused by active voltage vectors, the value of tanθ can be

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Transactions on Industrial Electronics
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calculated. Because the angle range is fixed, the position of 1 T

current track could be confirmed. Therefore, judging from the d opt = u (k ) 2 + u (k ) 2 s (19)
2 Ls
direction of the current track, the applied active voltage can be
known. Finally, the direction of the current track in the reference frame
After the selection of active voltage vector, the selection α’-β’ is similar to that of the active voltage. The selection of the
of zero voltage vector will relieve the torque ripple. The switching state for every sample period is based on the direction
difference between the actual values of currents and the of the current track in Fig.8. The sampling frequency is different
from the switching frequency. Because the continuous model
references in the reference frame α’-β’ is obtained by (18),
needs to be transformed into discrete model. Therefore, the
which is demonstrated in Fig. 7.
value of sampling frequency set in simulation determines the
(i ' 2 , i ' 2 ) ' (i '6 , i '6 ) accuracy of the proposed strategy. The switching frequency
sector2 depends on the electrical specification of power converter. The
A6 sector6
switching frequency setting in the RTI of dSPACE cannot
d

surpass the maximum value of IGBT. The optimal vector

d A0
A sector4 duration is different in the sampling period, which will require
(i '3 , i '3 )
d B3
B
d B0 (i ' 4 , i ' 4 ) the variable switching frequency. The duration is obtained by
the amplitude and direct of reference current track in the
d D0 d D4  ' reference frame α’-β’. As a result, the cost function is cancelled
sector3 d C0 D
to reduce the computational burden.
C Compared with the DCMPCC, the proposed MPCC has
d C1
sector1
sector5 the following advantages. First, the methods of selecting
optimal voltage vectors are different. In the duty-cycle-based
(i '1 , i '1 ) (i '5 , i '5 )
MPCC, the optimal voltage vectors are composed of one active
Fig. 7. Current track distribution in the reference frame α’-β’.
vector and one zero vector by cost function. In the proposed
As can be seen, there are four typical current track points. MPCC, the optimal voltage vector is selected based on the
If the zero voltage vectors are not considered, the active voltage distance between the current track reference point and the
vectors can be selected simply according to the positions A, B, original point of the frame α’-β’ and the distance between
C and D. The optimal active voltage vectors are u6, u3, u1 and current track reference point and actual current point. When the
u4, respectively. The distance can be calculated as the following: distances are equal to each other, they are defined as dm. dm is
d = (i* − i ) 2 + (i* − i ) 2 supposed as a constant value and determines whether or not
 n ' ' ' '
active or zero voltage vectors should be selected. Second, only
 (18)

 d 0 = (i
* 2
' ) + (i
* 2
' ) one active or zero voltage vector must be predicted to reduce
the computation complexity in the proposed MPCC. Different
When (i*α’(k+1), i*β’(k+1)) is at point A, B, C or D in turn,
points of reference current determine the different active or zero
dA0, dB0, dC0 and dD0 are the distances between the current track voltage vectors. Each point corresponds to a voltage vector, and
reference point and the original point of the frame α’-β’, and more and more zero voltage vectors are selected with the
dA6, dB3, dC1 and dD4 are the distances between current track increasing of dm to reduce the torque ripples.
reference point and actual current point, respectively. The
smaller one will be used to select the corresponding voltage SA
vector as the best voltage vectors. When the distances are equal
SB
to each other, they are defined as dm. dm is supposed as a
constant value and determines whether or not active or zero
SC
voltage vectors should be selected. From the above analysis, d0
is the distance between the current track point and the original
point of the frame α’-β’. If d0 is smaller than dm, one zero u0 u3 u7 u1 u4
voltage vector will be selected to keep the steady state Fig. 8. Switching state for every sample of the points A, B, C, and D
performance, otherwise, one active voltage vector will be above.
selected. With the increase of dm, more and more zero voltage
vectors will be selected to reduce the torque ripple. At typical IV. SIMULATION RESULTS
current position B in Fig.7, dD0 can be assumed as the optimal To confirm the effectiveness of the proposed MPCC, the
value of dm. The distance between the current track reference performance of the conventional MPCC, DCMPCC, and the
point and the original point of the frame α’-β’ dB0 is equal to the proposed MPCC are compared in this section based on
distance between current track reference point and actual simulation results. The one-step delay caused by digital
current point dB3. The optimal vectors are consisted of u3 and u7, equipment has been compensated, and the sampling frequency
which divide the duration. In order to reduce the switch loss, of each method is set to 10 kHz. Table Ⅰ lists the main
only one bridge arm SA is changed to produce fewer switching parameters of the PMSM drive system.
transitions.
The optimal value of d is obtained as: A. Comparisons under speed change condition
For the simulation, two situations are considered for the

