» The use of Permanent Magnet Synchronous Motors (PMSM)
combined with Direct Torque Control (DTC) scheme offers
many opportunities to achieve rapid and accurate torque
control in servo applications.
» The DTC is implemented by selecting the proper voltage
vector according to the switching status of inverter which
was determined by the error signals of reference flux linkage
and torque with their measured real values.
» Here, model of Interior type of PMSM is studied. Its
performance for various motor parameters is tested on
» DTC was proposed by TAKAHASHI and NOGUCHI in
1986 for application in Induction Motors. Their idea
was to control the stator flux linkage and the torque
directly, not via controlling the stator current.
» This was accomplished by “ OPTIMUM SWITCHING
» M. F. RAH MAN investigation of direct torque control
(DTC) for PMSM drives.
» It was mathematically proven that the increase of
electromagnetic torque in a PMSM is proportional to
» Control of the amplitude and rotating speed of the stator
flux linkage are analyzed.
» Torque response with DTC was found to be 7 times faster
than with PWM current control.
» JAWAD FAIZ introduced a new analytical technique for
generating the reference flux from the torque. It is shown
how the maximum torque per ampere (MTPA) can be
followed in the control process.
» Salient-pole PMSM motor is simulated using the
maximum torque per flux (MTPF) and the reference flux
» In Permanent magnet synchronous motors the
rotor winding are replaced by permanent
» A permanent magnet synchronous machine is
basically ordinary AC machine with winding
distributed in the stator slots so that the flux
created by stator current is approximately
» Permanent magnet drives are replacing classic DC
and induction machine drives in a variety of
industrial applications such as industrial robots
and machine tools.
Introduction to PMSM
» Two types of permanent magnet ac motor drives are
1) PMSM drive with a sinusoidal flux distribution.
2) Brushless dc motor drive with a trapezoidal flux
There are two major topologies of rotors of PMSMs
» The modeling of PM motor drive system is required for
proper simulation of the system.
» The d-q model has been developed on rotor reference
frame as shown in figure:
Modelling of PMSM
Stator and Rotor flux linkages in different frames
» The model of PMSM without damper winding has been
developed on rotor reference frame using the following
» Saturation is neglected.
» The induced EMF is sinusoidal
» Eddy currents and hysteresis losses are negligible.
» There are no field current dynamics.
» The angle between the stator and rotor flux linkage δ is the
load angle when the stator resistance is neglected.
» In the steady state, δ is constant corresponding to a load
torque and both stator and rotor flux rotate at
» In transient operation δ varies and the stator and rotor flux
rotate at different speeds.
» Since the electrical time constant is normally much
smaller than the mechanical time constant, the rotating
speed of the stator flux with respect to the rotor flux can
be easily changed
» Voltage equations in rotor reference frame are given by
» The flux Linkages are given by
» Substituting the flux linkages in the above voltage equations
» Arranging above equations in matrix form
qqfddrqsq iLiLiRV )(
)( fddqqrdsd iLiLiRV
» The developed motor torque is being given by
» Substitution of the flux linkages in terms of the inductances and current
» The mechanical torque equation is
» The rotor mechanical speed is given by
» id and iq in terms of Im
» The electromagnetic torque equation is given by
dqqdqfe iiLLiPT )(
» V/F control is among the simplest control. The control is an
open-loop and does not use any feedback loops.
» The idea is to keep stator flux constant at rated value so
that the motor develops rated torque/ampere ratio over its
entire speed range.
CONTROL SCHEMES FOR PMSM
Variable Frequency Control
Field Oriented Control
Direct Torque Control
DTC vs FOC
There are 3 signals which affect the control
action in a DTC system;
» Torque –
» The amplitude of the Stator Flux linkage –
» The angle of the resultant flux linkage vector –
(angle between stator flux vector and rotor flux
» The stator flux linkage of PMSM is
» Neglecting the stator resistance, the stator flux
linkage can be directly defined as
dtRiV sss )(
0 stsss dtiRtV
0 stss tV
Amplitude Control of Stator Flux
0 stss tV 0 stss tV
HB- hysteresis-band width
Flux and torque variations Due to
Applied Voltage vector
» For counter-clockwise operation,
» if the actual torque is smaller than the reference, the
voltage vector that keeps Ψs rotation in the same direction
» Once the actual torque is greater than the reference, the
voltage vectors that keep Ψs rotation in the reverse
direction are selected
» By selecting the voltage vectors in this way, the stator flux
linkage is rotated all the time and its rotational direction is
determined by the output of the hysteresis controller for
The control of the rotation of stator
If the actual flux linkage is smaller than the
reference flux value then Ø = 1.
