AN2291
Application note
Sinusoidal control simulink and software library of a PMSM
Introduction
This application note describes a software library for the electric motor control implementing
a (SC) Sinusoidal Control on ST10 Microcontrollers.
March 2007 Rev 1 1/36
www.st.com
Contents AN2291
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Sinusoidal control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 PMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Mathematical model of the machine . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Sinusoidal control structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 The Space vector modulation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 The 3-phase inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 The Space vector pulse width modulation . . . . . . . . . . . . . . . . . . . . . . . 14
3 EMSC simulink library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Using the simulink library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.1 How to install simulink library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.2 Test environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Parameters format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 PI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4.2 Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4.4 Simulink block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4.5 Test case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.5 Phase advance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5.2 Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5.4 Simulink block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5.5 Test case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.6 Space vector modulation look up table . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.6.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.6.2 Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.6.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.6.4 Simulink block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
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AN2291 Contents
3.6.5 Test case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.7 Rescaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.7.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.7.2 Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.7.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.7.4 Simulink block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.7.5 Test case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Sinusoidal control software library . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Using the software library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.1 How to install software library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.2 Tool chain compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.3 Calling a function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.4 ST10 MAC configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.5 Real time aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.6 Naming convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.7 Test environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.8 Sinusoidal control library benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3 Library functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3.1 PI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3.2 Description: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3.3 Arguments: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3.4 Algorithm: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3.5 Notes: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3.6 Test: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.4 Phase advance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.1 phase_advance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.2 Description: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.3 Arguments: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.4 Algorithm: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.5 Notes: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.6 Test: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.5 SVM modulation look up table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.5.1 SVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.5.2 Description: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
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Contents AN2291
4.5.3 Arguments: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.5.4 Algorithm: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.5.5 Notes: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.5.6 Test: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.6 Rescaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.6.1 rescaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.6.2 Description: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.6.3 Arguments: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.6.4 Algorithm: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.6.5 Notes: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.6.6 Test: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 C code auto generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.2 Steps to generate optimized C code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.3 Real-Time Workshop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.4 How to generate C code using real time workshop . . . . . . . . . . . . . . . . . 31
5.4.1 Step 1 - Simulink schematic constructor . . . . . . . . . . . . . . . . . . . . . . . . 31
5.4.2 Step 2 - Real Time Workshop options configuration . . . . . . . . . . . . . . . 31
5.5 Automatic configuration of RTW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6 Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4/36
AN2291 List of tables
List of tables
Table 1. Time frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Table 2. Data representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Table 3. Sinusoidal Control library capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Table 4. Document revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5/36
List of figures AN2291
List of figures
Figure 1. Vector diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Figure 2. Cross-section of PMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Figure 3. Stator current space vector and its components in (a,b,c) . . . . . . . . . . . . . . . . . . . . . . . . 10
Figure 4. Phase motor with 2 pole pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 5. Schema of sinusoidal control for PMSM-motor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Figure 6. 3-phase power inverter scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Figure 7. Space vector diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Figure 8. SVM in the 1
Figure 9. Example of a switching pattern in Sector 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Figure 10. Simulink library structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Figure 11. PI block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Figure 12. Phase advance block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Figure 13. SVM block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Figure 14. Rescaling block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Figure 15. File structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Figure 16. Flow chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Figure 17. Configuration parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Figure 18. Hardware implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Figure 19. RTW system target file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Figure 20. Generate HTML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Figure 21. Generate code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
st
sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
6/36
AN2291 Introduction
1 Introduction
This document describes a simulink and software library for the electric motor control
implementing a (EMSC) Sinusoidal Control targeted to ST10 Microcontrollers.
The library consists of:
● Simulink Library;
● C optimized Software Library;
● ASM optimized Software Library.
The EMSC Simulink Library is a set of Simulink blocks for implementing in Matlab-Simulink
environment the functions and the algorithms used in the electric motor control. These
blocks can be used either to conceive and to test new electric motor controls and to produce
automatic generated code in ANSI C, downloadable on microcontroller.
The Software Library is a set of routines for the electric motor control obtained from the code
generated in automatic, by Real Time Workshop Embedded Coder, starting from EMSC
Simulink library blocks, and then optimized in C and Assembler.
The SC software library for ST10 is fully compatible with SC simulink library.
This document begins with an introduction on Sinusoidal Control, the permanent magnet
synchronous machine (PMSM) and a short description of its mathematical model. Then, it
describes the Sinusoidal Control implementation on Simulink and details the space vector
modulation (SVM) technique and the used algorithm.
After the technical introduction, the EMSC Simulink Library is described, followed by the
Software Library.
