The 33rd Annual Conference of the IEEE Industrial Electronics Society (IECON) Nov. 5-8, 2007, Taipei, Taiwan
Synchronous Motor Current Controler Quality Augmentation with Adaptive Control I. Uhlir, M. Cambal, M. Novak, J. Novak Czech Technical University in Prague, Faculty of Mechanical Engineering, Department of Instrumentation and Control Engineering, Prague, Czech Republic uthor
[email protected],
[email protected],
[email protected],
[email protected] Abstract- This paper presents practical aspects and results obtained with a controller structure based on two phase current control. Adaptive controllers were used to improve the control quality. At the end, controller structures for magnetic flux weakening mode are proposed.
I.
INTRODUCTION
There is a continuous growth of synchronous motors usage, mostly with permanent magnets in the field of electric drives. The motors are used mainly as servo drives, but are more and more used also as traction drives. Other applications for synchronous motors are special and auxiliary motors, where they replace commutator motors. At the division of electrical engineering of the faculty of mechanical engineering at the Czech Technical University in Prague, we focus our attention on synchronous motor usage in the field of transportation. This research is done in the scope of Josef Bozek's research center of engine and automotive engineering. We are interested in traction motors, special and auxiliary motors for the automotive industry were DC motors or non electric motors are being used. In some cases there is a need for high speed motors. Besides some specificity of automotive engineering there is also a high pressure on low cost components as large quantities are produced and due to high pressure on the market. Therefore one of our goals is also the low cost of the proposed solution. The methods for synchronous motor torque control can be divided into two main groups: control of phase current immediate values based on rotor position and control in the transformed coordinate system. The most used method based on coordinate system transformation is linear vector control in d,q axes, coupled to rotor position. This method is an analogy to asynchronous motor vector torque control. This method gives good controller results also for the reason that it is used to control steady state variables instead of instantaneous phase current values. It is used mainly for drives with higher dynamics demands, middle and higher power drives including traction drives. Thanks to the computing power of today's processors and build-in HW peripherals, its implementation is not difficult. Methods based on phase current control with feedback to rotor's instantaneous position were used previously when today's microcontroller techniques were not available.
1-4244-0783-4/07/$20.00 (C2007 IEEE
These methods were implemented in analog or hybrid controllers. The advantage of these methods are lower computation demands as in is not necessary to calculate the coordinate system transformations as it is the case for coordinate system control techniques. The disadvantage is the need to calculate time variable phase current values - control variables. This leads to problems in achieving higher quality control, mainly for higher speeds. This becomes more significant as we are decreasing the ratio between PWM frequency and the frequency of the first current harmonics. Phase current controllers can be used with the inverter having a voltage input as linear controllers or on-off controllers. On-off controllers can be found in servo drives or in low power brushless motors. In our work we focused on improving phase current control properties. On-off controllers were tested [1] but due to the necessary increase in controller computation frequency and inverters switching frequency and due to potential EMC problems for this controller solution we focused mainly on linear control. The main goal was to preserve a simple algorithm as this method is to be used on simple, universal and low cost microcontrollers. This is one of the conditions for DC motor replacement in automotive industry. Another application field of this method is the control of two or more motors with one microcontroller or in the field of high speed motors. One of the goals of our work is also to set the limits of this method for high speed motors with lower dynamic demands. At the end of this paper a controller structure for magnetic flux weakening mode based on feedback from phase current instantaneous values is presented. As this mode has higher computational demands, it is not meant to be used for the very simple drives. The proposed magnetic flux weakening structure can also be used for d,q coordinate system control. II. LABORATORY TESTS
