Recent Developments of Electrical Drives - Part 17 ppsx

SENSORLESS CONTROL OFSYNCHRONOUS RELUCTANCE MOTOR USING MODIFIED FLUX LINKAGE OBSERVER WITH AN ESTIMATION ERROR CORRECT FUNCTION Tsuyoshi Hanamoto, Ahmad Ghaderi, Teppei Fukuzawa and Ter

II-1 High-Frequency Position Estimators 151

By using (36), the high-frequency current vector, observed from the estimated system ( qd) ,

is given by

i dq s ,i(θr , θr , ωi t)= I0+ I1· e j 2( θ r − ˆθ r)

By removing the offset I0 in (40) or in the modulus of the current in (42) and by using the inverse tangent function, the argument of the exponential function in (40) or in (42)

is calculated From this result, the rotor angle can be estimated It follows from I1 in (39) that the higher the value ofL, the higher the resolution of a position estimation, which is

already concluded for an estimator that uses PWM generated pulses

Estimation errors

As mentioned before, in most position estimators the magnetizing current direction is

approximated by the d-axis direction However, for high loads, the controller forces an important stator current along the q-axis This means that the magnetizing current direction deviates from the d-axis Consequently, the model in (22) or (24) introduces an estimation

error Compensating this error is done in [5,6] by measuring the error during the self-commissioning of the drive The error can also be predicted by simulating the drive, modeled with (10), with an estimator that uses a high-frequency voltage pulse train and that is based

on (22) The simulation results as a function ofμ are presented in Fig 5 The error on

θr is zero if the magnetizing current is aligned with one of the magnetic axes The higher

the deviation of i m from the d-axis, the higher the estimation error; an increased error

is shown if saturation becomes more important However, as permanent demagnetization

of the magnets has to be avoided and the stator current has to be limited, the results are meaningful for small deviations ofμ from π/2 only.

Figure 5 Estimation error on the rotor angle of an IPMSM as a function ofμ for various magnetic

states in the case of an approximated magnetizing current

152 De Belie et al.

Figure 6 Estimation error on the rotor angle of an IPMSM as a function ofβ in the case of neglecting

the presence of multiple saliencies

In most estimators the influence of multiple saliencies on the current response is consid-ered as a source of disturbance Simulating an unloaded IPMSM, with (10) and (18), and a position estimator, that uses a PWM generated high-frequency voltage and equation (22), predicts the estimation error Simulation results, based on a multiple saliency as modeled

in Fig 4, are shown in Fig 6 Clearly, the error onθroscillates as a function ofβ.

Conclusions

This paper discusses fundamental equations used in high-frequency signal based IPMSM position estimators For this purpose, a small signal dynamic flux model is presented that takes into account the nonlinear magnetic condition and the magnetic interaction between the direct and the quadrature magnetic axis An addition to the model is proposed to tackle mul-tiple saliencies Using the novel equations some recently proposed motion-state estimators are described It is shown that the higher the inductance difference between the two orthog-onal magnetic axes, the higher the position estimation resolution Furthermore simulation results reveal the estimation error caused by estimators that neglect the presence of multiple saliencies or that approximate the magnetizing current angle byπ/2.

References

[1] M Schr¨odl, Sensorless control of permanent magnet synchronous motors, Electr Mach Power Syst., Vol 22, No 2, pp 173–185, 1994

[2] E Robeischl, M Schr¨odl, Optimized INFORM measurement sequence for sensorless PM synchronous motor drives with respect to minimum current distortion, IEEE Trans Ind Appl., Vol 40, No 2, pp 591–598, 2004

[3] M.J Corley, R.D Lorenz, Rotor position and velocity estimation for a salient-pole permanent magnet synchronous machine at standstill and high speeds, IEEE Trans Ind Appl., Vol 34,

