DSP-Based Sensorless Speed Control Drive System ...

DSP-Based Sensorless Speed Control Drive System for Two-Phase Synchronous Motors Saleh Ziaeinejad, Younes Sangsefidi, and Ali Mehrizi-Sani

Abbas Shou1aie

School of Electrical Engineering and Computer Science

Department of Electrical Engineering

Washington State University

Iran University of Science and Technology

Pullman, WA, 99164

Tehran, Iran, 16846-13114

Email: {saleh.ziaeinejad, younes.sangsefidi}@wsu.edu; [email protected]

Email: [email protected]

Abstract-A basic direct torque control (DTC) drive system

enables effective control of stator flux modulus and electromag­

netic torque. This high performance method can be further improved to a sensorless speed control method, which adjusts the stator flux modulus and motor speed. Based on the DTC method, this paper proposes a sensorless speed control drive system for two-phase synchronous motors. The block diagram of the two-phase sensorless speed control drive is proposed. The small-signal model of the system is then derived based on the proposed block diagram of the system. Based on the small-signal model of the system, the phase margin and crossover frequency of the gain of the control loop are calculated and then used for the design of the speed controller. The design process of the speed controller is verified using Bode plot. The effectiveness of the proposed two-phase sensorless speed control drive system is validated by an experimental setup using a TMS320F2812 digital signal processor (DSP).

I. INTR OD UCTI ON A two-phase synchronous motor presents attractive features such as simple and robust structure, high torque density, and high efficiency [1], [2]. Line-start, two-phase synchronous motors [3] are of special interest because they can operate either in constant speed mode while being supplied by a single phase grid or in variable speed mode while being supplied by a two-phase inverter [4]. To have an adjustable speed control drive system, the control algorithm of the drive system should be augmented with a speed control loop as an external control loop [5], [6]. This speed control loop requires the data of the motor speed, which might be measured using a mechanical sensor. However, the cost of employed mechanical sensor, required signal conditioning circuit, and necessary mechanical mount­ ing makes a mechanical sensor-based approach an expensive solution for the industry. In addition, using a mechanical sen­ sor necessitates data transmission between the sensor mounted on the motor shaft and the controller which might be far from the motor. This data transmission can be adversely affected by the noise produced by the motor or its environment [7]. As an alternative to mechanical sensor-based speed control drive systems, sensorless speed control drive systems are proposed in the literature [8]. The attempt of sensorless speed control schemes is to derive the motor speed by processing the electrical waveforms of the electric motor. The elimination of the mechanical sensors results in reduced cost of the drive system, immunity of the drive system against the noise, possibility of motor control from long distances, and increased

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reliability [7]-[12]. These advantages have made sensorless speed control drive systems attractive for the industry. In general, current control or direct torque control (DTC) methods are used to control a two-phase synchronous mo­ tor [1], [13]. A current control drive system requires the data of the rotor position for its control system. However, a DTC drive system, which enables fast and independent control of the electromagnetic torque and stator flux modulus, can be implemented without a mechanical sensor [1], [14] because it measures and controls the motor variables in the stationary reference frame. Therefore, a DTC drive system is advanta­ geous because of its lower cost and higher reliability [15]. To augment a basic DTC method with a sensorless speed controller, the motor speed can be estimated using the esti­ mated stator flux vector [5], [6]. A DTC drive system mea­ sures both the angle and the modulus of the stator flux vector. By calculating the rate of the change in the angle of the stator flux vector, the speed of the rotating field can be calculated. In steady-state operation of a two-phase synchronous motor, the rotor speed equals the rotating field speed [5]. Therefore, in a DTC-based sensorless speed control drive system, the stator flux-based estimator can reliably calculate and control the steady-state motor speed. Common structures of two-phase inverters are studied in [1], [11]. A two-phase inverter can be implemented in two­ leg, three-leg, or four-leg configurations. All of these configu­ rations can be used in a sensorless speed control drive. Among these configurations, the two-leg configuration proposes the lowest cost; however, the four-leg configuration proposes the highest performance and the maximum AC voltage from a specific DC link voltage. The optimum selection of the inverter configuration depends on the cost limitation and the required performance of the drive system. This paper proposes a DTC-based sensorless speed control drive system for two-phase synchronous motors. This drive system estimates the motor speed by calculating the rate of the change in the stator flux angle. The small-signal model of the system is derived. Based the small-signal model, the phase margin and the crossover frequency of the system loop gain are calculated and then used in the design of the speed controller. The design of the speed controller is verified using Bode plot. A DSP-based experimental setup is implemented to validate the proposed DTC-based sensorless speed control drive system.