At the time of the first test, a suitable PMSM was not accessible. For this reason, the tests were done on a synchronous motor with rotor excitation winding. This winding was powered with a constant current. The used synchronous motor was a 4kW, 1500 min-', A/Y 127V/220V, 50Hz motor. The tests were made for both A and Y connection. The disadvantage of this motor was mainly the shape of the induced voltage which was not purely sinusoidal -fig. 1. This shape was
1198
measured for the unloaded motor with the rotor excitation winding fully powered and disconnected stator winding. 100
>
80 60 40 20 0 -20
Where Ff is the rotor magnetic flux, Ld is the longitudinal stator winding inductance and Lq is the transversal stator winding inductance. If the motor is working with full magnetic flux, the id stator current component is zero and we get:
*Fjiq M=1.5*ppf D
I
\
X 10
20
If the motor has an insignificant rotor's magnetic asymmetry (Ld=Lq), which is often the case for permanent magnet synchronous motors, equation (3) is valid even for magnetic flux weakening mode. The armature interference, given by the id current component, is in this mode acting against the induced voltage and allows using the motor for increasing speeds while maintaining the stators effective voltage. Equation (3) describes an analogy with DC motor. This can be used equivalently in both the coordinate system transformation control or in the phase current instantaneous values control coupled with rotor position. In this case, for the full magnetic flux mode the requested value of the phase current for the given phase is calculated to have a maximal value when the rotor is perpendicular to this winding axis. The requested values for each phase are shifted by 120 and its instantaneous phase angle is given by rotor's instantaneous position. The stators spatial phase current vector is parallel to the induced voltage and is 90° ahead of the rotor. In the magnetic flux weakening mode the stator's spatial current vector is ahead of the induced voltage and the phase angle between these two is higher than 90°. Generally, the situation for magnetic flux weakening mode and Ld=Lq =L, the situation
60
50
0
30
(3)
-40 -60 -80 -100 Vmsl
Fig. 1. Motor's measured induced voltage, f=32Hz
Higher induced voltage harmonic componen this case like a disturbance variable. The motor tas ore athi gti Ath thes coupled with a DC dynamometer measuring tht synchronou present time we have prepared for tests oth( c 4n motors with permanent magnets: 8kW, 3000 nnines and 40000 min-'. Even if there is a high research interest in si ensorless position estimation for synchronous motors, s used in practical applications. For this test, a tvvo pole was used and connected to our own signal processing . providing IRC simulation and parallel bus for communication with the controller. This system has an absoluite resolution of 2048 positions per one revolution [2]. by the phasor diagram on fig. 2. For the full The synchronous motor was powered by an IGBT inverter is described magnetic flux mode, id =0 and the stators spatial current vector with integrated driver. The inverter was for the Itime of the tests is parallel to the q axis. In fig.2 R is the stators winding power with a 220V DC dynamo. This permitted thetestsi U stators voltage and U. is the induced voltage. both motor and generator mode without any problems. The resistance, PWM switching frequency was 5kHz. A controller based on the TI TMS 320F24 0 digital signal processor with a controller algorithm coded irl assembly was used for the tests - [3]. RI?
forq.
er
areoto .resouve
joLI_f'
III. THEORETICAL BACKGROUND
thi
Methods for synchronous motor torque control are based on this equation
(1)
M=1.5-pp .(Fd 'q -Fq 'd ) -
1)
-
Where Fd is the magnetic flux component in the d axis, Fq is the magnetic flux component in the q axis, id is the d axis stator current component, iq is the q axis stator current component, pp is the pole pair component number. Using the mathematical model of the synchronous drive, the equation can further be transformed into:
M=1.5.pp [(Ff +Ld id).)q-Lq 'q =t1.5Pppliq4(Ff
+Ld * id-Lq i)d)
id' =
(2)
ItA
I.....A
0
I
d/
Fig. 2. Synchronous motor diagram of phasors for torque control
IV. PHASE CURRENT CONTROL TESTS WITHOUT CONTROLER PARAMETER ADAPTATION
The results of this tests will be presented in abbreviated form, there are available in [1] in more detail.