No 4, pp 784–789, 1998

[4] M Linke, R Kennel, J Holtz, “Sensorless Position Control of Permanent Magnet Synchronous Machines Without Limitation at Zero Speed”, Proceedings of the 28th Annual Conference of the IEEE Industrial Electronics Society, Sevilla, Spain, CD-ROM, November 5–8, 2002 [5] C Silva, G.M Asher, M Sumner, K.J Bradley, Sensorless rotor position control in a surface mounted PM machine using HF rotating injection, EPE J., Vol 13, No 3, pp 12–18, 2003 [6] M Schr¨odl, “Zuverl¨assigkeit sensorloser INFORM-geregelter Permanentmagnetmotor-Antriebe im Transient-betrieb bis Stillstand”, Elektrotechnik und Informationtechnik, Heft 2,

pp 48–57, Febuary 2004

[7] U.H Rieder, M Schr¨odl, “Optimization of Saliency Effects of External Rotor Permanent Magnet Synchronous Motors with Respect to Enhanced INFORM-Capability for Sensorless Control”, Proc of the 10th European Conference on Power Electronics and Applications, Toulouse, France, CD-ROM, September 2003

II-1 High-Frequency Position Estimators 153

[8] M.W Degner, R.D Lorenz, Using multiple saliencies for the estimation of flux, position, and velocity in AC machines, IEEE Trans Ind Appl., Vol 34, No 5, pp 1097–1104, 1998 [9] J.A.A Melkebeek, “Small Signal Dynamic Modelling of Saturated Synchronous Machines”, Conf Proc Int Conf El Mach., Lausanne, Switzerland, Part 2, September 18–21, 1984,

pp 447–450

[10] J.A.A Melkebeek, J.L Willems, Reciprocity relations for the mutual inductances between orthogonal axis windings in saturated salient-pole machines, IEEE Trans Ind Appl., Vol 26,

No 1, pp 107–114, 1990

II-2 SENSORLESS CONTROL OF

SYNCHRONOUS RELUCTANCE MOTOR USING MODIFIED FLUX LINKAGE OBSERVER WITH AN ESTIMATION ERROR CORRECT FUNCTION

Tsuyoshi Hanamoto, Ahmad Ghaderi, Teppei Fukuzawa

and Teruo Tsuji

Kyushu Institute of Technology, 2-4 Hibikino, Wakamatsu-ku, Kitakyushu 808-0196, Japan

hanamoto@life.kyutech.ac.jp, ahmad-ghaderi@edu.life.kyutech.ac.jp, tsuji@life.kyutech.ac.jp

Abstract The modified flux observer with an estimation error correct function for the sensorless

control method of synchronous reluctance motor is presented The validity of the proposed method

is verified by experiments The experimental setup is based on the Real Time Linux for operating system and Field programmable Logic Array interface board

Introduction

Recently, a motor control for a motion control is widely used in various industrial applica-tions AC motors are better to be used because they have some advantages, such as easiness

of maintenance In addition, sensorless speed control of the AC motors has been proposed for the demand of the reduction of weight, size, and total cost

Synchronous reluctance motor (Syn.RM) is a kind of the AC motors and has the advantage that it is mechanically simple and robust because they need not the permanent magnet for

a material of a rotor, then many researchers are proposed the sensorless algorithm [1–4]

In this paper, we propose a novel sensorless control method for Syn.RM The sensorless control is based on the modified flux linkage observer, which is proposed by authors for permanent magnet synchronous motors (PMSM) [5] The observer is able to estimate the modified flux linkage and the electromotive force (EMF) simultaneously, and the motor speed and the rotor position are calculated from these estimated values But as same as the other method, the precision of the observer-based estimation is affected by the parameter fluctuations [7] In this paper, we propose the new estimation method for Syn.RM using the modified flux linkage observer with an estimation error correct function A Proportional-Integral (PI) type controller is added to the system to compensate the estimation error It operates that the estimated magnitude of the flux corresponds to the nominal value The high-speed experimental system is required to achieve the proposed method because the observer matrix is changed for every control period and the gains must be recalculated

S Wiak, M Dems, K Kom˛eza (eds.), Recent Developments of Electrical Drives, 155–164.

