CES TRANSACTIONS ON ELECTRICAL MACHINES AND SYSTEMS, VOL. 1, NO. 3, SEPTEMBER 2017 219

Abstract—This paper reviews the classification and application

of the model predictive control (MPC) in electrical drive systems.

Main attention is drawn to the discrete form of MPC, i.e. finite

control set model predictive control (FCS-MPC), which outputs

directly the switching states of power converters. To show the

diversity and simple realization with various control

performances of the strategy, in this paper, several different

FCS-MPCs with their working mechanisms are introduced.

Comparison of FCS-MPC with conventional control strategies for

electric drives is presented. Furthermore, extensive control issues,

e.g. encoderless control and disturbance observation are also

included in this work. Finally, the trend of research hot topics on

MPC is discussed.

Index Terms—Disturbance observer, electrical drive,

encoderless control, predictive control.

I. INTRODUCTION

ODEL predictive control (MPC), as a conventional

nonlinear control technology in process industry such as

petrochemical areas, is becoming an emerging control strategy

in the areas of electric drives and power electronics. Though it

has undergone around 30 years of development [1] and much

research has been devoted for its realizations on electric drives

and power electronics, the product-level applications in these

areas are still very limited. Thanks to the sustained

development of semiconductor science and powerful

microprocessors, the era of MPC’s wide applications for fast

real time systems such as electric drives and power electronics

is approaching [2]-[5].

Electrical drive systems are essentially an application sub

area of power electronics [6] because the drives for electric

machines, i.e. power convertors, are a class of power

electronics’ applications. When controlling electrical drives,

MPC contains merits such as faster dynamics, easier concept of

design, simpler structure and realization, etc. [7]. Specially, for

This work was supported in part by the National Natural Science Foundation

of China under Grant 51507172.

Fengxiang Wang is with Quanzhou Institute of Equipment Manufacturing, Haixi Institutes, Chinese Academy of Sciences, Jinjiang, 362200, China

(e-mail: fengxiang.wang@fjirsm.ac.cn).

Xuezhu Mei and Ralph Kennel are with the Institute for Electrical Drive Systems and Power Electronics, Technical University of Munich, Munich,

80333, Germany (e-mail: xuezhu.mei@tum.de; ralph.kennel@tum.de).

José Rodríguez is with the Faculty of Engineering, Universidad Andrés Bello, Santiago, 8370146, Chile (e-mail: jose.rodriguez@unab.cl).

FCS-MPC, because it includes cost function, system

constraints as well as further nonlinearities can be easily

considered and controlled [8].

So far, MPC has been realized through different controllers

with different control requirements on various types of electric

machines. Examples of the control platforms are digital signal

processors (DSPs) [9], field programmable gate arrays (FPGAs)

[10] and dSPACE semi-physical simulation system [11]-[12].

These controllers, using microprocessor units with

exponentially increasing calculation ability, can meet the

requirements of most applications, even for multiple-step

predictions and multi-level converters [13]. Moreover, MPC is

not machine type dependent. It can be applied to all AC

machines such as induction machines (IMs), permanent

magnetic synchronous machines (PMSMs), synchronous

reluctance machines (SRMs), blushless DC machines (BLDCs)

as well as multiphase machines [14]-[18], as long as the

machines’ mathematics models are correctly built and

integrated in the controller design.

With the ever-increasing calculation power, more control

strategies and related considerations of MPC are enabled. For

example, there are many researches on MPC with artificial

intelligence based controls such as fuzzy logic control, neural

network control; with modern controls such as self-adaptive

control and robust control; and with disturbance observers as

well as encoderless speed estimators based on system’s

controllability and observability analyses. MPC, when

combined with these control methods, though demanding

further calculation efforts, becomes a more powerful and

effective control strategy for industrial servo drives requiring

high performance.

When being applied to electric drives and depending on

whether continuous reference voltage vector is calculated and

pulse width modulator (PWM) is therewith needed or not, MPC

can be classified into two classes [6], [19], [20]: continuous

control set MPC (CCS-MPC) and finite control set MPC

(FCS-MPC). For the former class, with the continuous voltage

reference, PWM is applied to generate switching states

according to the modulation principles and inverter topologies.

The latter class, together with direct torque control (DTC), is

categorized as direct control strategy for electric drives [21].

Based on the machine model and current sampling states, a

prediction of machine variables is done for the length of

prediction horizon with respect to all feasible voltage vectors

that can be offered by the specific inverter [22]. The selection

Model Predictive Control for Electrical Drive

Systems-An Overview

Fengxiang Wang, Member, IEEE, Xuezhu Mei, Student Member, IEEE,

José Rodríguez, Fellow, IEEE, Ralph Kennel, Senior Member, IEEE

(Invited)

M

220 CES TRANSACTIONS ON ELECTRICAL MACHINES AND SYSTEMS, VOL. 1, NO. 3, SEPTEMBER 2017

of the optimal voltage vector, namely, the voltage vector to be

applied in the next sampling period, is achieved through a

predefined cost function. The optimal value is the one

minimizing the cost function’s value. Since the feasible voltage

vectors of the inverter are discrete, the optimal voltage vectors

are of similar characteristics, rendering the output values to be

random and discontinuous, thus leading to varying switching

frequencies. Finally, the switching state signals corresponding

to the discrete optimal voltage vectors are directly sent to

trigger the inverter IGBT so that the equivalent voltages for the

electric motors can be supplied. It is worth mentioning that,

based on some subdivision or refinement strategies of voltage

vectors, the number of feasible voltage vectors for prediction

and cost function of FCS-MPC can be enlarged to generate

continuous or quasi-continuous voltage vectors that can be

applied for the PWM [23].