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600
starting process, no-load and load, then speed/load changes are 500
applied to the drive system to investigate the dynamic responses. 400

Nr(rpm)
300
Fig. 9 shows the dynamic responses of three control methods 200
with no-load starting for the PMSM drive system. For each 100
0
control method, three response curves are given. They are, from 0 0.05 0.1 0.15 0.2 0.25
t(s)
0.3 0.35 0.4 0.45 0.5

top to bottom, the rotor speed, electromagnetic torque and 25

20
phase-A stator current. In the simulation, the initial reference

Te(Nm)
15

speed for the starting process is 300 rpm, then a speed change 10
5
(from 300 to 500 rpm) is applied at time 0.15 s and a load torque 0
change (from 0 to 10 Nm) is applied at 0.35 s. -5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
t(s)
30
TABLE I 20
IPMSM DRIVE SYSTEM PARAMETERS 10

Ia(A)
0
Parameter Symbol Value -10
Number of pole pairs 𝑃 5 -20
-30
Stator resistance 𝑅𝑠 0.18 Ω 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
t(s)
d-axis inductance 𝐿𝑑 0.174 mH
q-axis inductance 𝐿𝑞 0.29 mH (c)
Permanent-magnet flux linkage ψf 0.0711 Wb Fig. 9. Simulation starting response from standstill to 300 rpm with
Inertia J 0.067 kgm2 speed change: (a) Conventional MPCC, (b) DCMPCC, and (c) Proposed
Rated speed N 2000 rpm MPCC.
Rated power 𝑃𝑁 60 kW As shown, all three MPCC methods can reach the
reference speed quickly. However, the conventional MPCC has
600
500
a relatively large overshoot when the rotor speed reaches 300
400 rpm and changes to 500 rpm at 0.15 s. Meanwhile, the
Nr(rpm)

300
200 electromagnetic torque and phase current have significant
100 oscillations. Fig. 10 shows total harmonic distortion (THD) of
0
0 0.05 0.1 0.15 0.2 0.25
t(s)
0.3 0.35 0.4 0.45 0.5 the current for three control methods. As shown, the current
25
20
THDs of the three control methods are 17.4%, 3.58% and
1.42%, respectively. It can be seen that the proposed MPCC has
Te(Nm)

15
10
5
the best performance in terms of steady state and dynamic
0 response in this low-speed simulation because it has the lowest
-5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 torque ripples and current harmonics.
t(s) Fundamental (20Hz) = 3.6034 , THD= 17.4032%
30 20
15
6
20 10 5
Hn/H1(%)
Ia(A)

5 4
10 0
3
Ia(A)

-5
0 -10 2
-15 1
-10 -20
0
-20 0.39 0.395 0.4 0.405 0.41 0.415 0.42 0 500 1000 1500 2000
t(s) Harmonic order
-30 (a)
Fundamental (20Hz) = 3.5282 , THD= 3.5812%
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 20
t(s) 15 6
10 5
Hn/H1(%)

(a) 5
Ia(A)

0
4
600 -5 3
-10 2
500 -15 1
-20
400 0
0.36 0.37 0.38 0.39 0.4 0 500 1000 1500 2000
Nr(rpm)

t(s) Harmonic order

300 (b) Fundamental (20Hz) = 2.8612 , THD= 1.4172%
200 20
15 6
100 10 5
Hn/H1(%)

5 4
Ia(A)

0 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -5 3
t(s) -10 2
25 -15 1
-20
20 0
0.36 0.37 0.38
t(s)
0.39 0.4 0 500 1000 1500 2000
Harmonic order
Te(Nm)