7/36
Sinusoidal control AN2291
2 Sinusoidal control
The Sinusoidal Control is a control strategy, characterized by sinusoidal waveforms so as to
drive the three motor windings with currents that vary smoothly and sinusoidally, obtaining a
negligible torque ripple and improved high-torque characteristics at both low and high
speeds compared with other control strategies.
In order to generate a smooth sinusoidal modulation as the motor works, it is necessary an
accurate rotor position feedback from a sensor, as encoder or similar devices.
The position information is used to synthesize three modulation signals shifted by 120°
degrees each other then multiplied by the command signal provided as output of a PI
controller. These signals are used to feed the motor windings with the three voltages,
proportional to desired command signal and appropriately phased, through a voltage source
inverter (VSI).
There are three basic methods to control the voltage vector direction, each with different
advantages and requests of measurement:
1. Vector of stator voltage is placed 90° relative to the vector of rotor permanent magnet
flux;
2. Vector of stator current is placed 90° relative to the vector of rotor permanent magnet
flux;
3. Voltage vector is kept in the direction of the current vector.garte06
Figure 1 shows the vector diagram of each control strategy:
Figure 1. Vector diagram
1)
Us space vector of stator voltage
Is space vector of stator current
Ys space vector of stator flux
Yr space vector of rotor flux
Y space vector of magnetic flux
E space vector of back emf
Rs stator resistance
w angular rotor speed
2)
8/36
AN2291 Sinusoidal control
In Figure 5, the control of the motor speed forces the amplitude of the voltage vector
obtained in output from the PI controller starting from the speed error while an offset is
added to the actual rotor position in order to keep the voltage space vector in a desired
position respect to the rotor flux space vector.
2.1 PMSM
The necessity of reducing the charge of the combustion engine and of eliminating the weight
due to the mechanical connections in several applications, like in automotive field, induces
to use more and more electric motors, that assure a wide range in speed and torque control
satisfying the load demand.
The DC machine fulfils these requirements but needs periodic maintenance.
The AC machine, like induction motor and brushless permanent magnet motor, hasn’t
brushes, and its rotor is more robust because there aren’t commutator and/or rings. That
means a very low maintenance, other than increases the power-to-weight ratio and
efficiency.
In particular, in the automotive field the Permanent Magnet Synchronous Machine (PMSM)
seems to be the best solution.
The brushless permanent magnet motors (PMSMs) have the same electromagnetic
structure of a synchronous machine, without the brushes. As shown in the cross-section in
the below Figure 2, they have a wound stator, similar to an induction machine, and a rotor
with some permanent magnets instead of a wound rotor fed with DC current like the one that
is used in the classical synchronous machines. Besides, they need of an internal or external
device for sensing of the rotor position, like Hall sensors, encoder or resolver.
Figure 2. Cross-section of PMSM
The PMSMs are not self-commuting motors and to produce useful torque, the currents and
the voltages applied to stator phases must be controlled as a function of rotor position.
Therefore it is generally required to count the rotor position with a sensor so that the inverter
phases which feed it, acting at any time, are commuted depending on the rotor position.
That explains the necessity of a closed-loop speed/position feedback.
9/36
Sinusoidal control AN2291
There are two kinds of brushless permanent magnet machines classifiable in account of the
shape of the BEMF (back-electromagnetic force):
● DC brushless machine having trapezoidal flux distribution and a trapezoidal BEMF fed
by quasi-square wave currents;
● AC brushless machine having approximately sinusoidal air-gap flux density and a
quasi-sinusoidal BEMF fed by sinusoidal stator currents.
Generally the DC brushless machines have a simpler control strategy than AC brushless
machines.
For trapezoidal flux distributions, to impose quasi-square wave currents on stator windings,
it is only needed a six position sensor, with a resolution of at least 60 electrical degrees.
On the contrary, for the sinusoidal current type, the angular position needs to be known with
a very accurate precision in order to control each of the three phases currents.
For each kind, the high reliability control makes this type of machine a powerful system for
electric vehicle application.
2.1.1 Mathematical model of the machine
In order to model the fields produced by the stator windings in terms of windings current,
“current space vectors” are used. The current space vector for a given winding has the
direction of the field produced by that winding and a magnitude proportional to the current
through the winding. This allows us to represent the total stator field as a current space
vector that is the vector sum of three space vector components, one for each of the stator
windings.
The three-phase voltage, currents and fluxes of AC motors can be analyzed in terms of
complex space vectors.
For instance, with regard to the currents in the stator windings, the current space vector can
be defined as follows.