The structure of the paper is as follows: section II introduces

the fundamental working mechanism and principles with

respect to both classes of MPC for electric drives. Section III

explains the main sub-strategies of FCS-MPC through

implementation examples. Section IV compares MPC with

conventional linear and nonlinear control strategies. Section V

extends the topic of MPC with respect to its integration of

encoderless control and disturbance observation. The trend and

research hot spots of MPC are further discussed in section VI.

II. MPC MECHANISM

The fundamental mechanism and principles of MPC for

power electronics, not merely for electric derives, will be

introduced in this section.

A. CCS-MPC Principles

When the continuous reference voltage vectors can be

calculated in MPC, either analytically or numerically, and a

PWM is required to generate the gate signals, it is referred to as

CCS-MPC.

a) Generalized Predictive Control (GPC)

GPC is a linear CCS-MPC proposed in 1980s. It is called

“generalized”, because it unifies different predictive controls

by generating a sequence of future behaviors in every sampling

period. This is realized through the optimization with a cost

function. The research on its implementation on electric drive

systems started from 2001 [24].

Fig. 1 shows the fundamental structure of GPC. z

indicates the drive inverter and PWM. It works with long

prediction horizon, i.e. a sequence of future control signals are

generated in every sampling period, but only the first prediction

in the sequence is given to z as reference. represents the

system output, which can be stator current, electromagnetic

torque or rotor flux for electrical drive systems. It is composed

of “free response” and “forced response” representing the

predicted behavior and additional components of y,

respectively. Since it is a linear control strategy replacing the

ones with PI controllers, total response is the sum of the two

responses. And a future error is derived as the difference of

reference and total response. This error forces the output to

track its reference.

optimizer

constraints

cost function

predictor

model

model

process

-

future

error

total

response

free

response

+

forced

response

𝑑𝐽(𝑢, 𝑤, ⋯ )

𝑑𝑢

𝐺 𝑧

𝐺 (𝑧)

𝐺 (𝑧)

𝑢1 𝑦

𝑦

𝑦(𝑡 − 𝑖|𝑡)

𝑢(𝑡 − 𝑖|𝑡)

𝑢 *

future

reference

value

Fig. 1. Block diagram of GPC.

Take a squirrel cage induction machine (IM) driven by a

voltage source inverter (VSI) as an example. GPC controller is

implemented as both speed and current controllers. With the

classic set of IM electrical and mechanical mathematics model

and after some manipulations, the signal flow chart of the GPC

IM control system can be illustrated in Fig. 2. In this figure, the

control system is constructed with upper electrical and lower

mechanical systems. The rotor speed, , converges to its

reference, , under the control effects of three GPCs.

stator winding

𝑘𝑟

- -

rotor winding

𝑘𝑆

mechanical system

-

-

- ×

× ×

3𝛽 4 𝑘𝑟

- svr

r

sv

T

lT

*

sjrj

s rs

m

Fig. 2. Signal flow graph of IM with GPC.

GPC can achieve good performance and high robustness

against model parameters deviations, thus it is general a

compact strategy for control in theory under model mismatch,

varying dead time and disturbance conditions. However, the

theory of GPC is as complex as its implementation process,

which takes up high computational resources, thus GPC is not

popular nowadays.

b) Deadbeat MPC

As another category of CCS-MPC and model inverse

predictive control, deadbeat MPC calculates the ideal or

expected voltage vectors given to PWM in a direct manner

based on the machine model. Fig. 3 is a schematic of current

control based deadbeat MPC for an active RL load. The load is

powered by a 2-level voltage source inverter (2L-VSI). It is

shown in the figure that based on the measured current at

instant and current prediction at instant , the reference

voltage is directly calculated. Though the system

WANG et al. : MODEL PREDICTIVE CONTROL FOR ELECTRICAL DRIVE SYSTEMS-AN OVERVIEW 221

requires discretization, for a continuously operating system, the

reference voltage is monotonously changing, thus can be

treated as continuous values and given to a PWM.

Deadbeat

ControlPredictive

model

2L-VSI

as

bs

cs3

jg( )s ki

*( )s ki

PWM

*( )s kv

RL load

( 1)s kiˆ

Fig. 3. Deadbeat MPC for IM.

Reference voltage can be directly calculated by equating its

reference current, , to predicted current, in the

discrete form as [6], [25]:

* *( ) ( ) 1 ( )ss s s

s

R T Lk k k k

L T

v i i e (1)

where R and L are the load resistance and inductance; is the

sampling period; represents the load back EMF; and

is the measured current value in the present sampling period.

It is shown that continues MPC such as deadbeat MPC is

very intuitive in concept and simple to be implemented. And

there exist some other continuous MPCs, which can also

achieve similar performance with either intuitive controller

design or sophisticated derivation processes. However, since

there exists no cost function in most CCS-MPCs, for the system

requiring controls of nonlinearities and other constraints, it is

difficult to be realized. For this purpose, FCS-MPC with cost

function optimization came into being.

B. FCS-MPC Principles

The idea of FCS-MPC comes slightly later than deadbeat

MPC and is a variation from it. Different from deadbeat MPC,

which is model inverse MPC, FCS-MPC is a model forward

MPC.

Its block diagram is shown in Fig. 4, which is an example of

stator current control based MPC [25]-[26].

In contrast to deadbeat MPC, that calculates , which is

assumed to be unknown , at instant k, FCS-MPC calculates the

next step’s currents corresponding to all feasible finite number

of VSI’s voltage vectors, that are known but pending.