15 (c)
10
Fig. 10. Simulation current harmonic spectrum at 500 rpm with torque
5
0
10 Nm: (a) Conventional MPCC, (b) DCMPCC, and (c) Proposed MPCC.
-5
0 0.05 0.1 0.15 0.2 0.25
t(s)
0.3 0.35 0.4 0.45 0.5 B. Comparisons under torque change condition
30
20 Fig. 11 illustrates the dynamic responses of three control
10 methods for the PMSM drive system with an initial load torque
Ia(A)

0
-10 reference of 15 Nm and an initial reference speed of 2000 rpm.
-20 For each control method, three response curves are given as
-30
0 0.05 0.1 0.15 0.2 0.25
t(s)
0.3 0.35 0.4 0.45 0.5 well. They are, from top to bottom, the rotor speed,
(b) electromagnetic torque and phase-A stator current. In the
simulation, there are two changes for the load torque, i.e., from
15 to 0 Nm at 0.15 s and from 0 to 10 Nm at 0.35 s. As shown,
the DCMPCC and proposed MPCC present better dynamic and

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steady-state performance in terms of rotor speed, torque ripple proposed MPCC in the reduction of current harmonics, under
and current harmonics than the conventional MPCC. Obviously, the condition of 15 Nm at 2000 rpm. The current THD is
the proposed MPCC is more effective in reducing torque ripples calculated up to 20 kHz. Apparently, the low-order harmonics
and current harmonics. in the DCMPCC and proposed MPCC are much lower than
2800
2400
those in the conventional MPCC. The current THD of the
2000
conventional MPCC is 16.7%. It is higher than the values of
Nr(rpm)

1600
1200 DCMPCC (9.5%) and the proposed MPCC (3.5%). Again, the
800
400 proposed MPCC has the smallest current harmonics.
0
0 0.05 0.1 0.15 0.2 0.25
t(s)
0.3 0.35 0.4 0.45 0.5 The switching frequencies are determined by the
30 requirements of software and hardware. In the RTI of dSPACE,
20 the average switching frequencies are all set as 10 kHz, and they
Te(Nm)

10 cannot surpass the maximum value of IGBT. It needs to sample

0 at least once per period and then compute once. In theory, the
-10
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 higher sampling frequency, the more conducive to reduce
t(s)
40
30
latency and discretization error, but most commonly used
20
10
controller computing power allows only switch cycle per
Ia(A)

0
-10
sample and calculate the twice, the higher sampling frequency
-20
-30
cannot complete the calculation of switch signal within a
-40
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 sampling period. Consequentially, the next sampling period
t(s)
will not be able to update the switch state. Hence, the sampling
(a)
2400 frequencies are equal to switching frequencies in this paper.
2000
However, by counting the total switching steps during a
Nr(rpm)

1600
1200 short period, e.g., 0.05 s, it is found that the average switching
800 frequencies of DCMPCC and the proposed MPCC at the steady
400
0 state of 2000 rpm are much lower than 10 kHz. They can reduce
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
30
t(s) switching loss effectively.
Fundamental (200Hz) = 3.6255 , THD= 16.7022%
30
20 12
20
10
Te(Nm)

10

Hn/H1(%)
10
Ia(A)

8
0
6
0 -10
4
-20 2
-10 -30
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 100 150 200
0.056 0.06 0.064
t(s)
0.068 0.072 0 50
t(s) Harmonic order
40 (a)
30 Fundamental (200Hz) = 3.5824 , THD= 9.481%
30
20 12
20
10 10
Ia(A)

Hn/H1(%)

10
Ia(A)

0 8
-10 0 6
-20 -10 4
-30 -20 2
-40 -30 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.056 0.06 0.064
t(s)
0.068 0.072 0 50 100 150 200
t(s) Harmonic order
(b)
(b) Fundamental (200Hz) = 3.5214 , THD= 3.481%
30
2400 20
12
10
Hn/H1(%)

2000 10
Ia(A)

8
0
Nr(rpm)