1199
The first structure used to implement the phase current control for torque control was based on the idea to use a separate controller for each phase current, determining by its output the inverters state for the phase in question. In this basic form, tests were made for linear and on-off controllers. In the case of on-off controllers this is the final structure for the moment. In this paper we will focus on linear PI controllers. There were some disadvantages for the case of linear controller for all three phases where the controllers output gives a proportional voltage UR to the PWM modulator input. The first disadvantage was that with the controllers integration component turned on, there was a non zero mean value for the proportional voltage UR, used as PWM modulator input. The currents were shifted to the end of the controllers control band. This was removed by the modification of the control algorithm. Phase currents are now calculated only for two phases and the third controller's proportional output voltage is based on equation UAR +UBR+UCR .Fig. 3 shows the current controllers waveforms for the calculation in this two phases where the controllers output is directly fed into the PWM modulator as the requested value of the proportional voltage UAR , UBR in two invertors phases. The third phase proportional voltage UCR is based on the previously mentioned equation. 10 8 6 4
2
=Ri+LLdildt+ui =UPI +Ui
UR
(4)
Where R and L are resistance and inductance of the stator winding, UR iS the proportional voltage in phase, u. is the induced voltage, i is the current and up, is the phase current controller output. Equation (4) is the equation describing the voltage in stators phase winding. It is clear that the controller is in principle controlling the current in an RL circuit, meaning a first order system. To control this system, a PI controller is known to be suitable. The described induced voltage compensation procedure has the same effect on the phase current control as a decoupling circuit in the coordinate transformation control. The measured waveforms for motor with frequency 41Hz are shown on fig. 4. The quality of the real phase current value from fig. 4 is not higher that from fig.3. A relatively high control deviation is 14 12
-
10 , 8 Z.
iiset iact
-
426-4
0-8
10
4
30
4
uR
50
-10 -12 -14 t/ms/
Fig. 4. Waveforms for induced voltage compensation u, f=41Hz
iset iact 2
60
0
100
ui
-10
Vms/
Fig. 3. Waveforms for controller without compensation ui , f=24Hz
In fig 3., the phase current requested value is show in red, phase current real value in blue, the proportional voltage in green and the first harmonic of the induced voltage calculated from motors RPM and instantaneous position in magenta. The waveforms are show in relative units. These waveforms were measured for frequency 24Hz. It is clear from these figures that even for this low frequency, the first harmonic of the real phase current is permanently phase shifted behind the requested value and in the region of its maximum, the real current is alternating, which is caused also by the poor quality of the induced voltage - fig. 1. It did show impossible to improve the quality of the real phase current by changing the proportional or integrating controller component. A major quality improvement was achieved by modifying the controller structure so that the proportional voltage, the input to PWM modulator, is calculated as the sum of phase current controller output and calculated first harmonic of induced voltage in phase. The controller output is then the voltage caused by the voltage drop on the resistance and inductance of the stator winding following equation:
noticeable near the maximum value. However, it is important to note that this control deviation was measured for almost twice the frequency as the frequency in fig. 3. For the same frequency (18Hz), the control quality is significantly higher. Fig. 5 shows a transition state for a change from motor to generator mode. Fig. 6 shows the used controller structure including the magnetic flux weakening mode. The structure for full magnetic 10l
Z
2 1
\
0 60
m
-
8
100
iset iact uR
-6 -8 -10-
t/msl
Fig. 5. Waveforms for induced voltage compensation, f=1 8Hz, transition from motor to generator mode
flux mode used up to this moment is in fig. 6 shown as unframed. Fig. 7 shows the dependency of statically measure torque as dependency on the phase current amplitude for the Y connection, f=18Hz and Ff =1/3 Fffi. The dependency is linear as expected. The fact that it is not going through the beginning of the coordinate system is due to mechanical looses.
