AN205343
FM3 MB9B500 Series Phase Lock Loop
This application note describes the phase lock loop in motor control about theory, block, function, flow, sample,
parameter and so on.
Contents
1
Introduction ...............................................................1
1.1
Purpose ...........................................................1
1.2
Definitions, Acronyms and Abbreviations ........1
1.3
Document Overview ........................................1
2
Purpose of PLL .........................................................2
2.1
Overview ..........................................................2
2.2
Field Oriented Control (FOC) ...........................2
2.3
Phase Lock Loop (PLL) ...................................3
3
PLL Theory ...............................................................5
1
Introduction
1.1
Purpose
4
5
6
7
8
PLL Estimate Parameter Introduce .......................... 6
4.1
Speed and angle estimator block diagram....... 6
4.2
The step of the estimate module ..................... 7
The flowchart of estimate module ............................. 8
Application ................................................................ 9
6.1
Function Description ........................................ 9
Additional Information ............................................... 9
Document History ................................................... 10
This application note describes the phase lock loop in motor control about theory, block, function, flow, sample,
parameter and so on.
1.2
Definitions, Acronyms and Abbreviations
FOC - Field Orient Control
PLL - Phase Lock Loop
1.3
Document Overview
The rest of document is organized as the following:
Chapter 2 explains the purpose of PLL control.
Chapter 3 explains the theory of PLL.
Chapter 4 explains the introduction of the PLL estimate parameter .
Chapter 5 explains the flowchart of estimate module.
Chapter 6 explains the PLL application in Cypress solution.
Chapter 7 explains the additional information.
Chapter 8 explains the appendix.
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Document No. 002-05343 Rev.*A
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FM3 MB9B500 Series Phase Lock Loop
2
Purpose of PLL
PLL arithmetic purpose introduces
2.1
Overview
Current industry trends suggest the Permanent Magnet Synchronous Motor (PMSM) as the first preference for motor
control application designers. Its strengths, such as high power density, fast dynamic response and high efficiency in
comparison with other motors in its category, coupled with decreased manufacturing costs and improved magnetic
properties, make the PMSM a good recommendation for large-scale product implementation.
Cypress Semiconductor produces a wide range of Digital Signal Controllers (DSCs) for enabling efficient, robust and
versatile control of all types of motors, along with reference designs of the necessary tool sets, resulting in a fast
learning curve and a shortened development cycle for new products.
2.2
Field Oriented Control (FOC)
In case of the PMSM, the rotor field speed must be equal to the stator (armature) field speed (i.e., synchronous). The
loss of synchronization between the rotor and stator fields causes the motor to halt. Field Oriented Control (FOC)
represents the method by which one of the fluxes (rotor, stator or air gap) is considered as a basis for creating a
reference frame for one of the other fluxes with the purpose of decoupling the torque and flux-producing components
of the stator current. The decoupling assures the ease of control for complex three-phase motors in the same manner
as DC motors with separate excitation. This means the armature current is responsible for the torque generation, and
the excitation current is responsible for the flux generation. In this application note, the rotor flux is considered as a
reference frame for the stator and air gap flux.
The control scheme for FOC is presented in Figure 1. This scheme was implemented and tested using the Cypress
Inverter control platform, which can drive a PMSM motor using different control techniques without requiring any
additional hardware.
Figure 1. Sensorless FOC for PMSM Block Diagram
ωr +
ef
-
P
I
Iqref +
-
Idref +
P
I
P
I
-
Park-
Vq
Vd
α,β Vβ
Iq
Id
θesti
m
ω
mR
Vα
1
d,q
A
C
Isα
d,q
α,β
Pa
rk
I
Position
and speed
Estimator
Isβ
sβ
α,β
a,b,
c
Clark
e
B
Ib
Ic
Isα
Vβ
V
α
Softwar
e
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3Phase
Bridge
SVPW
M
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FM3 MB9B500 Series Phase Lock Loop
2.3
Phase Lock Loop (PLL)
The particularity of the FOC in the case of PMSM is that the stator’s d-axis current reference Idref(corresponding to the
armature reaction flux on d-axis) is set to zero. The rotor’s magnets produce the rotor flux linkage, ΨPM, unlike ACIM,
which needs a constant reference valueIdref, for the magnetizing current, thereby producing the rotor flux linkage.