A generalized form of predicted current of FCS-MPC for RL

load is shown as below:

ˆ ( 1 1 ) ( )) (s ss ss

R T Tk k k

L Lk

i v ei (2)

where is one of the feasible voltage vectors to be

substituted.

These currents are compared with the current reference

through the cost function to select the predicted current being

closest to the reference. Because a 2L-VSI contains 8 switching

states with 7 different ones, the selected 1-out-of-7 voltage

vector that has been substituted into the predicted current, is

treated as the optimal vector and its corresponding switching

state is given to VSI at the next sampling period.

Minimization

of cost

functionPredictive

model

2L-VSI

7

as

bs

cs3

*( )s ki

( )s ki

RL load

jg

( 1)s ki

Fig. 4. FCS-MPC.

For single step current control based MPC, the cost function

requires no weighting factor and it is designed as:

* *| ( ) ( 1) | | ( ) ( 1) |j j j

g i k i k i k i k

(3)

where ,

,and

,

,are the real and

imaginary parts of the reference and predicted current vectors,

respectively. j = 0...6 corresponding to all 7 different switching

states of the inverter.

The process for FCS-MPC realization can be summarized as

following steps:

a) Current measurement;

b) Predict next mpl ng per od’ urrent for ll nverter’

feasible voltage vectors;

c) Select the optimal prediction and its corresponding voltage

vector that minimizes the cost function;

d) Apply the switching state corresponding to this optimal

voltage vector in the next sampling period.

One important issue should be noticed for FCS-MPC is time

compensation, which is critical for all digital control based real

time implementations. Because the application of the optimal

voltage vector cannot be achieved in the same sampling period

where it is calculated, thus one further step prediction, namely

“compensation”, is required to solve this time confliction.

As the emerging comprehensive proposals of different novel

control algorithms in MPC, there is no strict boundary between

CCS-MPC and FCS-MPC. FCS-MPC can also be varied to

generate continuous reference voltage vectors for PWM. A

continuous FCS-MPC is proposed in [23], which refines and

enlarges the scale of the candidate voltage vectors substituted

into current predictions. This continuous or quasi-continuous

FCS-MPC can achieve similar performance as deadbeat MPC.

However, since it includes cost function, it surpasses deadbeat

MPC in light of its nonlinearities and system constraints control

capability. Though more computational efforts are needed, it

can be applied to situations that requires continuous reference

voltage vectors, which is a limitation for the application of

conventional FCS-MPC generating only discrete switching

states.

In light of the easiness for nonlinearities and constraints

control, compared to CCS-MPC, FCS-MPC has more overall

advantages [25]. Thus, in the later sections of this paper, only

FCS-MPC is discussed. For simplicity, unless specially

mentioned, FCS-MPC is hereafter referred as MPC and only

one step prediction is adopted.

222 CES TRANSACTIONS ON ELECTRICAL MACHINES AND SYSTEMS, VOL. 1, NO. 3, SEPTEMBER 2017

III. MPCS FOR ELECTRICAL DRIVES

The mutual characteristics and merits of MPCs are easy

inclusion of nonlinearities control and system constraints,

simple structure, intuitive design and implementation, even for

technicians without much knowledge of control theories. There

are mainly three kinds of MPCs for electrical drives: predictive

current control (PCC) [27], predictive torque (and flux) control

(PTC) [28], and predictive speed control (PSC) [29], [30]. PTC

and PCC replace the inner current PI controllers with nonlinear

predictive controllers, making the inner current control

bandwidth to be theoretical infinite. For PSC, the outer speed PI

controller is even replaced by a nonlinear controller, and the

speed control loop is also included in the cost function.

A. PCC

Among all MPCs, only PCC is realized with rotor flux

orientation, thus in some literature, PCC is also referred to as

predictive field oriented control (PFOC). Fig. 5 is the block

schematic of PCC for IM with a 2L-VSI. As explained in II-B,

the stator currents are predicted for all feasible voltage vectors

of VSI before these predictions are evaluated in the cost

function. And as explained in II-A-1), for long prediction steps,

only the first voltage vector (corresponding to the next step) of

this optimal set is applied to the inverter following the receding

horizon principle [31].

+-

PI *T

qi

di

*| |r

d q

Cost function

Currentprediction

Rotor fluxestimation

, ,a b cS

( 1)i k ( 1)i k

IM

( )s ki

( )s ki

* ( )i k

* ( )i k

( )r k

* ( )di k

*( )qi k

( )k

*( )k

( )bi k

( )ai k

*( )r k

*( )T k

( )k

( )k

Fig. 5. PCC for IM.

Based on the classic IM model in [33], the stator current can

be described as:

1 1

( ( ) )ss r r s

r

dL k j

R dt

ii v (4)

where r r , r m r . and r are the stator and

rotor resistances. with to be leakage factor and

, r , m are stator, rotor and mutual inductances. And

r r r.

To predict the next step value, forward Euler discretization is

considered:

sT

kxkx

dt

dx )()1( (5)

With (4) and (5), the stator current can be predicted as:

s 1ˆ ( 1) (1 ) ( )

1( ( )) ( ) ( )

ss s

r r s

r

T Tk k

R

k j k k k

i i

v

(6)

where r is the rotor flux, .

Similar as the RL load application in II-B, the classical cost

function is presented as following:

* *

1

( ) ( ) ( ) ( )N

j j j

h

g i k i k h i k i k h

(7)

h is the prediction step number, and N is the predictive horizon

or number of total prediction steps. In this work only one step

PCC is considered, thus .