2006 Springer.

156 Hanamoto et al.

Thus, the experimental setup is based on the Real Time Linux (RTLinux) [8] for operating system The RTLinux is used for achievement of the real time control and it guarantees

to satisfy hard real time constraints in light of maintaining soft real time requirements To acquire the data from sensors and to output the gate signals to the system, the interface board is accomplished designed by the Field programmable Logic Array (FPGA)

The environment of the system development is so convenient and sophisticated to com-bine the RTLinux operating system and the FPGA-based interface board

The validity of the proposed method is verified by experiments

Mathematical model of Syn.RM

Fig 1 shows the mathematical model of Syn.RM, where d , q show the dq axes rotating at

ωe, α, β show αβ axes, u, v, w show three phase axes, θeshows the electrical angle fromα (or u) axis and ωe = dθ e/dt.

The voltage equations of the Syn.RM inαβ axes are described as follows



v α

v β



=





i α

i β



+ PL β



cos 2q e sin 2q e sin 2q e − cos 2q e



i α

i β



(1)

where,v: armature voltage, i:armature current, R: armature resistance, L: armature induc-tance, P: differential operation ( = d/dt), subscript d,q denotes d-axis component, q-axis

component, respectively

Ld , L q are calculated using, L α , L βas follows



L d

L q



=





L α

L β



(2)

q axis

n axis

b axis

a axis

u axis

d axis

w axis

we

we

qe

Figure 1 Analytical model of synchronous reluctance motor.

II-2 Sensorless Control of Syn.RM Using Modified Flux Linkage Observer 157

Equation (1) is rewritten as follows [2] when the de-coupling control for dq axes is achieved

in the speed control system of the Syn.RM



v α

v β



= R



i α

i β



+ P



y α

y β



(3)

where, flux linkage y α , y βare defined as follows,



y α

y β



=



L α + L β cos 2q e L β sin 2q e

L β sin 2q e L α − L β cos 2q e



i α

i β



(4)

Use the well-known relationship described in (5), y α , y βare calculated as follows,

cos 2q e= 2 cos2qe− 1 = 1 − 2 sin2

qe sin 2q e = 2 sin q e cos q e





y α

y β



= L q



i α

i β



+ (L d − L q)



cos q e 0



cos q e sin q e cos q e sin q e



i α

i β



(6) When we set

the flux linkage are described as follows



y α

y β



= L q



i α

i β



+ Y



cos q e sin q e



(8)

Y is able to be treated as a constant because it changes slowly compared with the sampling

period Then the derivative of (8) is

P



y α

y β



=



PLq i α −Y w e sin q e PLq i β Y we cos q e



(9)

In this paper, the EMF of each axis (e a, eb) are determined as the following equation

e α = −Y w e sin q e

e β = Y w e cos q e



Finally, (3) is described as follows

P



i α

i β



=

⎡

⎢

⎣

R

L q

0

L q

⎤

⎥

⎦



i α

i β



Lq



e α

e β



Lq



vα vβ



(11)

This equation is equivalent of the equation for a PMSM [5], then we can also apply the flux linkage observer for the Syn.RM

Sensorless speed control method of Syn.RM

Modified linkage observer with an estimation error correct function

In this chapter, we consider the estimation method of the rotor speed and the position The EMF is assumed that it consists the fundamental component, which rotate the

con-stant angular speed, w and the DC component denoted as follows The DC component is

158 Hanamoto et al.

not necessary in the ideal case, but in the real system this term is very effective for the ripple reduction of the estimated speed calculation



e α

e β



=



A α cos q e + B α sin q e + e α0

A β cos q e + B β sin q e + e β0



=



e α1 + e α0

e β1 + e β0



(12) From (8), the following equation are obtained



y α

y β



=



y α − L qi α

y β − L qi β



=



Y cos qe

Y sin qe



(13) The derivative of the EMF is given by the following equation

P



e α

e β



=



−w2

e Y cos qe

−w2

e Y sin qe



= −w2

e



y α

y β



(14)

But in the practical case, the estimated rotor position has the estimation error, and L d,