Figure 3. Stator current space vector and its components in (a,b,c)
Assuming tha
complex stator current vector
Equation 1 i
t is1,is2,is3 are the instantaneous currents in the stator phases, then the
i
is defined by:
s
2
-- -
3
i
s1is2
s
α⋅ is3α2⋅++()⋅=
10/36
AN2291 Sinusoidal control
where α = e
j(2π/3)
and
α
2
= e
j(4π/3)
represent spatial operators. The Figure 3 shows the
stator current complex space vector.
In terms of space vectors it is possible to write the mathematical model of an AC brushless
machine in a stator frame, as follows:
Equation 2
u
s
RsisL
di
d
s
---- -
+⋅+⋅=
-------
s
dt
dt
jpθ
⎛⎞
ψ
⎝⎠
r
e
⋅
f
where:
ψ
f
R
s
L
s
ω
r
p Number of pole pairs
θ
r
and the space vectors:
2
Equation 3
-- -
u
s
3
Modulus of the magnetizing flux-linkage vector
Stator resistance
Total three phase stator inductance
Rotor angular speed
Mechanical position
2π
------ -
⎛⎞
⋅=
t() u2t() e
++
u
⎜⎟
1
⎝⎠
j
3
⋅ u3t() e⋅
4π
------ -
j
3
Equation 3 space vector of the stator voltage
Equation 4
2π
------ -
2
t() e
j
3
⋅ i
s
3
⎛⎞
2
-- -
i
⋅=
t() i
i
s
⎜⎟
s1
3
⎝⎠
s
t() e
⋅++
4π
------ -
j
3
Equation 4 shows space vector of the stator current
Note: The mechanical position of the electric motors is related to the rotation of the shaft while the
electrical position is relate to the rotation of the rotor magnetic field.
So being the motor with p pole pairs, its rotor needs only to move 360/p mechanical degrees
to obtain an identical magnetic configuration as when it started.
Figure 4. Phase motor with 2 pole pair
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Sinusoidal control AN2291
Consequently the electric position of the rotor is linked to the mechanical position by the
relation:
Equation 5
θ
θrp⋅=
e
To complete the mathematical model of the motor, we include the D’Alembert equation of
mechanical equilibrium:
dω
r
Equation 6
J
---------
dt
TmTν+()–=
T
e
and substituting the expression of the electric torque, it yields:
Equation 7
dω
---------
dt
1
1
r
-- -
T
J
eTmTν
+()–()⋅
3
⎛⎞
---
---
⋅==
pψfi
⎝⎠
J
2
αsp θ⋅r–()TmTν+()–()sin⋅
s
where:
T
e
T
m
T
ν
α
s
J Inertia momentum of the machine
Electromagnetic torque
Mechanical torque
Viscose friction torque
Phase of the current space vector respect
Note: In the Matlab-Simulink environment, the PMSM discrete model has been implemented
using a model of the machine in a stationary stator reference (D,Q) frame.
2.2 Sinusoidal control structure
This application runs closed-loop control based on the difference between the reference
speed
Figure 5. Schema of sinusoidal control for PMSM-motor
12/36
*
ω
and actual speed
r
ω
of the motor.
r
AN2291 Sinusoidal control
● The speed set point is established via software while the actual speed and the rotor
position in electrical degrees are calculated by a Rotor Position Block using the signals
coming from sensors (Hall Effect sensors, resolver or encoder).
● PI interpretations of the speed error determine the amplitude of the voltage signal
wave, which in turn controls the motor speed.
● To impose the phase of the voltage space vector respect to the phase of the rotor flux
space vector is used the ‘Phase advance calculation Block’ that adds an offset at the
rotor position. In this way, it is possible to generate three signals, one for each motor
phase, shifted by an angle in electrical degrees compared with calculated phase.
● Space Vector Modulation Look Up Table, is a table in which is stored an entire period of
modulation. It uses the values of the Phases, calculated from the Phase Advance, to
generate the three duty-cycle signals scaled between 2
-15
and 215. The PWM module
converts the duty cycle inputs into modulated square waves, which drive an external
inverter.
● Rescaling, according to the duty-cycles from the SVM Look Up Table and the
Amplitude of the voltage from the PI, re-scales the duty-cycles in order to let them to be
compliant with the PWM peripherals of the microcontroller.
The chosen modulating signal, stored in the look up table, implements the SVM algorithm
described in the following.
2.3 The Space vector modulation theory
The SVM technique is a sophisticated continuous modulation method used, independently
from the type of implemented control on the motor, to generate a desired voltage space
vector at the output of the inverter that feeds the AC motor, in our case a PMSM. It uses a
special scheme to switch the power transistors generating pseudo-sinusoidal currents in the
stator windings.