The generation of the current references is necessary for

PCC. Fig. 5 shows that the torque reference is generated by a

speed PI controller, and the reference of rotor flux magnitude is

considered as a constant value. The corresponding reference

values for the stator field- and torque producing currents d and

are produced by:

*

*( )

( ) r

d

m

ki k

L

(8)

*

*

*

2 ( )( )

3 ( )

rq

m r

L T ki k

L k (9)

where is the reference torque. r

is the reference

rotor flux amplitude.

In the cost function, the state current values in frame are

required, so inverse Park transformation is presented to satisfy

this requirement as following:

**

**

( )( ) cos( ) sin( )

( )( ) sin( ) cos( )

d

q

i ki k

i ki k

(10)

where the rotor flux angle is written as for concision.

Experiments are conducted on an IM whose parameters are

shown in Table I.

TABLE I

PARAMETERS OF IM

Symbol Quantity Value

DC link voltage 582V

stator resistance 2.68Ω

rotor resistance 2.13Ω

mutual inductance 275.1mH

stator inductance 283.4mH

rotor inductance 275.1mH

pole pair number 1

nominal rotor speed 2772.0rpm

nominal electromagnetic torque 7.2Nm

moment of inertia 0.005kg/m2

Fig. 6 is a test result showing the control performance in the

whole speed range. This test evaluates the algorithms at

different operating points. The speed reverses from its positive

nominal value to negative nominal value. As we can see that

PCC method works well in the whole speed range. Though its

torque has slightly ripples, the current quality is fine.

[]

TN

m[

]i

A

[]

rpm

0 0.2 0.4 0.6 0.8 1 1.2

0 0.2 0.4 0.6 0.8

1.4 1.6

1 1.2 1.4 1.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Time [s]

4000

0

4000

5

5

10

0

5

10

0

5

10

Fig. 6. Speed, torque, stator current waveforms of PCC during a full speed

reversal maneuver.

WANG et al. : MODEL PREDICTIVE CONTROL FOR ELECTRICAL DRIVE SYSTEMS-AN OVERVIEW 223

B. PTC

The architecture of PTC method is described in Fig. 7.

Similar as PCC, the core of PTC is the torque and flux

predictions and the design of a cost function.

+-

Cost function

Torque and Fluxprediction

FLux estimation

IM

( )s ki , ,a b cS*( )T k

*( )k

( )k

( )r k

( )s ki

( )k

*( )s k

PI

( )s k( )ai k

( )bi k

ˆ( 1)T k ˆ ( 1)s k

Fig. 7. PTC for IM.

In the predictive algorithm, the next-step stator flux

and the electromagnetic torque must be calculated. By

using (5) to discretize the voltage model of IM [33], the stator

flux prediction can be obtained as:

ˆ ( 1) ( ) ( ) ( )s s s s s s sk k T k R T k v i (11)

According to IM’s mechanical equation, and with

predictions of the stator flux (11) and the predicted current (6),

the electromagnetic torque can be predicted as:

*3 ˆˆ ˆ( 1) Im ( 1) ( 1)2

s sT k p k k i (12)

The classical cost function for PTC method is as following:

* *

1

ˆ ˆ( ) ( ) N

j j s s j

h

g T T k h k h

(13)

Fig. 8 shows the performance in the whole speed range. PTC

has comparable well performance as PCC. Its torque ripples are

less than PCC, but as trade-off, it contains higher current

harmonics.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.64000

0

4000

5

5

10

0

5

10

0

5

10

Time [s]

[]

TN

m[

]i

A

[]

rpm

Fig. 8. Speed, torque, stator current waveforms of PTC during a full speed reversal maneuver.

C. PSC

PSC contains no linear controller. Its speed and current

control are integrated in the same cost function and it can

simultaneously manipulate the speed and electrical variables,

without using any external PI-speed controller. Fig. 9 illustrates

a PSC for permanent magnet synchronous machine (PMSM),

which is explained in details in [29], [33].

System

model

Cost

function

Observer

2L-VSI

PMSM

*( )k

( )x k

, ,a b cS( 1)x k

( )s ki

( )s ki

( )k( ) ( ) ( ) ( )

T

d qx k i k i k k

Fig. 9. PSC for PMSM.

The cost function can be of the following form:

sd sd sqf sqfi i i i c cg g g g g (14)

where, g

is the error between the prediction of the rotor speed

and its reference, g

minimizes the magnitude of direct

current prediction, g f

is a constraint that minimizes the

high-frequency components of the torque. And x is the

weighting factor to be designed or tuned for each optimization

term. Constraint is included to limit the values of predicted

currents as follows:

max max

min min

ˆ ˆ

ˆ ˆ0

q q d d

c

q q d d

if i i or i ig

if i i and i i

(15)

The test results of PSC for PMSM are shown in Fig. 10, in

which the speed is reversed from its rated value to its negative.

It verifies that PSC can achieve a fast dynamics and smooth

steady state performance with little torque ripples and current

harmonics. The torque producing currents respond almost with

no time to achieve the speed deceleration at the highest rate.

Time [s]

·

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

*

2000

1000

2000

1000

0

10

20

10

0

30

10

20

10

0

20

qidi

,[

]d

qi

iA

,,

[]

ab

ci

ii

A*

,[

]rp

m

Fig. 10. Test results of reference and measured rotor speed, stator currents in dq-frame and three-phase stator currents for the operation of a PMSM, using

the PSC.

IV. COMPARISON OF MPC WITH CONVENTIONAL CONTROLS

STRATEGIES FOR ELECTRICAL DRIVES

This section compares the dynamics performances and

robustness characteristics of MPC with conventional high

performance linear and nonlinear direct control strategies for

electrical drives, i.e. field oriented control (FOC) and direct

torque control (DTC). For MPC, only PCC and PTC are

discussed, which contain speed PI controller that makes them

more comparable to the other strategies.

