DSP Based Implementation of Sliding Mode Speed

DSP Based Implementation of Sliding Mode Speed Controller for Direct Torque Controlled PMSM Drive Bhim Singh, B.P. Singh and Sanjeet Dwivedi Department of Electrical Engineering, Indian Institute of Technology, Hauz Khas, New Delhi, India- 1 10016 E-mail- bsinghgee.iitd.ac.in, bpsinghgee.iitd.ac.in and sanjeetkdggmail.com Abstract- This paper deals with the DSP based implementation

of a Sliding Mode (SM) speed controller for Direct Torque Controlled (DTC) Permanent Magnet Synchronous Motor (PMSM) drive. The drive system consists of power circuit and control hardware. The former has insulated gate bipolar transistor (IGBT) based voltage source inverter (VSI) and gate driver circuit, while the latter has voltage and current sensors and their interfacing circuits. The rotor speed estimation from the sensed position signals, SM speed controller, torque, flux, and sector estimator and optimum voltage vector selection table for gating pulse generation of VSI are implemented in assembly language of DSP-ADMC401. The simulation model of the PMSM drive system is developed in MATLAB environment with simulink and PSB toolboxes to analyze the performance of the proposed drive system. The simulated performance of SM speed controlled PMSM drive is validated with the test results for starting, speed reversal, load perturbation and steady-state operating conditions.

I. INTRODUCTION Availability of fast digital signal processors (DSPs) and new digital control techniques together with the improvement in high power solid-state devices, have significantly contributed towards the development of high performance Permanent These PMSM Magnet Synchronous Motor (PMSM) drives. drives are meeting the requirement ofr1-1 high operational efficiency and small size. The permanent magnets develop air gpaei , results in gap magnetic flux without external excitation, which 1n higher efficiency of the PMSM drive and smaller size helps in giving fast dynamic response in variable speed drive (VSD) [14]. Unlike the induction motors, which can run with fixed frequency AC mains, PMSM needs,y betwe en frequency AC m ains, PMSM needs synchronization the frequency of AC excitation source and the position of the rotor magnets for the self controlled mode. Takahashi et. al. [5] and Depenbrock [6] have pioneered the application of the DTC scheme for the control of induction motors in the mid of 1980's and since then it is becoming popular due to its attractive features of simple control and easy implementation. For high performance operation and control of PMSM, many researchers have explored the desirability of using DTC scheme [7-8]. The DTC scheme has advantages over the vector control, as it is relatively simple and robust owing to the absence of PWM current controller. In addition it is less sensitive to external disturbances, needs no reference frame transformation, as it needs only sector wise rotor position information, and most importantly, it has good dyai repos [59] Moevr moencnrlagrtm such as switching hyperplane based sliding mode control [10wc

1-4244-0726-5/06/$20.OO '2006 IEEE

r

s

14] have been used for motion control to achieve high level of

performance of different electric motor drives. In this work, a Sliding Mode Control

(SMG)

based speed

controller is implemented for direct torque controlled PMSM drive. It uses minimum number of components employing a dedicated motion control DSP ADMC40 1 developed by Analog Devices (AD) for Power Electronics applications [15].

DTL based M ode of the conter reth DTCbasedPMSMdrive is developedandthe simulatedresults are validated with test results obtained from the DSP based control of PMSM drive system. II. OPERATING PRINCIPLE OF SMC BAsED DTC-PMSM DRIVE SYSTEM Fig. 1 shows the basic building block of the DTC based PMSM drive. In this drive, a direct torque and flux control method is used to control the speed of PMSM. The drive consists of SMC speed controller, torque and flux comparators, optimum voltage vector selection table, resolver Sin and Cos position signals demodulation circuit, current sensors, voltage sensors, based voltage source inverter and PMSM. The rotorIGBT speed iS compared with the(VSI) reference speed w i ( eerror i speed (,e) iS processed the SMC speed . * This which the reference controller, torque (Tk*). reference isgenerates limited using a limitertorque and the limited reference torque (Tref) is used to generate the torque error by comparing it with the estimated torque of the motor (Test).