This strategy offers the following advantages to the application:
● Higher performance to control mid/high dynamic motors;
● higher efficiency (86%);
● improved torque management;
● better start up performance;
● constant torque, less torque ripple;
● improved dynamic reaction.
To better understand the space vector modulation algorithm, it is before explained an other
fundamental component of the control system: the 3 phase inverter.
2.3.1 The 3-phase inverter
The inverter is a d.c. to a.c. converter. The Figure 6 shows the structure of a typical 3-phase
power inverter connected to the star motor windings, where Vdc is the DC Link voltage.
The six switches can be power BJT, GTO, IGBT etc. The state-of-the-art solution for the
inverter power stages uses MOSFETs in low-voltage applications (i.e. automotive field).
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Sinusoidal control AN2291
The ON-OFF sequence of all these devices must respect the following conditions, so as to
feed in any time all three stator windings:
– three of the switches must always be ON and three always OFF.
– to avoid shortcut, the upper and lower switches of the same leg are driven with two
complementary pulsed signals.
Figure 6. 3-phase power inverter scheme.
On base of the aforementioned conditions, the inverter has only eight permissible switching
states of which six states apply a no-zero voltage to the motor windings and two states with
(V0 and V7) zero volts when the motor is shorted through the upper or lower transistors.
It is useful to express the eight states of the inverter as space vectors: V
three voltages V
, VBn, VCn, that are spatially separated 120° apart, as a space vector for
An
expresses the
0-7
each of the switching states 0-7.
The six vectors including the zero voltage vectors can be expressed geometrically on the
complex plane as shown in the following Figure 7:
Figure 7. Space vector diagram
In order to generate a rotating field into the machine to produce a useful torque, the inverter
has to be switched in all the possible eight states.
2.3.2 The Space vector pulse width modulation
The inverter is able to apply only eight space vector positions to the stator winding of an
electric machine, while the control imposes a voltage space vector that vary in all the inner
cycle of the hexagon in order to create a smooth rotating field (see Figure 7).
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AN2291 Sinusoidal control
A reference voltage vector Vs, can be realized by a combination of the two adjacent active
vectors and the zero vectors inside of sector where it lies. The output space vector voltage
(choosing an appropriate PWM period, T
so as to suppose steady the vector Vs in this
PWM,
period), can be computed by the integral:
Equation 8
∫
T
0
PWM
V
s
δ
⎛⎞
=
td⋅()
V
⎜⎟
07⁄
∫
⎝⎠
0
α
++
∫
0
β
V
V
k
∫
0
k1+
from which it yields:
Equation 9
V
V
s
07⁄
δ
---------------- - V
T
PWM
α
---------------- - V
k
T
PWM
k1+
---------------- -
⋅+⋅+⋅=
T
PWM
β
where:
Equation 10
Vk and V
included, T
V
0/V7
(k=0,..7) are the vectors that bound the sector in which the reference vector is
k+1
PWM
vectors in that sector.
is the switching period and α, β and δ are the time frames of Vk, V
T
PWM
αβδ++=
and
k+1
The resulting equation is:
Equation 11
V
---------------------------------------------- -=
S
T
PWM
Vkα V
k1+
β⋅+⋅
For example, assuming that the vector Vs is in the 1st sector, we have the following situation:
Figure 8. SVM in the 1
st
sector
in which α and β are the times during which the vectors V
To create reference vector V
inside one of the six sectors, the reference vectors which
s
100
and V
are applied.
110
bound that sector, have to be “time weighted”, like shown in the equation Equation 11. It is
possible to modulate the reference voltage vector and to apply the better switching pattern in
terms of power dissipation, on the power switches of the inverter and to make it necessary
to choose the strategy to apply the vector V
and V
k
15/36
(active vectors) in each sector.
k+1
Sinusoidal control AN2291
We have same freedom degrees to choose the modulation algorithm as:
– The choice of the zero vector- whether V
(000) or V7(111) or both;
0
– Sequencing of the vector;
– Splitting of the duty cycle of the vectors without introducing additional
commutations.
Literature demonstrates that, in order to reduce the number of commutation and switching
losses, it is preferable to utilize a states sequence where the states are adjacent.
This means that passing from a state to the successive one should occur with only one
switch commutation.
According to that, the chosen scheme is a symmetric sequence in which there are seven
conduction states, so called “Seven states Space Vector Modulation”.
Dividing the conduction time of every component of inverter in opportune time frames, as
shown below for a vector into Sector 1:
Figure 9. Example of a switching pattern in Sector 1
every component switches two times for every PWM period.