The schematics of PCC and PTC are already given in the

previous section.

Fig. 11 is the block diagram of FOC for an IM, in which

linear controllers and PWM are applied to control the

fundamental component of the load voltages.

224 CES TRANSACTIONS ON ELECTRICAL MACHINES AND SYSTEMS, VOL. 1, NO. 3, SEPTEMBER 2017

Fig. 12 is the block diagram of DTC for IM, in which two

hysteresis controllers and a LUT serve as the inner control

loops.

IMPWM

Variable

Estimations

d q

d q

PI PI

PI PI

*( )k

( )k

*( )qi k

* ( )di k

( )k

*( )r k

, ,a b cS

( )ai k

( )bi k

( )s ki

( )r kˆ

* ( )qv k

* ( )dv k

* ( )v k

* ( )v k

( )i k

( )i k

( )qi k

( )di k

Fig. 11. FOC for IM.

IM

PI*( )k

( )kSwitching

selection

table

Sector decision

Estimation and

Compensation

ht

hf

, ,a b cS

( )s ki

( )ai k

( )bi k

Sector number

*( )T k

ˆ( )T k*

( )s k

*( )s k

Im ( )kRe ( )k

Fig. 12. DTC for IM.

Before the comparison of their system performance, the

theoretical discussions of the aforementioned four strategies are

conducted [28]:

All strategies have a speed PI control. DTC, PCC and PTC

are nonlinear strategies that generate directly the switching

states of voltage vectors without a modulator while FOC is

linear control strategy. FOC needs a modulator to handle the

continuous variables. FOC and PCC are transferred to rotor

flux reference frame while DTC and PTC algorithms are in

stator reference frame.

To guarantee a fair comparison, four strategies are tuned to

have a very similar switching frequency (16 kHz), though

direct control methods including DTC, PTC and PCC have

variable switching frequencies. This can be realized by tuning

the parameters of PTC and PCC and the carrier of FOC with the

frequency of DTC as the average.

A. Dynamics Comparison

This section compares the dynamics performances of four

control strategies under varying loads for electrical drives. The

machine under test is the aforementioned IM.

A step torque from 0 Nm to the rated value is given as

reference. Fig. 13(a) illustrates FOC needs 3 times of settling

time as the other three methods. The switching vectors of PTC

during this process are observed to find out the reason. Fig.

13(b) shows that in this dynamic process, only one active

switching vector (here is the 6th vector) is selected and no zero

vector is applied. However, in FOC, zero vector is inserted with

respect to the PWM operation principles. Moreover, the inner

current PI control loop of FOC limits the bandwidth of the outer

speed PI control loop; this, to some extent, verifies that direct

control methods have theoretical infinite inner current control

bandwidth.

0 1 2 3 4 5 6 7 80

5

10

0

5

10

0

5

10

0

5

10

0

4

8

0

2

4

6

0 1 2 3

FOC

DTC

PTC

PCC

Time [ms]Time [ms]

[]

TN

m

[]

TN

m

[]

TN

m[

]T

Nm

[]

TN

m

Sw

i. V

ecto

r

(a) Torque dynamic response of four strategies. (b) Torque dynamic response of PTC and switching vectors

2 ms

600 s

600 s

Fig. 13. Torque responses of four strategies.

B. Robustness Comparison

In MPC, the correctness of machine parameters is critical for

precision [34], thus, this section compares the system

robustness against parameters variations of the four strategies.

The sensitivity of the magnetizing inductance m and stator

resistance are investigated experimentally under the

operating point with reference speed of 100 rpm without load.

Fig. 14(a), (c) and (e) show the robustness against m

variations. FOC, DTC and PTC have good robustness, with a

16~20 times variations without losing the stability, while PCC

is rather weak with a 10% variation of m making system lose

the stability. This is because the reference currents in PCC are

generated by equations (8) and (9) that contains m, a variation

of m directly leads to an incorrect control from even the

reference.

varies typically with the variations of the stator

temperature. Fig. 14(b), (d) and (f) illustrate the robustness

against variations. DTC and PTC lose their stability at

around 2.5 times of the parameters mismatch, but FOC and

PCC are very robust against variation. The reason lies in that

DTC and PTC require voltage model for the stator flux

estimation and prediction, which is shown in equation (11). For

low speed application, the voltage model is even more sensitive

to variations.

C. General Comparison

A conclusion of comparison is shown in Table II. It is seen

that MPC strategies have comparable performance as

conventional control strategies for electrical drives, with even a

better behavior of torque ripple and fast dynamics. The

experimental implementation time, which is a main concern for

MPC application, is recorded.

TABLE II

COMPARITIVE ISSUES IN EXPERIMENTS

FOC DTC PTC PCC

Cal. Time s8 s8 s24 s8.17

Current THD Better Worse Good Good

Torque Ripple Smaller Larger Small Small

Dynamics Slower Faster Faster Faster

Swit. Freq. Constant Variable Variable Variable

Lm Sensitivity Good Good Good Weak

Rs Sensitivity Better Good Good Better

WANG et al. : MODEL PREDICTIVE CONTROL FOR ELECTRICAL DRIVE SYSTEMS-AN OVERVIEW 225

[]

Nm

[

]N

m

[]

Nm

[

]m

LH

[]

mL

H[

]m

LH

[]

Nm

[

]N

m

[]

Nm

[

]N

m

[]

sR

[

]s

R

[

]s

R

Time [s] Time [s]

Time [s]Time [s]

Time [s] Time [s]

200

100

0

200

100

0

200

100

0

200

100

0

200

100

0

200

100

0

200

100

0

200

100

0

5432

01

54

32

0

1

DTC

PTC

FOC

PCC

0.20.25

0.3

0.35

0.4

1412108

46

765432

765432

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

(a) Lm Variaiton: FOC

(c) Lm Variaiton: PCC

(e) Lm Variaiton: DTC and PTC

(b) Rs Variaiton: DTC

(D) Rs Variaiton: PTC

(f) Rs Variaiton: FOC and PCC

[]

Nm

Fig. 14. Sensitivities of and m at speed of 100 rpm without load.