1600 6
-10
1200 4
-20
2
800 -30
0.056 0.06 0.064 0.068 0.072 0
400 t(s) 0 50 100 150 200
Harmonic order
0 (c)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
t(s) Fig. 12. Simulation current harmonic spectrum at 2000 rpm with torque
30
15 Nm: (a) Conventional MPCC, (b) DCMPCC, and (c) Proposed MPCC.
20
Comparing the THD both in low speed (300 to 500 rpm as
Te(Nm)

10
shown in Fig. 10) and high speed (2000 rpm as shown in Fig.
0
12) ranges, it can be found that the performance in low speed is
-10
0 0.05 0.1 0.15 0.2 0.25
t(s)
0.3 0.35 0.4 0.45 0.5 more remarkable. This is because the required voltage vector is
40
30 small, and zero vectors are used in switching period for a long
20
10
time at low speeds. The conventional MPCC only uses six basic
Ia(A)

0
-10 voltage vectors, which cannot provide the required voltage
-20
-30 vector. As for the proposed MPCC, active voltage vectors and
-40
0 0.05 0.1 0.15 0.2 0.25
t(s)
0.3 0.35 0.4 0.45 0.5 zero voltage vectors are combined to obtain the required voltage
(c) vectors. Therefore, the proposed MPCC based on the current
Fig. 11. Simulation starting response from standstill to 2000 rpm with track circle can reach the optimal voltage vectors which yield
load torque change: (a) Conventional MPCC, (b) DCMPCC, and (c) low current harmonics and current THD.
Proposed MPCC.
Fig. 12 shows the effectiveness of DCMPCC and the

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C. Comparisons of converter output voltage experiment.

400
300
200 A. Comparisons under speed change condition
100
250rp 250rp
Ua

0 m/div m/div

-100
rotor speed rotor speed
-200
-300
-400
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
t(s) 250rpm/div
(a)
400 250rpm/div
300
200
5Nm/ 5Nm/
100 div div
Ua

0
-100
-200
-300 torque torque
-400 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
t(s)
(b)
400
300 5Nm/div 5Nm/div
200 10A/div 10A/div
100
current current
Ua

0
-100
-200
-300
-400 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
t(s)
(c) 10A/div 10A/div

Fig. 13. Simulated converter output voltage for phase A: (a)

Conventional MPCC, (b) DCMPCC, and (c) Proposed MPCC. (a) (b)
The simulated phase output voltage of the converter is 250rp
m/div

shown in Fig. 13. Inverter's nonlinearity has influence on the rotor speed

motor performance, for the nonlinearity would result in

harmonic components in the stator currents which certainly
deteriorate the torque ripple. The sinusoidal alternating voltage 250rpm/div
is needed for PMSM drive which is generated by inverter.
5Nm/
Therefore, the performance of steady and dynamic state is div

directly affected by the converter output voltage. Different

control strategies have different effects on converter output torque

voltage stability. It can be seen that the voltage controlled by

the proposed MPCC has the best performance.
5Nm/div

V. EXPERIMENTAL RESULTS 10A/div

current
In order to validate the simulation results, some
experimental tests are carried out on a two-level inverter PMSM
platform. Fig. 14 shows the experimental setup. The proposed
control scheme is implemented in a dSPACE DS1007 PPC. 10A/div

(c)
Fig. 15. Experimental starting response from standstill to 300 rpm with
speed change: (a) Conventional MPCC, (b) DCMPCC, and (c) Proposed
MPCC.
As shown in Fig. 15, all three MPCC methods can reach
the reference speed quickly in this no-load starting process.
However, the conventional MPCC has a relatively large
Fig. 14. Experimental setup. overshoot when the rotor speed reaches 300 rpm and changes
Figs. 15 and 16 show the experimental results (the rotor to 500 rpm. The dynamic performance of the proposed MPCC
speed, torque and phase-A stator current) of the PMSM with is the best. For the steady-state performance, the proposed
three MPCC methods. For the purposes of a smooth comparison, MPCC has the best performance because it has the lowest
the same conditions are applied to obtain Fig. 15 and Fig. 9, i.e., torque ripples and current harmonics.
starting with no-load, then a speed change at 0.15 s and a load B. Comparisons under load change condition
torque change at 0.35 s. Similarly, same conditions are applied
As shown in Fig. 16, for a starting process with load and a
to obtain Fig. 11 and Fig. 16, i.e., starting with load, then two
higher initial reference speed, the DCMPCC and the proposed
load torque changes at 0.15 and 0.35 s, respectively. The current
MPCC have better steady-state and dynamic performances than
waveform is given under the load torque 10 Nm in the
the conventional MPCC. The proposed MPCC is the best one