The time frames calculated from this algorithm must be processed with a look up table in
order to establish on which phase must be applied.
Table 1 shows the time calculations to be done:
Table 1. Time frames
Sector 1 Sector 2 Sector 3 Sector 4 Sector 5 Sector 6
δ
-- -
α
---
2
T
PWM
----------------
2
4
δ
-- -+
4
δ
-- -–
4
t1
t2
t3
β
-- -
2
T
PWM
----------------
2
δ
-- -+
4
δ
-- -
4
T
PWM
----------------
2
δ
-- -
4
α
δ
-- -–
4
δ
---
-- -+
2
4
T
δ
-- -–
----------------
4
PWM
2
β
-- -
2
δ
-- -–
4
δ
-- -+
4
δ
-- -
4
α
---
2
T
PWM
----------------
2
δ
-- -+
4
δ
-- -–
4
δ
-- -
4
T
PWM
----------------
2
β
-- -
2
δ
-- -
4
δ
-- -+
4
δ
-- -–
4
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AN2291 EMSC simulink library
3 EMSC simulink library
3.1 Description
The EMSC Simulink Library implements all needed functions for electric motor control using
the following blocks, here listed:
● PI;
● Space Vector Modulation Look Up Table;
● Phase Advance;
● Rescaling;
3.2 Using the simulink library
The library package consists of 2 main directories:
● 1 directory for all test cases: 1 subdirectory per library function;
● 1 directory for all .mdl files.
The file structure is the following:
Figure 10. Simulink library structure
3.2.1 How to install simulink library
The Simulink Library is delivered as an archive file with .zip extension. To install one you
need to unzip the file in the directory where you want the library to be copied into.
Note: it is required a license of Matlab version 7.0.0 or upward to use this library, plus a
licence for Fixed-Point-Precision Toolbox to use the “convert block“ in each scheme block
and a licence of RTW Embedded Coder Toolbox.
3.2.2 Test environment
.mat: it is possible to find the input and output data obtained by Simulink in the double
format, stored in vectors that you preload in the Workspace of Matlab, opening the .mdl file.
The name of each test-file begins with the (yyy) function name that it refers, followed by
underscore and the suffix “data”.
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EMSC simulink library AN2291
3.3 Parameters format
The EMSC library in Simulink and the optimized C-code have the same inputs/outputs so
keeping the compatibility between them, using for the data coding a fixed point precision
number representation.
In the Table 2 the variables and their representations are listed:
Table 2. Data representation
variable representation description
speed_ref sfix(16,5) reference speed
speed_fdk sfix(16,5) measured speed
err sfix(16,5) error
PI_stato sfix(32,26)
kp sfix(16,5) proportional constant
ki sfix(16,15) integral constant
theta ufix(16,16) electrical angle
offset ufix(16,16)
PH_1 ufix(16,16) theta 1
PH_2 ufix(16,16) theta 2
PH_3 ufix(16,16) theta 3
SVM1 sfix(16,15) duty-cycle
SVM2 sfix(16,15) duty-cycle
SVM3 sfix(1615) duty-cycle
Module sfix(16,5) Amplitude of the voltage signal wave
PWM_per1 uint16 duty-cycle
PWM_per2 uint16 duty-cycle
PWM_per3 uint16 duty-cycle
In the following, the Simulink implemented blocks are described in details.
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AN2291 EMSC simulink library
3.4 PI
3.4.1 Description
From the difference between the (
by Hall sensors) the PI determines the amplitude of the voltage to feed the motor.
3.4.2 Arguments
err (reference signal)-(measured signal);
speed_ref reference speed;
speed_fdk speed;
kp proportional constant;
ki integral constant;
Module Amplitude of the voltage signal wave;
3.4.3 Algorithm
*
ω
) reference speed and (
r
ω
) actual speed (estimated
r
The following equations are implemented:
Equation 12
3.4.4 Simulink block
As shown here below in the Figure 11, the PI block, implemented in Simulink, receives in
input the reference speed and calculated speed signals, in sfix(16,5) format and returns in
output the voltage module in the same format.
Figure 11. PI block
U
k
KpekKie
k1–
en
+⋅+⋅=
k
∑
n0=
3.4.5 Test case
You find in pi_data.mat file the inputs and outputs data to test this function.
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EMSC simulink library AN2291
3.5 Phase advance
3.5.1 Description
To impose the phase of the voltage space vector respect to the phase of the rotor flux space
vector it adds an offset at the actual rotor position.
3.5.2 Arguments
θe = pθ
offset offset;
PH
PH
PH
r
1
2
3
3.5.3 Algorithm
The following equations are implemented:
Equation 13
Equation 14
Equation 15
3.5.4 Simulink block
Figure 12. Phase advance block
rotor position in electrical degrees;
theta1;
theta2;
theta3.