V. MPC WITH EXTENSIVE CONSIDERATIONS

As is shown in the previous section, MPC, as a class of direct

control strategies, together with DTC, is known with their fast

dynamics response. However, compared with DTC, it requires

speed encoder, thus it is not inherently encoderless; compared

with FOC, it has larger torque ripples and overshoot under

sudden torque variations (Fig. 13), thus it is susceptible to load

disturbance. As a matter of fact, further extensive control issues

should be always considered. With respect to the

aforementioned two drawbacks, this section introduces the

encoderless control and disturbance observer/observation (DO)

for MPC. The experimental implementation is realized on the

same IM.

A. MPC with Encoderless Control

There are mainly two categories encoderless control of

electrical drive systems for different speed operation scale. For

zero/low speed, rotor saliency based signal injection methods

that are not sensitive to the low speed signal noise ratio (SNR)

are necessary, while machine model based encoderless control

satisfies the precision requirement of medium and high speed

control. For model based encoderless control, there are many

methods, such as model reference adaptive system (MRAS),

sliding mode observer (SMO), Luenberger observer (LO) and

extended Kalman filter (EKF), etc. [9], [35]-[38]. The basic

principles of encoderless control is based on the fundamental

machine electrical and mechanical models, following the

stability criterion, and through the design and implementation

of a speed/position estimator/observer to track the machine

speed/position by forcing its measurable variables (e.g. stator

currents, voltages) to align with their references. When system

converges, the more correct the machine model parameters

match the ones of real machine, the more precise the estimation

will be. Thus, the model precision and system convergence

ability are the two kernel factors for a good encoderless control.

Since model precision is also critical for MPC, model based

encoderless control strategies will be discussed in this

sub-section, in light of their mutual interests for control.

Fig. 15 shows the encoderless PCC with EKF as speed

observer for IM. An EKF is needed to estimate the rotor flux

and speed. The whole control system is designed with the

following steps [39]:

• Estimate the required states such as speed and rotor flux by

using EKF.

• Predict the stator current by using PCC method with the

estimated states.

• Define a cost function to choose the optimal switching state of

inverter.

• Feedback the estimated speed to the speed controller.

PCC

Cost

function

Predictive

model

EKF

observer

IMPI

*( )k , ,a b cS( )s ki

, ,a b cS

*( )r k

( )k

d q

abc

( )ai k

( )bi k

( 1)i k ( 1)i k

*T qi

*| |r

di

*( )T k *( )qi k

* ( )di k

* ( )i k

* ( )i k

( )i k

( )i k

ˆ( )T k

ˆ ( )r k

( )k

Fig. 15. Encoderles PCC with EKF observer.

Similar as all other Kalmen filter design, the EKF speed

observer also undergoes two phrases: prediction and correction;

and five steps: predicted state estimation, predicted covariance

estimation, EKF gain matrix construction, predicted state

correction and error covariance update. The integrated EKF

observer for IM is shown in Fig. 16. In this figure, state

corresponds to the variable x.

IM Measurement

Real System

EKF EKF Gain

Measurement

Function

Predicted

EstimationSystem

Function

Unit

Delay

Corrected

Estimation

Applied State

Estimation

System

noiseMeasurement

noise

kx kyku

ke

k kv

k kK e

1 , ,k d k k kx f x u k ,k d k ky h x k v

1kx ˆ

1 1k kx

ˆ

1kx ˆ 1,d kh x kˆ1k k

xˆ

.f 1z .h

kK

Fig. 16. EKF observer.

where the state vector x contains the rotor speed term.

Fig. 17 shows the test results of measured speed, estimated

speed, speed error, load torque and stator current during rated

speed reversal. The system works well with maximum value of

the speed error between the measured and estimated speed less

226 CES TRANSACTIONS ON ELECTRICAL MACHINES AND SYSTEMS, VOL. 1, NO. 3, SEPTEMBER 2017

than 70 rpm and an average value of the speed error at steady

state to be only 20 rpm (0.7% of reference). And during the

reversal, there is no obvious speed mismatch between the

estimated and real speeds, which shows a fabulous speed

tracking capability.

Low speed with load is the most difficult condition for

control. Fig. 18 shows system performance with a 50% load

impact at low speed. From this figure, it is seen that both speeds

can retrieve their reference with only a slight drop for an instant

shorter than 0.1s. And the torque is increased immediately to

balance this load. This shows the strong speed tracking and load

disturbance rejection capability of the encoderless MPC for IM

drives system.

Time [s]

0 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0

0 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0

0 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0

0 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0

0 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0

[

]rp

m[

]rp

m

[]

erro

rrp

m[

]ai

A[

]T

Nm

0

3000

3000

0

3000

3000

0

70

70

0

10

10

0

30

30

Fig. 17. Rated speed reversal maneuver performance of encoderless PCC with EKF observer.