1200
Fig. 6. Used controller structure for full magnetic flux mode (unframed) including proposed form for magnetic flux weakening mode (framed) E
controller settings for good control quality for lower speeds but with unsatisfactory results for higher speeds where the signals agreed approximately the signals on fig. 4. For this reason, the adaptation of controller setting was used. The first tested possibility was based on adapting according to instantaneous derivation of the requested phase current value. In this case the actual controller setting was based on equations:
16 14 12 10 8642u
-10 -9 -8 -7 -6 -5 -4 -3 -2
1
/-6
2 3 4 5 6 7 8 9 10
Imax IAJ
-10 -12 -14 -16-18
KP = KPO + CP1 * Aset / At KI = KIO + CI1 Ajset / At
Fig. 7. Measured dependency of motor torque depending on the phase current amplitude (motor and generator mode)
V. CONTROLLER PARAMETER ADAPTATION
The effort to find an optimal controller setting of its proportional and integration component for the phase current controller considering the induced voltage was failing on the following problem. It was possible to set the controller constants to achieve good control quality for higher speed (approximately above 30Hz) but with unsatisfactory results for lower speeds as for the lower speed the control loop was becoming unstable. Or vice versa, it was possible to find
(5)
Where KP is the current value of the controller proportional constant, KI is the current value of the integration constant, KPO is the proportional constant for optimal setting for low frequencies, KIO is the integration constant for optimal setting for low frequencies, Cp1 and C1l are weight coefficients for requested current derivation used for the actual proportional or integration constant, Aiset is the change in current requested value after the computation period, At is the controller computation period, in this case it is equal to the PWM period
1201
200gs. Constants Cp1 a C1l were set to achieve optimal current waveform (amplitude, phase shift). This described adaptation was only partially successful as can be seen by comparing fig. 4 and fig. 8. 14 12 10
Ci
P4 30
-2 Q)
-4 -6
40
500
iset iact uR
-
-10 -12-14-
t/ms/
Fig. 8. Waveforms after controller adaptation based on current requested value derivative, f=40Hz
The problem for setting the constants Cpl and C1l was that there were still control deviations in the maximal current region. The reason for this is that the controller is not capable to act with sufficient speed in this region as the second derivative of the requested current value is maximal. When adaptation based on the first derivative is used, it does not reflect this fact. The second adaptation possibility is therefore to use also the second derivative of the requested current value for adaptation following equations:
the induced voltage by a variable of the same size as the induced voltage that is however phase shifted by angle ac meaning the current space vector phase shift with respect to induced voltage and its size depends on the id stator current component decreasing the total magnetic flux Fd in the d axis. While the adjusting of KPo , KIo , Cp1 , CIl , Cp, and Cl, in equation (7) was made, it was found out that to achieve good quality control it is sufficient to adapt only the proportional controller constant based on the first derivative of the requested current value and on the instantaneous value of the induced voltage. C1, = ClU = 0, KI = KIO are therefore zero. Moreover, the weight coefficient for the component based on the induced voltage is significantly higher that from the first derivative of the requested current value and it is expected that it will not be necessary for other motors with different parameters to use it for adaptation. The following figures show the motor's waveforms for this adaptation technique based on proportional controller constant adaptation from first derivative of the requested current value and on instantaneous induced voltage value. There were measured for different frequencies for steady states and for transition states. 15 l
5
KP KPO CPI At+Cp2A*iset /At2 KI = KIO + CI1 *AAset /At + CI2* set / At2 +
=
* A set
A.
10 -iset - iact uR
-
(6)
10
20
300
-ui
-10 -15
CP2 and C12 are weight coefficients of the second derivative
of the requested current value calculated for actual controller settings. For practical reasons, however, this approach brings inaccurate results as the sine look-up table used for instantaneous current values calculation is discrete and the second derivative is therefore highly inaccurate. For this inaccuracy another adaptation method was chosen. An adaptation component based on first's harmonics induced voltage instantaneous value was chosen. It is calculated as it was previously mentioned. In the full magnetic flux mode, the induced voltage has its maximum value in the moment of the maximum value of the phase current and is reflecting therefore the current's second derivative. Moreover, its value is also coupled with frequency and the adaptation can be described by
vv
A
Vlmsl
Fig. 9. Waveforms for proportional controller constant adaptation based on di/dt and ui , f=41Hz
By comparing fig. 9. with fig. 8. and fig. 4 it is clear that this adaptation technique brings the real current value more closer to the requested value than the previous method. However, there are still fluctuations in the region of the maximum value. These are expected to be caused by the non sinusoidal induced voltage (fig. 1) of the examined motor and it is expected to be more clear after the tests with a newly shipped 8kW PMSM. For this motor a sinusoidal induced voltage is expected. 5
equations:
1
KP KPO + CPI * Aset I At + CPU * Ui KI KIO +CI1 *AjAset lAt+C1u Ui =
=
(7)
CPU and ClIU are weight coefficients for instantaneous induced voltage values ui in a given phase for current controller constants. This adaptation technique will however be more complicated for the magnetic flux weakening mode. In this mode, the equation (7) has to be modified by a replacement for
1202
-21 A)
-iset
X
50
100
iact
15,0
200
257
300
Illset Illact
i0
Vmsl
Fig. 10. Waveforms for proportional controller constant adaptation based on di/dt and ui, f=3,5Hz
Fig. 10 shows the waveforms for a transition state from motor to generator mode for f=3,5Hz. Illset meaning the given value of the stator' s spatial current vector's module corresponding to motor's torque. Illact is the real value of this module calculated from instantaneous measured values of the stator's current transformed into rectangular coordinate system. 12 l
:
Itf t. 8
m
.