PH1 θ
PH2 PH1
PH3 PH1
e
offset+=
1
-- -–=
3
1
-- -+=
3
3.5.5 Test case
You find in phase_advance_data.mat file the inputs and outputs data to test this function.
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AN2291 EMSC simulink library
3.6 Space vector modulation look up table
3.6.1 Description
An entire period of modulation is stored in a look up table whose input is the value
calculated from the Phase Advance Block, so an electrical angle, and in output it generates
a duty-cycle signal, represented by a number scaled between 2
3.6.2 Arguments
-15
and 215.
PH
1
PH
2
PH
3
SVM
1
SVM
2
SVM
3
3.6.3 Algorithm
3.6.4 Simulink block
Figure 13. SVM block
theta1;
theta2;
theta3;
duty-cycle;
duty-cycle;
duty-cycle;
3.6.5 Test case
You find in svm_lut_data.mat file the inputs and outputs data to test this function.
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EMSC simulink library AN2291
3.7 Rescaling
3.7.1 Description
Rescale the duty-cycles from the SVM Look Up Table and the Amplitude of the voltage from
the PI in order to let them to be compliant with the PWM peripherals of the microcontroller
according to the duty-cycles
3.7.2 Arguments
Module Amplitude of the voltage signal wave;
SVM
1
SVM
2
SVM
3
PWM
1
PWM
2
PWM
3
3.7.3 Algorithm
_per1 duty-cycle;
_per2 duty-cycle;
_per3 duty-cycle;
duty-cycle;
duty-cycle;
duty-cycle;
3.7.4 Simulink block
Figure 14. Rescaling block
3.7.5 Test case
You find in rescaling_data.mat file the inputs and outputs data to test this function.
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AN2291 Sinusoidal control software library
4 Sinusoidal control software library
4.1 Description
The Sinusoidal Control Software library provides the functions for mixed “C” and Assembly
programmers targeted to ST10 necessary to implement the (EMSC) electric motor control.
4.2 Using the software library
The two main directories of the library package are:
● Testcase directory;
● Source directory.
The file structure is the following one:
Figure 15. File structure
4.2.1 How to install software library
The Software Library is delivered as an archive file with .zip extension. To install the
Software Library you need to unzip the file in the directory where you want the library to be
copied into.
Note: Please, read the README.txt file in the archive file for specific details on the release.
4.2.2 Tool chain compatibility
EMSC library is compatible with Altium/Tasking tool chain (V7.5r2 and upward).
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Sinusoidal control software library AN2291
4.2.3 Calling a function
The functions have been written to be called by a C language program.
To include a function in a C language program, it is needed to:
● include the “SCSP10.h”,
You find this .h file in the Source directory of the library package.
4.2.4 ST10 MAC configuration
This library has been done for implementing electric motor control functions (EMSC control).
The implemented functions have been optimized with the use of MAC commands using the
default configuration (the user have not to change the configuration registers of MAC) in
order to improve the execution time performance.
4.2.5 Real time aspects
Any DSP code developed for ST10 can be interrupted at any time and execution resumed
after the interrupt routine. There is no added latency when the DSP library is used.
Interrupt routine requirements: the only requirements are only when the DSP unit is used
by other tasks that have different priorities: the interrupting task that may interrupt another
task using the DSP should save and restore the MAC registers at the entry point and exit
point of the routine. (use #pragma savemac in Altium/Tasking tool chain).
4.2.6 Naming convention
The name of each functions refers to the name of the Simulink equivalent block, that it
implements on micro, followed by underscore “step”.
Example: phase_advance_step
It translates the function of the Simulink block “Phase_Advance“.
For the input/output variables, the convention is:
name function underscore “U“ underscore variable name for the inputs;
Example: Phase_Advance_U_Theta
name function underscore “Y“ underscore variable name for the outputs
Example: Phase_Advance_Y_PH1.
4.2.7 Test environment
yyy_data.c : you find the input data vectors in int format and the output data vectors
obtained by Simulink for the same function block in int format.
The name of each test-file begins with the (yyy) function name that it refers, followed by
underscore and the suffix “data”.