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

0

10

-10

0

10

-10

0

10

-10

75

150

0

75

150

0

Time [s]

[]

rpm

[

]rp

m

[]

lTN

m[

]T

Nm

[]

aiA

Fig. 18. 50% load performance of encoderless PCC with EKF observer.

B. MPC with Disturbance Observer

Compared to linear control strategies, MPC has larger torque

ripples and overshoots as well as long adjustment time during

torque variations, thus the inhabitation of this torque

disturbance is important. A disturbance observer can not only

fulfill this purpose, but also reduce the parameter mismatch

effect for flux estimation and current prediction, because it

utilizes a feedforward based estimator to compensate the

undesirable external disturbance and parameters uncertainty

[40], [41]. Thus, the system robustness and disturbance reject

ability are improved.

For PTC, the torque reference generating rate and accuracy

are very important in the cost function, especially when the load

torque and inertial value are varying. Thus, a PTC with DO for

IM was proposed and shown as example. Fig. 19 is its control

system schematic [41].

Disturbance

Observer

Cost function 2L-VSIIM

Enhanced

Variable Prediction

( )s ki

( )k

*( )s k

*( )T k

*( )k

( )k

( )k

( )s ki

( )s kv( )s kv

ˆ( 2)T k ˆ ( 2)s k

ˆ ( 1)s k

ˆ ( 1)r k

( 1)s ki

Fig. 19. PTC with DO for IM.

In this system, a DO is designed to observer the lumped

disturbances caused by load torque variations and parameter

deviations. Based on the speed mechanical model (16), the

speed equation is designed as (17), where the lumped

disturbance is denoted as (18).

−

−

(16)

n d t (17)

t

n

−

−

(18)

Based on the DO theory, the disturbance estimation d t is

designed as:

n d t (19)

with , d t - , and .

where J is the moment of inertia, B is the viscous fiction

coefficient. Both and n are the intermediate variables.

The reference, after compensation with DO, is given in the

form of Fig. 20.

kp

*T

*

1J

Tz

n

)( 11 z

( )d t

( )d t

( )d tJn ˆ

ˆ

Fig. 20. DO as feedforward compensator.

Fig. 21 shows the performance of the PTC with DO for IM

during rated speed reversal, in which the speed reference is

reversed from the rated value to its negative and back to rated

value. As is shown in the figure, during the dynamic response

process, the electromagnetic torque reaches its saturation value

for the fastest acceleration and settling. The reference value of

WANG et al. : MODEL PREDICTIVE CONTROL FOR ELECTRICAL DRIVE SYSTEMS-AN OVERVIEW 227

stator flux magnitude is stably kept at its reference of 0.71Wb.

Also, the accurate flux responses are achieved in the whole

range, this is because the flux is considered in the design of cost

function.

0

Time [s]

[]

rpm

[

]T

Nm

[]

aiA

[]

sW

b

0

0

-10

10

0

0.2

1

0.40.6

0.8

10

-10

2000

-2000

-4000

4000

0 0.2 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.4

0 0.2 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.4

0 0.2 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.4

0 0.2 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.4

Fig. 21. Speed dynamics performance of PTC with DO for IM.

VI. RESEARCH HOT SPOTS AND TREND ON MPC

Ever since it was introduced into the areas of power

electronics including electrical drives, the development of

MPC is very fast. There are increasing diverse novel proposals

and contributions for its control related issues. This section

chooses some of the most intensive ones for discussion.

A. MPC with Long Prediction Horizon

As mentioned in the previous sections, there exists MPC of

longer prediction horizons, i.e. prediction can be more than one

step. Theoretical speaking, the longer the prediction horizon is,

the better steady-state performance and shorter adjustment time

the system show. Similarly, shorter prediction horizon

considers more with the near behavior, thus it can achieve

better transient-state performance, i.e. smaller torque ripples

and or speed overshoot. However, MPC with longer prediction

horizons, especially for those inverters of complex topologies,

e.g. multi-level inverter and matrix inverter, long horizons

mean exponentially increase of calculation efforts. Though the

calculation ability of controller hardware is also increasing at

an exponential rate nowadays, this is so far still a main problem

limiting the widely application of long horizon MPC. As a

result, many methods appear to solve this problem with no

sacrifice of the performance as trade-offs. Examples are

methods to improve the calculation efficiency and methods to

reduce the number of predictions in order to eliminate the

computational redundancy from the algorithm point of view

[42]-[44]. Moreover, longer prediction horizon MPC’s

performance has even more dependencies on model parameters

than short prediction horizon one. Because when model

parameters’ mismatch exists and is large enough to cause

cumulative errors in the predefined horizon, it leads the control

precision of long horizon MPC to be even worse than the short

horizon one. This deteriorates the system performance. Thus, in

order to guarantee an effective control performance of long

horizon MPC for electrical drives, model mismatch should also

be considered. Thus, parameters’ online identifications are

usually required, which is a mutual consideration for all model

based controls, observations and estimations.

B. Discretization Approximation

As mentioned in section III, for the current prediction of

MPC, discretization is needed. Actually, all discrete control and

numerical control systems’ states must be discretized. And for

MPC, the precision of discretization has direct influences on its

torque, flux and current control errors. This is because MPC,

when compared with other control strategies for electrical

drives, requires more calculation efforts thus has comparatively

lower sampling and switching frequencies. Moreover, for high

power applications such as medium voltage drive or large

traction drive, the switching frequency is constrained to a

relative low value because of the high heat load caused by the

switching loss due to the high switching frequency. Also, a low

sampling frequency creates a chance to exploit the long horizon

prediction capability of MPC to optimize the inverter switching

sequence. Last but not least, lower sampling frequency means

energy and money savings.