The air gap flux is equal to the sum of the rotor’s flux linkage, which is generated by the permanent magnets plus the
armature reaction flux linkage generated by the stator current. For the constant torque mode in FOC, the d-axis air
gap flux is solely equal to ΨPM, and the d-axis armature reaction flux is zero.
On the contrary, in constant power operation, the flux generating component of the stator current, Id, is used for air
gap field weakening to achieve higher speed.
In sensorless control, where no position or speed sensors are needed, the challenge is to implement a robust speed
estimator that is able to reject perturbations such as temperature, electromagnetic noise and so on. Sensorless
control is usually required when applications are very cost sensitive, where moving parts are not allowed such as
position sensors or when the motor is operated in an electrically hostile environment. However, requests for precision
control, especially at low speeds, should not be considered a critical matter for the given application.
The position and speed estimation is based on the mathematical model of the motor. Therefore, the closer the model
is to the real hardware, the better the estimator will perform. The PMSM mathematical modelling depends on its
topology, differentiating mainly two types: surface-mounted and interior permanent magnet. Each type has its own
advantages and disadvantages with respect to the application needs. The proposed control scheme has been
developed around a surface-mounted permanent magnet synchronous motor (Figure 2-2), which has the advantage
of low torque ripple and lower price in comparison with other types of PMSMs. The air gap flux for the motor type
considered is smooth so that the stator’s inductance value, Ld= Lq (non salient PMSM), and the Back
Electromagnetic Force (BEMF) is sinusoidal.
Figure 2. Surface Mounted PM PMSM Transversal Section
Armature (Stator)
Air gap
Armature slots with Armature winding
Rotor’s permanent
magnets
Rotor core
Rotor shift
The fact that the air gap is large (it includes the surface mounted magnets, being placed between the stator teeth and
the rotor core), implies a smaller inductance for this kind of PMSM with respect to the other types of motors with the
same dimension and nominal power values. These motor characteristics enable some simplification of the
mathematical model used in the speed and position estimator, while at the same time enabling the efficient use of
FOC.The FOC maximum torque per ampere is obtained by uninterruptedly keeping the motor’s rotor flux linkage
situated at 90 degrees behind the armature generated flux linkage (see Figure 2-3).
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FM3 MB9B500 Series Phase Lock Loop
Figure 3. FOC Phase Diagram (Base Speed)
β
jIsXs
Umax
RsIs
Is=IIq
Us
E
ψPM
α
In Figure 3 and Figure 4
jIsXs is voltage drop in the stator inductor.
RsIs
is voltage drop in the stator resistance.
E is Back Electromotive Force.
ψPM is rotor’s permanent magnets flux linkage.
Us is stator terminal voltage.
Considering the FOC constant power mode, the field weakening for the motor considered cannot be done effectively
because of the large air gap space, which implies weak armature reaction flux disturbing the rotor’s permanent
magnets flux linkage. Due to this, the maximum speed achieved cannot be more than double the base speed for the
motor considered for testing. Figure 2-4 depicts the phase orientation in constant power – Field Weakening mode.
Figure 4. FOC Phase Diagram (High Speed - FW)
β
Umax
jIsXs
RsIs
Is
E
Us
Iq
ψPM
α
Id
LsdI
d
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FM3 MB9B500 Series Phase Lock Loop
3
PLL Theory
Theory of PLL
The estimator has PLL structure. Its operating principle is based on the fact that the d-component of the Back
Electromotive Force (BEMF) must be equal to zero at a steady state functioning mode. The block diagram of the
estimator is presented in Figure 5.
Figure 5. PLL Estimator’s Block Schematic
Par
α,βk
Esα
Esβ
Ed
LP
F
Eq
LP
F
d,
q
Edf
Sign
Eqf
+
θestim
-
1
𝐾𝛷
Integrator
ωmR
Starting from the closed loop shown in Figure 5, the estimated speed (ωmR) of the rotor is integrated in order to obtain
the estimated angle, as shown in Equation 1:
Equation 1:
𝜃𝑒𝑠𝑡𝑖𝑚 =
𝜔 𝑚𝑅 𝑑𝑡
(1)
The estimated speed, ωmR, is obtained by dividing the q-component of the BEMF value with the voltage constant, ΚΦ,
as shown in Equation 2.