4.2.8 Sinusoidal control library benchmark
The following table gives the characteristics of the main functions of the library:
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AN2291 Sinusoidal control software library
Table 3. Sinusoidal Control library capabilities
Function Code size (bytes) Nb cycles
PI 128 21
SVM 40 20
Phase Advance 22 16
Rescaling 152 20
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Sinusoidal control software library AN2291
4.3 Library functions
4.3.1 PI
pi_step(int32_T * PI_state, int16_T speed_ref, int16_T speed_fdk, int16_T kp, int16_T
ki,int16_T* amplitude)
4.3.2 Description:
It implements classical PI scheme receiving in input the reference signal, the feedback
signal and the state, calculating the error, defined like reference signal - calculated signal,
and produces in output the reference voltage signal.
4.3.3 Arguments:
PI_state PI_state;
speed_ref Reference speed;
speed_fdk Speed;
kp Proportional constant;
ki Integral constant;
amplitude Amplitude of the voltage wave.
4.3.4 Algorithm:
4.3.5 Notes:
4.3.6 Test:
To test this function, include the pi_data.c file in the current directory.
In the .c file you find the inputs and outputs vectors defined as const.
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AN2291 Sinusoidal control software library
4.4 Phase advance
4.4.1 phase_advance
phase_advance_step (uint16_T Phase_Advance_U_Theta, uint16_T
Phase_Advance_U_Offset, uint16_T* Phase_Advance_Y_PH1,
uint16_T* Phase_Advance_Y_PH2, uint16_T*
Phase_Advance_Y_PH3)
4.4.2 Description:
The input signal waves are shifted by an angle that aims to optimize the efficiency of the
motor.
4.4.3 Arguments:
Phase_Advance_U_Theta Rotor position in electrical degrees;
Phase_Advance_U_Offset Offset;
Phase_Advance_Y_PH1 Angle on phase1:Theta1;
Phase_Advance_Y_PH2 Angle on phase2:Theta2;
Phase_Advance_Y_PH3 Angle on phase3:Theta3.
4.4.4 Algorithm:
4.4.5 Notes:
4.4.6 Test:
To test this function, include the phase_advance_data.c file in the current directory.
In the .c file you find the inputs and outputs vectors defined as const.
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Sinusoidal control software library AN2291
4.5 SVM modulation look up table
4.5.1 SVM
SVM_step (uint16_T LUT_U_PH1, uint16_T LUT_U_PH2, uint16_T LUT_U_PH3,
int16_T* LUT_U_SVM1, int16_T* LUT_U_SVM2, int16_T* LUT_U_SVM3)
4.5.2 Description:
It uses the motor phases calculated from Phase_Advance Block as index to enter in a
look up table and calculate the duty cycle.
4.5.3 Arguments:
LUT_U_PH1 Angle on phase1:Theta1;
LUT_U_PH2 Angle on phase2:Theta2;
LUT_U_PH3 Angle on phase3:Theta3;
LUT_U_SVM1 Duty-cycle on Phase1;
LUT_U_SVM2 Duty-cycle on Phase2;
LUT_U_SVM3 Duty-cycle on Phase3.
4.5.4 Algorithm:
4.5.5 Notes:
4.5.6 Test:
To test this function, include the svm_data.c file in the current directory.
In the .c file you find the inputs and outputs vectors defined as const.
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AN2291 Sinusoidal control software library
4.6 Rescaling
4.6.1 rescaling
rescaling_step(int16_T Rescaling_U_Module, int16_T Rescaling_U_SVM1, int16_T
Rescaling_U_SVM2, int16_T Rescaling_U_SVM3, uint16_T*
Rescaling_Y_PWM_per1, uint16_T* Rescaling_Y_PWM_per2,
uint16_T* Rescaling_Y_PWM_per3)
4.6.2 Description:
Rescale the duty-cycles in order to let them to be compliant with the PWM peripherals
of the microcontroller.
4.6.3 Arguments:
Rescaling_U_Module Amplitude of the voltage wave;
Rescaling_U_SVM1 Duty-cycle on Phase1;
Rescaling_U_SVM2 Duty-cycle on Phase2;
Rescaling_U_SVM3 Duty-cycle on Phase3;
Rescaling_Y_PWM_per1 Duty-cycle on Phase1;
Rescaling_Y_PWM_per2 Duty-cycle on Phase2;
Rescaling_Y_PWM_per3 Duty-cycle on Phase3.
4.6.4 Algorithm:
4.6.5 Notes:
4.6.6 Test:
To test this function, include the rescaling_data.c file in the current directory.
In the .c file you find the inputs and outputs vectors defined as const.
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C code auto generation AN2291
5 C code auto generation
5.1 Overview
When the Simulink schematics are done, converted to fixed point precision and tested, the
last step is to generate C code downloadable on the microcontroller. This step is done using
two toolboxes of Matlab:
● The Real Time Workshop
● The Real Time Workshop Embedded Coder
The Real Time Workshop is an essential tool used in rapid prototyping with Simulink.