The same is true for the torque.
Working principle of Direct Torque
Control for PMSM
» When an upper transistor is switched on, i.e., when a, b or
c is “1”, the corresponding lower transistor is switched
off, i.e., the corresponding a’, b’ and c’ will be “0”.
VOLTAGE SOURCE INVERTER
switching voltage vectors
STATE Sa Sb Sc
V0 OFF OFF OFF
V1 ON OFF OFF
V2 ON ON OFF
V3 OFF ON OFF
V4 OFF ON ON
V5 OFF OFF ON
V6 ON OFF ON
V7 ON ON ON
» There are eight possible combinations of on and off patterns for
the upper power switches and lower power devices.
» STATE 1: ( 000 ) STATE 2: ( 100 )
» STATE 3: ( 110 ) STATE 4: ( 010 )
0,0,0 00 coba VVV
0,,0 00 codcba VVVV
dccodc0b0a VV,VV,0V dcco0b0a VV,0V,0V
dcco0bdc0a VV,0V,VV dccodc0bdc0a VV,VV,VV
» STATE 5: ( 011 ) STATE 6: ( 001 )
» STATE 7: ( 101 ) STATE 8: ( 111 )
Vao = Vdc ; Vbo = Vdc ; Vco = 0
The space vector is Vs = Vao + Vbo ej2/3 + Vco e-j2/3
Substituting the values of Vao, Vbo and Vco:
Vs = Vdc(1/2 + j 3/2) (in rectangular form)
= Vdc 600 (in polar form)
Similarly the switching vectors can be computed for the
rest of the inverter switching states.
Computation of Switching vectors
For state-2 (+ + -):
Different switching states & corresponding space
[a b c]
Space Vector Vs
Rectangular form Polar form
V0 = [0 0 0] Vdc (0 + j0) 0 0
V1 = [1 0 0] Vdc (1 + j0) Vs 0
V2 = [1 1 0] Vdc (0.5 + j ) Vs 60
V3 = [0 1 0] Vdc (-0.5 + j ) Vs 120
V4 = [0 1 1] Vdc (-1 + j0) Vs 180
V5 = [0 0 1] Vdc (-0.5 – j ) Vs 240
» To implement the Space Vector PWM, the voltage
equations in the abc reference frame can be transformed
into the stationary d-q reference frame that consists of the
horizontal (d) and vertical (q) axis.
» The three-phase variables are transformed into d-q
axes variables with the following transformation
dtirv dsdd )( dtirv qsqq )(
Flux and Torque Estimator
Trajectory of stator flux vector in DTC
Inverter voltage vectors and corresponding
stator flux variation in time Δt
It receives the input signals Ф, τ θ and generates the
appropriate control voltage vector (switching states Sa, Sb, Sc)
for the inverter
1. Simulink model
of the controller
2. Sub block of the
direct torque control
Study of effect of magnet strength and change in M.I on
PMSM under no load and full load
Electromagnetic torque (1) and speed (2) for Ipm = 1.4 A under noload:
Electromagnetic torque (1) and speed (2) for Ipm = 1.4 A under full load:
Electromagnetic torque (1) and speed (2) for Ipm = 1.8 A under noload:
Electromagnetic torque (1) and speed (2) for Ipm = 1.8 A under fullload:
Electromagnetic torque (1) and speed (2) for M.I = 0.03 under noload:
Electromagnetic torque (1) and speed (2) for M.I = 0.03 under fullload:
Electromagnetic torque (1) and speed (2) for M.I = 0.09 under noload:
Electromagnetic torque (1) and speed (2) for M.I = 0.09 under fullload:
Torques produced in the PMSM
Excitation torque with varying the Ipm values
Induction torque with varying the Ipm values
Reluctance torque with varying the Ipm values
Study of effect of Ipm, change in M.I on PMSM with DTC for torques
» DTC strategy realizes almost ripple-free operation for the
electromagnetic torque and speed under no-load as well
as full-load for different values of Ipm and M.I.
» When magnetic strength value (Ipm) increases from 1.4 to
2.2, excitation torque and reluctance torque are increased
and induction torque remains unchanged.
» With the increase in moment of Inertia the response time
of drive without DTC is more, and with DTC, the drive has
smooth synchronization process.
» The simulation results verify the proposed control and also
shown that the transient response of torque and speed of
drive with DTC is much faster than the drive without DTC
Results and Conclusions