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among them as it has the lowest speed overshoots, torque have less impact compared to the high-speed drive. However,
ripples, and current harmonics. Therefore, the advantages of the there are always fluctuations in the conventional MPCC.
proposed MPCC have been confirmed by both simulation and Therefore, the sensitivity analysis of the proposed MPCC and
experimental results. conventional MPCC are verified experimentally.
1000rp 1000rp
2020 2004
m/div m/div

2010 2002
rotor speed rotor speed

Nr(rpm)
Nr(rpm)
2000 2000

1990 1998

1000rpm/div 1000rpm/div 1980

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28
1996
0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28
t(s) t(s)
20 4

10 2

ΔNr(rpm)
10Nm/ 10Nm/

ΔNr(rpm)
div div
0 0
torque torque
-10 -2

-20 -4
0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28
t(s) t(s)

10Nm/div 10Nm/div (a) (b)

Fig. 17. Measured motor speed under the variation of stator resistance:
(a) Conventional MPCC, (b) Proposed MPCC.
15A/div 15A/div 2020 2200

current current 2010 2100

Nr(rpm)
Nr(rpm)
2000 2000

1990 1900

1980 1800
0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28
t(s) t(s)
15A/div 15A/div 20 200

10 100

ΔNr(rpm)
ΔNr(rpm)

(a) (b) 0 0
1000rp
m/div
-10 -100

rotor speed -20 -200

0.2
0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28
t(s) t(s)
(a) (b)
1000rpm/div Fig. 18. Measured motor speed under the variation of d-axis inductance:
(a) Conventional MPCC, (b) Proposed MPCC.
2020 2200

10Nm/ 2010 2100

div
Nr(rpm)

Nr(rpm)
2000 2000
torque
1990 1900

1980 1800
0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28
t(s) t(s)

10Nm/div 20 200

10 100
ΔNr(rpm)

ΔNr(rpm)

15A/div 0 0

-10 -100
current
-20 -200
0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28
t(s) t(s)
(a) (b)
Fig. 19. Measured motor speed under the variation of q-axis inductance:
15A/div (a) Conventional MPCC, (b) Proposed MPCC.
A steady-state performance comparison of the three
(c) methods is illustrated in Fig. 20. The comparison is divided into
Fig. 16. Experimental starting response from standstill to 2000rpm with low speed and high-speed ranges. As can be seen, although the
load torque change: (a) Conventional MPCC, (b) DCMPCC, and (c)
Proposed MPCC.
reduction of computation time is not significant between
DCMPCC and the proposed MPCC, the torque ripples and
C. Sensitivity analysis current THDs are reduced significantly by using the proposed
Figs. 17-19 show the experimental results of motor speed MPCC for both speed ranges. For the low-speed situation, the
response under the changes stator resistance, d-axis inductance, reduction of torque ripple and current THD are bigger than
and q-axis inductance, respectively. In the experiment, ±50% those for the high-speed situation, because the active voltage
step changes are applied to the stator resistance and d-q axis vectors and zero voltage vectors are combined to obtain the
inductances at 0.22, 0.24 and 0.26 s. The motor runs at 2000 required voltage vectors more accurately in low speed.
rpm for sensitivity analysis. As shown in Fig. 17, the variation Moreover, the computation times of dSPACE for the
of motor speed given by the proposed MPCC is much lower conventional MPCC, DCMPCC and the proposed MPCC are
than that of the conventional MPCC under the change of the 46.2, 35.4 and 32.1 s, respectively at low speed, which are
stator resistance. In the sensitivity test on the variation of
similar to those at high speed. Therefore, the proposed MPCC
inductance parameter, the proposed MPCC has a fluctuation but
can reduce the computation time greatly compared with the
it reaches to stable state rapidly. In addition, the speed ripples
conventional MPCC.