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This paper is organized as follows. Section II proposes the structure of the sensorless speed control of a two-phase synchronous motor based on the basic DTC. Section III gives the small signal model and the transfer functions of the drive system to design the speed controller. Sections IV and V include the experimental results and conclusions.

Two-Phase Voltage Sourced Converter

II. SENS OR LESS SPEED C ONTR O L OF A TWO-PH ASE S YNCHR ON O US M OT OR

A basic two-phase DTC drive system monitors the applied voltage vectors and the measured motor currents to estimate the stator flux vector and the electromagnetic torque based on the analysis in the stationary reference frame. Based on the outputs of the hysteresis controllers, a DTC drive system applies the voltage vectors to decease the difference between the estimated stator flux modulus and electromagnetic torque and their reference values. The stator flux and electromagnetic torque of a two-phase synchronous motor can be estimated as [1], [16]

Fig. l. Proposed block diagram of sensorless speed control drive for a two-phase synchronous motor.

WS,

drive system estimates and controls which results in rotor speed control in steady state conditions [5]. From (3) and (5),

Ws

s

1 dB

d

(tan-1 (�))

D s - QS (Abs+Abs) ADs(VQs - RiQs) - AQs(VDs - RiDs) (Abs+Abs) VQs VDs =

Pdt

1

=

\ /\

P

dt

dAQ8

----;[t

\ /\

dAn.,

----;[t

P

vQs, VDs, iQs, iDs, AQs, ADs, AQs It=o' ADs It=o As, is, rs,

and where are the components of stator voltage, stator current, stator flux, and initial stator flux in Q and D axes. Te, and P are the electromagnetic torque, stator flux vector, stator current vector, stator resistance, and the number of motor pole pairs. A Basic DTC synchronous motor drive system does not directly control the motor speed. To control the motor speed, the reference value of the electromagnetic torque should change in a way such that the rotor speed always tracks the reference speed regardless of the load behavior. To have a speed sensorless method, the motor speed is estimated by finding the rate of changes in the angle of the stator flux vector [6]. The mechanical speed of the stator flux vector can be expressed as

1 Bs Ws Pdt W1" B1', 5 d

1

=

=

d

P dt (B1'+5)

s

=

W1'+ P1 d5 dt

'

(5)

where and are the mechanical speed of the rotor, rotor flux angle, and load angle. B is the angle of the stator flux vector, which can be represented by

s

B

Ws

=

QS) tan-1 (AADs ' W1"

(6)

In steady state conditions, the load angle settles down to a constant value, and equals The sensorless speed control

(7)

P

In (7), might change anytime that a switching and action happens. Therefore, the estimated speed includes high­ frequency ripples, which adversely affect the speed control system. To reduce this effect, the speed estimated from (7) should be filtered by a low-pass filter. Cut-off frequency of the low-pass filter should be much lower than the switching frequency. To adjust the motor speed, the filtered estimated speed is compared with the reference speed. Based on the speed error, a Proportional-Integral (PI) controller sets the reference value of the electromagnetic torque. DTC method regulates the electromagnetic torque by using a hysteresis controller. The structure of the hysteresis controller depends on the structure of the two-phase inverter used to control the two­ phase synchronous motor. Fig. 1 shows the block diagram of the proposed sensorless speed control drive for a two-phase synchronous motor. III. DESIGN OF SPEED C ONTR O L LER IN THE PR OP OSED SENS OR LESS SPEED C ONTR O L DRI VE S YSTEM

The control loop of the motor speed includes the controller, DTC-based drive system as the plant, and low-pass filter to eliminate high frequency oscillations of the estimated speed. The transfer functions of the controller and the low-pass filter are assumed Gc(s) and HLP(S). The transfer function of the plant, which relates the motor speed to the reference electromagnetic torque, can be considered as the product

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Fig. 3.