Automatic program building allows you to make design changes directly to the block
diagram, putting algorithm development (including coding, compiling, linking, and
downloading to target hardware) under control of a single process.
In this part, a set of signal processing functions for C programmers on ST10 are presented.
5.2 Steps to generate optimized C code
● Design a model in Simulink
The rapid prototyping process begins with the development of a model in Simulink. Using
principles of control engineering, it’s possible to model plant dynamics and other dynamic
components that constitute a controller and/or an observer.
● Simulate the Model in Simulink
Using MATLAB-Simulink, and toolboxes it’s possible to develop algorithms and analyze the
results.If the results are not satisfactory, it’s possible to iterate the modelling and analysis
process until results are acceptable.
● Generate Source Code with Real-Time Workshop
Once simulation results are acceptable, it’s possible to generate downloadable C code that
implements the appropriate portions of the model. Simulink could be used in external mode
to monitor signals, tune parameters, and further validate and refine the model, quickly
iterating through solutions.
● Implement a Production Prototype
At this stage, the rapid prototyping process is complete.
5.3 Real-Time Workshop
The Real-Time Workshop Embedded Coder is a separate, add-on product for use with
Real-Time Workshop.
It is intended for use in embedded systems development to generate code that is easy to
read, trace, and customize for all production environment. The Real-Time Workshop
Embedded Coder provides a framework for the development of production code that is
optimized for speed, memory usage, and simplicity. It generates optimized ANSI-C or ISO-C
code for fixed point and floating point microprocessors. It extends the capabilities provided
by the Real-Time Workshop to support specification, integration, deployment, and testing of
production applications on embedded targets. The Real Time Workshop Embedded Coder
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AN2291 C code auto generation
addresses targeting considerations such as RAM, ROM, and CPU constraints, code
configuration, and code verification.
The Embedded Real-Time (ERT) target, provided by the Real Time Workshop Embedded
Coder, is designed for customization.
Figure 16. Flow chart
In our applications we use the ERT target with optimization for fixed point systems. Correct
specification of target-specific characteristics of generated code (such as word sizes for
char, int, and long data types, or desiderated rounding behaviors in integer operations) can
be critical in embedded systems development. The Hardware Implementation category of
options in the settings menu provides a simple and flexible way to control such
characteristics in both simulation and code generation.
5.4 How to generate C code using real time workshop
Starting from a model in fixed point precision it is described step by step how to generate C
code.
5.4.1 Step 1 - Simulink schematic constructor
The first step is the construction of the Simulink schematic implementing the considered
function.
Note: for improving the readability of the auto generated C-code it’s useful to include the
schematic of each single function in a single subsystem.
The model is now ready to be compiled in order to generate C code.
5.4.2 Step 2 - Real Time Workshop options configuration
Selecting from the Simulation menu the “Configuration Parameter” pane all the options are
shown:
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C code auto generation AN2291
Figure 17. Configuration parameter
The first thing to do is selecting the Hardware Implementation, in our case ST10. In this way
the format of data are chosen.
Figure 18. Hardware implementation
After the Real time Workshop options must be chosen. The first one is the RTW system
target. As before said we choose the ERT optimum for fixed point precision (Figure 19).
Figure 19. RTW system target file
a) b)
If only the code is needed (as in our case), the Generate code only box must be checked,
(Figure 20), furthermore you could auto generate the Generate HTML report checking the
apposite box.
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AN2291 C code auto generation
Figure 20. Generate HTML
In the Comments pane it’s possible to define the verbosity level of the compiler and the
comments that are automatically included in the generated C code.
Now everything is ready for generating code. Pushing the “Generate code“ button generates
some verbose comments in the Matlab command windows, as in Figure 21.
Figure 21. Generate code
When the process is completed the HTML report windows will appear generating the files:
● ert_main.c
● filename.c
● rtwtypes.h
Not all of them are useful for the next step code download.
5.5 Automatic configuration of RTW
Running RTWconfiguration.m file in the Command Window of Matlab available in the folder
C:\EMSC_Library\options, a set of parameters is loaded to configure the RTW and
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C code auto generation AN2291
associated with a given filename.mdl. For Automatic configuration the following steps has to
be followed:
● Open filename.mdl file;
● Copy RTWconfiguration.m and config_RTW.mat in the actual working directory;
● Run “RTWconfiguration” from Command Window of Matlab.
In this way you’ll get active the “RTW_configuration” set to run and auto generate the C
code.
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AN2291 Revision history
6 Revision history
Table 4. Document revision history
Date Revision Changes
09-Mar-2007 1 Initial release.
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AN2291
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