For simplicity of algorithm and efficiency of calculation,

usually, the crude first order forward Eular discretization as

shown in (5) is applied. However, this approximation has

obvious errors in low sampling frequency. Therefore, more

exact discrete time modeling is highly required. For this

purpose, higher order discretization methods are proposed and

more research efforts are therewith devoted. An example is the

improved Eular method based on trapezoidal rule introduced

and applied in [45], through which the accuracy of the discrete

machine model is increased.

C. Weighting Factors Optimization and Self-tuning

Except PCC, whose cost function contains only the currents

control terms that are of the same physical attribute, as for other

MPC strategies, the tuning of weighting factors for different

terms in cost function is not an intuitive or easy work [46], [47].

For cost function containing only two terms and for limited

applications, systematic methods of weighting factor

calculation can be applied. However, for the cost function with

more terms of different attributes, the selection of weighting

factors is either gained through trial and error procedures or

time-consuming offline simulations. Giving equivalent

importance to all objectives based on their rated values is

simple to realize, but it doesn’t necessarily lead to the optimal

control performance. Moreover, considerations such as

multiple attribute nature of the control objectives, further

control issues such as maximum torque per ampere (MTPA)

[48] and field weakening [49] can be included when designing

the weighting factors.

D. Switching Frequency Regulation

When considering the system reliability and stability,

especially for the application that strictly requires constant

switching frequency, the non-fixed and non-adjustable

switching frequency of MPC remains a drawback of the

algorithms. Moreover, it’s lacking of the continuous reference

voltage vector. Thus, though PWM is removed which reduces

the hardware cost and software complexity, it is still a

controversial topic on whether or not PWM should be applied

in MPC, thus switching frequencies can be regulated [50].

228 CES TRANSACTIONS ON ELECTRICAL MACHINES AND SYSTEMS, VOL. 1, NO. 3, SEPTEMBER 2017

VII. CONCLUSION

MPC for electrical drive systems is reviewed in this paper.

With the history of three decades sustained research and

experimental implementations on power electronics, many

categories of controls and sub-strategies have been designed

and verified through applications with different electrical

machines.

MPC can achieve comparative or even more competitive

dynamics performance than conventional control strategies of

electrical drive systems, and it maintains strong robustness

characters.

In order to make MPC more reliable and thus applicable, the

combination of further modern control strategies, such as

encoderless control and disturbance observation are considered.

Example of model-based encoderless MPC system shows that

it can achieve similar performance as the encodered MPC. The

MPC drives integrated with DO have obviously less torque

ripples and shorter settling time regarding torque variations,

thus it is less susceptible to load disturbance.

Several challenges and intensive research topics for high

performance MPC are also discussed.

To conclude, MPC, in light of its intuitive concept of design,

fast dynamics and torque response, is becoming the trend of

electrical drive systems in the upcoming years.

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Fengxiang Wang received the B.S.

degree in electronic engineering and the

M.S. degree in automation from Nanchang

Hangkong University, Nanchang, China, in

2005 and 2008, respectively, and the

Dr.-Ing. (Ph.D.) degree from Technical

University of Munich, Munich, Germany,

in 2014. In 2014, he started working at

Quanzhou Institute of Equipment

Manufacturing (QIEM), Haixi Institutes, Chinese Academy of

Sciences, China. He is currently a professor and the vice

director of QIEM. His research interests include predictive

control and encoderless control for electrical drives and power

electronics.

Xuezhu Mei received the B.S. degree in

electrical engineering in 2009 from

Guangdong University of Technology,

China and received the M.Sc. degree in

electrical engineering in 2010 from

University of Newcastle-upon-Tyne, UK.

She is currently working toward her Ph.D.

degree at the Institute for Electrical Drive

Systems and Power Electronics, Technical University of

Munich, Munich, Germany. Since 2014, she has become a joint

research assistant at QIEM. Her research interests include

predictive control for electric drives and power electronics.

José Rodríguez received the Engineer

degree in electrical engineering from the

Universidad Federico Santa Maria,

Valparaiso, Chile, in 1977 and the Dr.-Ing.

degree from the University of Erlangen,

Erlangen, Germany, in 1985. He has been

with the Department of Electronics

Engineering, University Federico Santa

Maria since 1977, where he is currently full professor and

rector. Now he is rector at Universidad Andres Bello. He has

co-authored more than 250 journal and conference papers. His

main research interests include multilevel inverters, new

converter topologies, control of power converters, and

adjustable-speed drives. He is associate editor of the IEEE

Transactions on Power Electronics and IEEE Transactions on

Industrial Electronics since 2002. He is member of the Chilean

Academy of Engineering and fellow of the IEEE.

Ralph Kennel got his diploma degree and

Dr.-Ing. degree in 1979 and1984 from the

University of Kaiserslautern. From 1983 to

1999, he worked on several positions with

Robert BOSCH GmbH (Germany). From

1994 to 1999, he was a visiting professor at

the University of Newcastle-upon-Tyne,

230 CES TRANSACTIONS ON ELECTRICAL MACHINES AND SYSTEMS, VOL. 1, NO. 3, SEPTEMBER 2017

UK. From 1999 – 2008, he was professor at Wuppertal

University, Germany. Since 2008 he is professor at Technical

University of Munich, Germany. He is a senior member of

IEEE, fellow of IEE and a chartered engineer in the UK. Within

IEEE he is Treasurer of the Germany section as well as ECCE

Global Partnership Chair of the Power Electronics society

(PELS). His main interests are encoderless control of AC

drives, predictive control of power electronics and

Hardware-in-the-Loop systems.