Fig. 2.

Test setup configuration and laboratory setup.

Small signal model of the speed control loop.

design of the speed controller can be ignored (COTe(s) '::0 1). In addition, the cut-off frequency of the low-pass filter, which is less than the switching frequency of the drive system, is much larger than the crossover frequency of the speed control loop. Therefore, the effect of the low-pass filter on the design of the speed controller can also be ignored (HLP(s) '::0 1). Consequently, using a PI controller with Kp and KJ gains i.e., Cc(s) the loop gain T(s) and the closed­ loop transfer function CW (s) of the speed controller can be derived as

(

of COTe(s) and CL(s): COTe(s) is the transfer function of DTC method, which relates the electromagnetic torque to its reference value, and Cds) is the transfer function of the motor load, which relates the motor speed to the electromagnetic torque. In what follows, q and ij are the actual value and the small signal variation of a generic quantity q around its equilibrium point 1j. Fig. 2 shows the small signal model of the speed control loop including the controller Cc(s), the plant CoTe(s)Cds), and the low-pass filter HLP(S). In this model, Cds) can be derived using the relationship between the motor speed and the electromagnetic torque, which is

T(s)

=

=

A

where

dWr J ----;]I +(Fr+ f' ) Wr

dWr , J ----;]I +Frwr) A

A

=

=

(9)

T and wr are torque and speed variations around

the nominal point, f' i;L. is the slope of the speedWe torque characteristics of the load at the equilibrium point, and F; Fr + f' is the linearized equivalent friction factor. Ignoring the small difference between and Wr, =

=

Ws

CL(s)

�s(s) =

Te(s)

'::0

�r(S) Te(s)

=

1 Js+F:

(0)

In Fig 2, the torque controller is much faster than the speed controller. Therefore, the effect of the torque controller on the

KpSs+K/),

Cc(s)CoTe(s)Cds)HLP(S)

=

ws (s) w;(s)

=

'::0

Kps+KJ . Js2+F:s

Kps+KJ Js2+(F:+Kp)s+K[·

(1)

(2)

The proportional and integral gains of the controller can be designed based on desired specifications for the loop gain T(s). Based on (1), the crossover frequency Wcg and the phase margin PM of the loop gain can be calculated as

Wc

g

j

= .

PM

=

_(F:2 _ Kp2)+ (F:2 _ Kp2)2+ 4J2K[2 2J2 90+

tan-1

(K��cg )

1 - tan-

(J;t )

(13)

.

(14)

In Section IV, the speed controller is designed for a case study. The design is then verified using Bode plot.

=

Te

=

CW (s)

(8) where TL is the load torque, J is the moment of the inertia of the system, and Fr is the coefficient of friction. Using the small signal variations the motor variables around their equilibrium point (Te Te + Te) TL TL + TL) and Wr wr+wr ) the small signal model of the relationship between the motor speed and the electromagnetic torque can be expressed as

=

IV. EXPERIMENTA L RES U LTS To evaluate the proposed drive system and the designed controller, a DSP-based sensorless speed control drive system is set up in the laboratory. A 2 kW two-phase synchronous motor with parameters mentioned in Table I is used. Fig. 3 shows the configuration of the implemented setup. The core of the setup is a TMS320F2812 DSP. A two-phase, four-leg inverter supplies the motor. The inverter is made up of two intelligent power modules (IPM). A DC generator is used as the load. An external mechanical speed sensor is used to validate the correctness of the estimated speed. The variables are monitored using a USB-4711A data aquisition module. In the design of the speed controller, it is assumed that the controller does not have a proportional (P) component; thus, it presents a smooth output regardless of the fluctuations of the

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i:rITrr±±miuum � ..,� Q5

a

1.5

2

�5

Time(s) (a)

200 150 E' 5100 18 50

3

15

4

We_

�5

5

0.5 E' b

i2

a

*

�

a

5

Time(s) (e)

2

2.5

Time(s) (b)

3

3.5

4

4.5

........, 1

� , -w 0.5

1

:

':

:

.