Equation 2:
𝜔𝑚𝑅 =
1
𝐾𝛷
𝐸𝑞𝑓 − sign 𝐸𝑞𝑓 ∙ 𝐸𝑑𝑓
(2)
Considering the initial estimation premise (the d-axis value of BEMF is zero at steady state) shown in Equation 2, the
BEMF q-axis value,Eqf, is corrected using the d-axis BEMF value, Edf, depending on its sign. The BEMF d-q
component’s values are filtered with a first order filter, after their calculation with the Park transform, as indicated in
Equation 3.
Equation 3:
𝐸𝑑 = 𝐸𝛼 cos 𝜃𝑒𝑠𝑡𝑖𝑚 + 𝐸𝛽 sin 𝜃𝑒𝑠𝑡𝑖𝑚
𝐸𝑞 = 𝐸𝛽 cos 𝜃𝑒𝑠𝑡𝑖𝑚 − 𝐸𝛼 sin 𝜃𝑒𝑠𝑡𝑖𝑚
(3)
With the fixed stator frame, Equation 4 represents the stators circuit equations.
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FM3 MB9B500 Series Phase Lock Loop
Equation 4:
𝐸𝛼 = 𝑉𝛼 − 𝑅𝑠 𝐼𝛼 − 𝐿𝑠
𝐸𝛽 = 𝑉𝛽 − 𝑅𝑠 𝐼𝛽 − 𝐿𝑠
𝑑𝐼𝛼
𝑑𝑡
𝑑𝐼 𝛽
(4)
𝑑𝑡
In Equation 4, the terms containing α – β were obtained from the three-phase system’s corresponding measurements
through Clarke transform. LsandRs represent the per phase stator inductance and resistance, respectively,
considering Y (star) connected stator phases. If the motor is Δ (delta) connected, the equivalent Y connection phase
resistance and inductance should be calculated and used in the equations above.
4
PLL Estimate Parameter Introduce
This section introduce the PLL estimate parameter
Estimate module is the most important module in the software, it estimate the angle speed ωmR and position θestim of
the rotor.
4.1
Speed and angle estimator block diagram
Figure 6. Estimator Diagram
𝑉𝛼
Park
𝐼𝑠𝛼
𝑑
𝑑𝑡
Ls
−
+𝐸
𝑠𝛼
𝐸𝑑
α,β
LP
F
𝐸𝑑𝑓
−
Rs
Sig
n
1
𝐾𝛷
Rs
𝐼𝑠𝛽
𝑉𝛽
𝑑
𝑑𝑡
Ls
−
−
𝐸𝑠𝛽
+
d,q
𝐸𝑞
LP
F
𝐸𝑞𝑓
+
−
𝜔𝑚𝑅
Integrator
𝜃𝑒𝑠𝑡𝑖𝑚
+
𝑉𝛼
𝜃𝑒𝑠𝑡𝑖𝑚
𝑉𝛽
𝐼𝑠𝛼
𝐼𝑠𝛽
Estimato
r
𝜔𝑚𝑅
Input variables for estimate block:
α and β component of the current signal Isα, Isβ from Clarke transform
α and β component of the stator voltage signal Vα, Vβ from SVM module
Output variables by estimate block:
Angle speed ωmRoutput to PI regulator for speed PI loop.
Estimated position θestimoutput to park and park inverse transform.
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FM3 MB9B500 Series Phase Lock Loop
4.2
The step of the estimate module
The estimator equations implemented in the application software are described as flows.
step1
The BEMF voltages are calculated as shown in equation 5,6 .
𝐸𝑠𝛼 = 1.5 −𝐼𝑠𝛼 𝑅𝑠 − 𝐿𝑠
𝐸𝑠𝛽 = 1.5 −𝐼𝑠𝛽 𝑅𝑠 − 𝐿𝑠
𝑑𝐼𝑠𝛼
𝑑𝑡
𝑑𝐼 𝑠𝛽
𝑑𝑡
+ 𝑉𝛼𝑛−1
(5)
+ 𝑉𝛽𝑛−1
(6)
Where
Esα is α component of the BEMF.