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Transactions on Industrial Electronics
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Transactions on Industrial Electronics
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

[27] Y. Zhou , H. Li , R. Liu, and J. Mao, “Continuous voltage vector model-

free predictive current control of surface mounted permanent magnet Jianguo Zhu (S’93–M’96–SM’03) received the
synchronous motor,” IEEE Trans. Energy Conver., vol. 34, no. 2, pp. 899- B.E. degree in 1982 from Jiangsu Institute of
908, Jun. 2019. Technology, Jiangsu, China, the M.E. degree in
[28] C. Xiong, H. Xu, T. Guan, and P. Zhou, “A constant switching frequency 1987 from Shanghai University of Technology,
multiple-vector-based model predictive current control of five-phase Shanghai, China, and the Ph.D. degree in 1995
PMSM with nonsinusoidal back EMF,” IEEE Trans. Ind. Electron., vol. from the University of Technology Sydney (UTS),
67, no. 3, pp. 1695-1707, Mar. 2020. Sydney, Australia, all in electrical engineering. He
[29] Y. Zhang, D. Xu, and L Huang, “Generalized multiple-vector-based was appointed a lecturer at UTS in 1994 and
model predictive control for PMSM drives,” IEEE Trans. Ind. Electron., promoted to full professor in 2004 and
vol. 65, no. 12, pp. 9356-9366, Dec. 2018. Distinguished Professor of Electrical Engineering
in 2017. At UTS, he has held various leadership
positions, including the Head of School for School of Electrical,
Xiaodong Sun (M’12-SM’18) received the B.Sc. Mechanical and Mechatronic Systems and Director for Centre of
degree in electrical engineering, and the M.Sc. and Electrical Machines and Power Electronics. In 2018, he joined the
Ph.D. degrees in control engineering from Jiangsu University of Sydney, Australia, as a full professor and Head of School
University, Zhenjiang, China, in 2004, 2008, and for School of Electrical and Information Engineering. His research
2011, respectively. interests include computational electromagnetics, measurement and
Since 2004, he has been with Jiangsu modelling of magnetic properties of materials, electrical machines and
University, where he is currently a Professor in drives, power electronics, renewable energy systems and smart micro
Vehicle Engineering with the Automotive grids.
Engineering Research Institute. From 2014 to
2015, he was a Visiting Professor with the School
of Electrical, Mechanical, and Mechatronic
Systems, University of Technology Sydney, Sydney, Australia. His
current teaching and research interests include electrical machines and
drives, drives and control for electric vehicles, and intelligent control. He
is the author or coauthor of more than 90 refereed technical papers and
one book, and he is the holder of 36 patents in his areas of interest.

Minkai Wu was born in Suzhou, Jiangsu, China,

in 1996. He received the B.S. degree in vehicle
engineering from Yangzhou University, Yangzhou,
China, in 2018, and he is currently working toward
the M.E. degree in Vehicle Engineering in Jiangsu
University, Zhenjiang, China.
His current research interests include control of
electrical drive systems and advanced control
strategy of electric machine.

Gang Lei (M’14) received the B.S. degree in

Mathematics from Huanggang Normal University,
China, in 2003, the M.S. degree in Mathematics
and Ph.D. degree in Electrical Engineering from
Huazhong University of Science and Technology,
China, in 2006 and 2009, respectively. He is
currently a senior lecturer in Electrical Engineering
at the School of Electrical and Data Engineering,
University of Technology Sydney (UTS), Australia.
His research interests include design optimization
and control of electrical drive systems and
renewable energy systems.

Youguang Guo (S’02-M’05-SM’06) received the

B.E. degree from Huazhong University of Science
and Technology, China in 1985, the M.E. degree
from Zhejiang University, China in 1988, and the
Ph.D. degree from University of Technology,
Sydney (UTS), Australia in 2004, all in electrical
engineering. He is currently a Professor in
Electrical Engineering at the School of Electrical
and Data Engineering, University of Technology
Sydney (UTS). His research fields include
measurement and modeling of properties of
magnetic materials, numerical analysis of
electromagnetic field, electrical machine design optimization, power
electronic drives and control.

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Authorized licensed use limited to: Fondren Library Rice University. Downloaded on May 18,2020 at 07:52:28 UTC from IEEE Xplore. Restrictions apply.