/\
f\
4
I
060
40
-4-
80
100
-iset -iact
phase angle oc between the q axis and the stator's spatial current vector - fig. 2. These values are fed to a calculating element that is calculating the instantaneous current values IA and iB* based on the instantaneous rotor position (d axis). Other functions of the structure are the same as in the full magnetic flux mode. This designed algorithm for the magnetic flux weakening mode can be used not only for the phase current control structure. This described method is tried out and implemented at the present time. Fig. 13 presents results of the preliminary tests without detailed optimization of controller settings.
Illset -Illact
12 10 8 6 4
-8-12
Vu
-
3
'M
V/msl
-
' l- 1
v
e
-
-
. 2-
-
0
Fig. 11. Waveforms for proportional controller constant adaptation based on di/dt and ui, f=30Hz
-ui
-4-6 -8 -10 -12
12
iset iact uR
Vmsl -2
E
7r
I5
4
Fig. 12. Waveforms for magnetic flux weakening mode, f=55Hz
Illset iact -*1 00 n -
0
CD
-4
-
VII. CONCLUSIONS
Illact
-12
tIsI
Fig. 12. Waveforms for proportional controller constant adaptation based on di/dt and ui , f=3,5Hz, torque and sense of rotation reversal
Fig. 11 shows the waveforms for torque reversal for f=30Hz. The slight instability in the maximum current region is again believed to be caused by the non sinusoidal motor's induced voltage (fig. 1). Fig. 12 shows the current and speed waveforms for the transition to the breaking mode and following a sense of rotation reversal from the initial speed approximately 570 min-'.
In the following work, we will focus on tests of this adapting controller structure for the 8kW, 3000 min-' and 4kW, 40 000 min-' motor's. For the high speed motor we are going to determine the limits of this described method including PWM frequency increase with on-off controller as this approach promises a maximal simplicity of the algorithm and minimizes HW demands this way. For the high speed motor, we are not considering the magnetic flux weakening mode at this time.
VI. CONTROLER STRUCTURE DESIGN FOR MAGNETIC FLUX
REFERENCES
WEAKENING MODE
The designed controller structure for the magnetic flux weakening mode is shown on fig. 6 as framed. In this mode the structure is in fact working in the d,q transformed coordinate system. The requested value of the stator current's component iq calculated from the requested torque value from equation (3), the requested value of the id stator's current component effecting the magnetic flux weakening is produced as the controllers output. The controller preserves a steady maximal value of the proportional voltage UR, meaning it preserves the stator' s voltage spatial vector's maximum module. The possible fluctuations of the inverters output voltage UDC is respected by recalculation elements on the PWM modulator inputs. The requested current values iq a id are recalculated to the requested amplitude value of the stator's current II and the
[1] Novak, M. - Cambal, M. - Novak, J.: Application of Sinusoidal Phase Current Control for Synchronous Drives. In ISIE 2006 International Symposium on Industrial Electronic [CD-ROM]. Montreal, Canada: IEEE Industrial Electronic Society, 2006, ISBN 1-4244-0497-5. [2] Cambal, M. - Novak, M. - Novak, J.: Study of Synchronous Motor Rotor Position Measuring Methods. In 13th International Conference on Electrical Drivers and Power Electronics. Zagreb, Croatia: KoREMA, 2005, p. 62-66. ISBN 953-6037-42-4. [3] NOVAK, J. - GREGORA, S. - SCHEJBAL, V.: Hardware for Real Time AC Drive Analyses. International Conference on Electrical Drives and Power Electronics, CD-ROM - T4.3 C14, s. 380 - 383, High Tatras, Slovakia 2003. ISBN 80-89 114-45-4 [4] CEROVSKY, Z.: Power electronics in automotive hybrid drives. 10th International Power Electronics and Motion Control Conference - EPEPEMC 2002, CD-ROM - T5-013, Dubrovnik 2002. ISBN953-184-046-6.
1203