Esβis β component of the BEMF.
Vαn-1is α component of the stator voltage for previous cycle .
Vβn-1is β component of the stator voltage for previous cycle.
Rsis Winding Resistance.
Lsis Winding Inductance.
Figure 7. Motor Equal Circuit
Is
Vs
Rs
+
Ls
+
es
Motor
−
−
Step 2
sin and cos value of the estimated rotor angle are calculated.
cos(θestim) and sin(θestim) are used to express the sin and value of the estimated angle.
Step 3
The calculated α-β components of the BEMF are transformed to the d-q coordinates.
as shown in Equation 7,8. The transformation angle is the estimated flux angle θesti .
𝐸𝑑 = 𝐸𝑠𝛼 cos 𝜃𝑒𝑠𝑡𝑖𝑚 + 𝐸𝑠𝛽 sin 𝜃𝑒𝑠𝑡𝑖𝑚
(7)
𝐸𝑞 = 𝐸𝑠𝛽 cos 𝜃𝑒𝑠𝑡𝑖𝑚 − 𝐸𝑠𝛼 sin 𝜃𝑒𝑠𝑡𝑖𝑚
(8)
Step 4
The d-q components of the BEMF Ed ,Eq should be filtered to reduce the noise. Edf,Eqfare the d-q components of the
BEMF, which is filtered by LPF function.
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FM3 MB9B500 Series Phase Lock Loop
Step 5
The estimated angular speed is calculated by the BEMF on the d-axis added or subtracted depending on the sign of
BEMF on the q-axis. As equation shows
𝜔𝑚𝑅 =
𝐼𝑁𝑉𝐹𝐴𝑌𝑀 𝐸𝑞 −𝑠𝑖𝑔𝑛 𝐸𝑞 ∙𝐸𝑑
𝐼𝑁𝑉𝐹𝐴𝑌𝑀 =
2𝑛
(9)
1
𝑖𝑛𝑑𝑢𝑐𝑡 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
The estimated angular speed should be limited to augment the stability and convergence of the estimator. On the
other hand, if ωmR>max value of ωmR, it should be limited to max value of ωmR
Step 6
Since there is the integral relationship between rotor position and angle speed. And the estimated rotor position θestim
can be calculated by integrating the angle speed.
𝜃𝑒𝑠𝑡𝑖𝑚 =
5
𝜃𝑒𝑠𝑡𝑖𝑚 +𝜔 𝑚𝑅 ∙𝐷𝐸𝐿𝑇𝐴 _𝑇
2𝑛
(10)
The flowchart of estimate module
Figure 8. Flowchart of Estimate Module
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FM3 MB9B500 Series Phase Lock Loop
6
Application
PLL application achieve in system code
6.1
Function Description
The following code is the example for this module.
/*************************************************
Function Name: RunMotorCtrlAlgo
C file name: DrvMotor_MCL.C, DrvMotor_MCL.H
Input:
WhichMFT
Format:
INT8S
Function interface:void RunMotorCtrlAlgo(INT8S WhichMFT)
*************************************************************/
void example_RunMotorCtrlAlgo ()
{
WhichMFT=0;
RunMotorCtrlAlgo(WhichMFT);
}
7
Additional Information
For more Information on MB9B500 Series Phase Lock Loop, visit the following websites:
http://www.cypress.com/32bitarmcore/fm3
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FM3 MB9B500 Series Phase Lock Loop
8
Document History
Document Title: AN205343 - FM3 MB9B500 Series Phase Lock Loop
Document Number: 002-05343
Revision
**
ECN
-
Orig. of
Change
CBZH
Submission
Date
Description of Change
08/27/2010
Initial release
03/24/2011
Changed the document format
06/26/2011
Redraw some picture and change the formula
Format
*A
www.cypress.com
5264273
CBZH
06/07/2012
Changed the document format
05/10/2016
Migrated Spansion Application Note MCU-AN-510104-E-13 to Cypress
format
Document No. 002-05343 Rev.*A
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FM3 MB9B500 Series Phase Lock Loop
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