1.5

2

:

:

2.5

Time(s) (d)

3

4

: :

: :

:

3.5

4.5

a

0.5

1.5

2

2.5

Time(s) (I)

3

3.5

5

A' -- AQ'

'

!-:�m

Time(s) (e)

5

:� a

:[

1.5

4

4.5

5

Fig. 5. Experimental results of the proposed drive system during the start-up process; (a) rotor speed and its reference value, (b) estimated stator flux speed, (c) filtered stator flux speed, (d) reference torque, (e) actual torque, and (f) stator flux components.

Fig. 5(b) shows the estimated speed calculated by the drive system, which contains large ripples. Fig. 5(c) shows the filtered estimated speed. Figs. 5(a) and 5(c) show that after filtering, the estimated speed is very close to the measured speed. In steady-state, estimated and measured speeds are equal. In the experiments, the speed sensor is used to validate the performance of the speed estimator, and is not used for control purposes. Figs. 5(d) and 5(e) show that the electromagnetic torque effectively tracks its reference, and the dynamics of the torque controller (inner loop) is much faster than that of the speed controller (outer loop). The control system also regulates the stator flux modulus to the reference value (1 wb).

50

�

2

o -50

I:l i.�. ··1 -180

_I

Fig. 4.

I

0

10

W

10

Frequency (rad/s)

2

W

3

10

Bode plot of the loop gain of the speed controller. TA B LE I

PARAMETERS OF THE TWO-PHASE SYNCHRONOUS MOTOR [1] Stator resistance d-axis inductance q-axis inductance Poles Rotor flux Rated power motor inertia linearized equivalent friction factor

Fig. 6 shows the behavior of DTC-based sensorless speed control of the two-phase synchronous motor, when the refer­ ence speed frequently changes. The control system effectively tracks both increase and decrease of the reference speed. Also, it effectively controls the stator flux modulus and the electromagnetic torque.

4.5 S1 323 mH 110 mH 2 pairs 1 wb 2 kW 0.0343 kg .m2 0.255

kg.m2 s

V. C ONC L USI ON

input, which eliminates the need to a filter. To have a fast and stable response, a phase margins close to 60° is appropriate. In the case study, the integral gain of the controller k I is set d to 1, which leads to the crossover frequency 3.5 r� and the phase margin 64.5°based on (13) and (14). Fig. 4 shows Bode plot of the loop gain, which verifies the controller design. Fig. 5 shows the performance of the proposed drive system during the start-up process with a 150 rpm reference speed.

In this paper the theory of previously presented two-phase DTC synchronous motor drives is studied and based on this theory, a sensorless speed control drive system for two-phase synchronous motors is proposed. By deriving and linearizing mathematical model of the system, small signal model of the system around the nominal point is found. Phase margin and crossover frequency of the speed controller are calculated and verified for a case study using Bode plot. Using a DSP-based experimental setup, the effectiveness of the proposed drive system is validated. The motor speed effectively tracks its

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400 .s200

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: : : � ........ � ........ ..: ' : ' ': .......... :, ......... . :

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:

.•. I

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' .......... :

-1

Fig. 6. Experimental results of the proposed drive system with frequent changes in the reference speed; (a) rotor speed and its reference value, (b) estimated stator flux speed, (c) filtered stator flux speed, (d) reference torque, (e) actual torque, (f) stator current, (g) stator flux, and (h) stator flux locus.

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