Lqare considered as a function of an armature current So, we propose to use the following

equation instead of (14), where K yis a compensation coefficient

P



e α

e β



= −K yw2e



y α

y β



(15) Finally, the voltage equation ofα-axis is written as

where,

x = i α y α e α1 e α0T

⎡

⎢

⎢

⎣

R

L q

− 1

L q

⎤

⎥

⎥

b=

 1

T

To apply the same manner forβ-axis, the flux linkage and the EMF of β phase are also

obtained

How to calculate the coefficient K yis as follows

1 The magnitude of the flux linkage is estimated by

Y =y2

α + y2

2 K y is obtained the output of the PI controller shown in Fig 2 In the figure, the flux

linkage reference Y n is calculated by the nominal values of the inductance and the d-axis reference i∗

d

Yn = (L d − L q )i∗

3 For every control period, K Y in (17) is recalculated

4 K is convergence to the appropriate value after several iterations

II-2 Sensorless Control of Syn.RM Using Modified Flux Linkage Observer 159

Figure 2 Estimation error correct function.

The flux linkage and the EMF are estimated directly applying the full order observer to (16) The speed referenceω∗and the voltage referencev∗

αare used instead ofωeandvαbecause these values are not measured in this system

To convert the discrete time system at control period T s, the following equation is obtained

x(k + 1) = (A d − g d c d ) x(k) + b d v∗

α (k) + g d i α (k) (20)

where,

A d = e −AT s

b d =

 T s

0

e A τ d τ · b

g d = ( g1 g2 g3 g4)

c d = ( 1 0 0 0 )

g dis the observer gain in the discrete time system We select the observer gains to have all

of the poles of ( A d − g d c d) on the real axis in unit circle as the multiple poles

In the proposed method, A d is changed because K Yis calculated for every control period and it is also the function of the speed reference Though the online calculation is required

to convert the discrete time system and calculation of the observer gains, the computer technology able to achieve the calculation within 200μs

Speed and position estimation

The estimated speed w eare obtained by the following equation A low pass filter (LPF) is

added after the output of w ein the experimental system

we=e β1 y α − e α1 y β

y2

α + y2

β

(21)

Since it is enough to estimated the sin q e and cos q e instead of the rotor position (q e) itself, then

sin q e=  y β

y2

α + y2

α

, cos qe y α

y2

α + y2

α

(22)

160 Hanamoto et al.

Experimental results

Experimental setup

To realize the validity of the control theory, there is a need for an appropriate operating system that could operate in real time The PC-based control offers great advantages like

a faster design cycle and increased productivity [6] Here, we refer to the real time system based on the RTLinux [8]

The RTLinux is a hard real time operating system that handles time-critical tasks and runs the normal Linux as its lowest priority execution thread Then the system includes the networking, GUI programming, and several other function

We can construct the PC-based experimental setup which includes not only the control program but also the user GUI, for example, data entry windows of the reference, controller gains, and so on Fig 3 is an example of the GUI using RTiC-Lab [9], which is a semi-detached open source software designed to run on the RTLinux

From the viewpoint of the hardware, the digital servomotor control system requires

a speed detector, a position detector, both for reference, the PWM pulse generator, and the interface circuit In this paper, we designed the interface circuit board, which in-cludes all of the necessary functions Fig 4 shows the interface board that consists

of the Field programmable Logic Array (FPGA), 10 MHz system clock, and an A/D converter

An Altera FLEX10K50 is selected for the FPGA device and the circuit is designed using the VHDL, which is one of the hardware description languages The speed and

Figure 3 GUI controller using RTiC.

II-2 Sensorless Control of Syn.RM Using Modified Flux Linkage Observer 161

Figure 4 Interface board using the FPGA.

position detectors with speed correction function, clock generator for A/D converter, and ISA interface circuit are designed in it

Fig 5 shows the configuration of the experimental system consists of the RTLinux-based

PC, an inverter, an interface board using the CPLD device, and the tested motor Table 1 shows the specification of the tested motor

Experimental results

Figs 6 and 7 show the ramp response where the speed command is changed from 500 to 1,500/min Fig 6 shows the results when the sensor is used for the speed control Here, the dashed line shows the estimated speed and the solid line shows the speed calculated by the

Figure 5 Configuration of the system.