(Wsr)

Similarly,'se flux reference q'

is obtained from the rotor speed (Cor) of the motor and it is compared with estimated stator flux of the motor Both torque error (AT ) and flux error (A,o) signals are used to determine the optimum switching vectors. In response to these signals, the VSI controls the winding currents of PMSM, thereby controlling the speed of the motor in the desired manner. The estimator block is used to estimate stator flux linkages in stationary reference frame and developed electromagnetic torque of PMSM. The input to the estimator are the dc link voltage (vd ), two phase currents of

POs.

tn a VSI obtained by optimum voltage vector selection table shown in Table-I. The phase voltages ofthe PMSM are obtained from the switching status of VSI and dc link voltage. These phase voltages and winding currents are used to estimate the flux and torque ofthe motor.

1301

After limiting the output of the SM controller T

TABLE-I

SWITCHING TABLE FOR SELECTION OF INVERTER OPTIMUM VOLTAGE

Flux

VECTOR

Torque [

Error

Error

*

IIIV 1

0

is taken as

. referencetorque T toqe (ret) Where C3 and C4 are gains of sliding mode controller

Sector

dTE

d(p,

(k)

V

Y (k) nd2(k) 1and

VI

±1 if ZX

Y

l(k)=+

1

V2

V3

V4

V5 lV6

V,

O

v, 0 V8V7v,

v, V8

v, V7

v, V8

V7

Y

-1

V6

V1

V2

V3

V4

V5

and, y2

I

V3

V4

V5

V6

V1

V2

0

V7 vl

V8 0

V7

V8

V7

V8

can be

>0

given as:

X(k)20

i

l1(k) =- if ZX 1(k) 0) which is given in eqn. (6). B Field Weakening Controller Below the base speed the reference value of the stator flux linkage is considered as:

The various components used in the SM speed controlled DTC based PMSM drive system are shown in Fig. 1. The modeling equations for the different blocks, which include SMC speed controller, field weakening controller, flux and torque hysteresis comparators, estimators, IGBT based VSI (8) and Permanent Magnet Synchronous Motor (PMSM) are given fsref = Cc in this section as per following modeling equations. The reference value of the stator flux linkage above based speed is considered as the function of rotor speed as: A. Sliding Mode Speed Controller (9) For obtaining robust performance of the PMSM drive with sref = Voc(Ob/ ) se parameter variation and load torque disturbance, SMC speed is the rated flux, ris base speed and or is the controller is used to stabilize the set point by forcing the drive Where response along a predefined trajectory in a phase plane using a rotor speed of the motor. switching control algorithm. The schematic block diagram of Hysteresis Comparators the SMC speed controller is given in Fig.2a and its phase plane C. Torque and The estimated stator flux linkage and torque are used as trajectory is shown in Fig.2b. The sliding mode speed controller is described by the following equations. feedbacks to compare with their reference values. The torque error and flux error are fed to the hysteresis band controller used for selecting the appropriate voltage vector according to Speed error can be given as: * (1) table of optimum switching (TOS) given in Table-I. The flux X1-o) r(k) r(k) error is given as: The rate of change of speed error can be given as: are -T Ao=Q sref (Os and torque error ATeT d e ref dest X2 =-X1 (2) the output signals of hysteresis comparator. Where Test is the dt * of the estimated value of the torque. The output of hysteresis sliding mode controller can be controller can be defined as the following set of equations. The control output T (k)

IOr

Flsuxr

given as: (k)

If 3

1(k) 1(k)

4

2(k) 2(k)

(3)f 1302

sref _-

Aqs then

dps =0

(10)

then

dq5 =1

(11)

Ps>/\P

Phse Flux 50 Hz, AC Hysterisis Supply

v

Bridg

r

Rectifier

stationary reference frame. The flux estimator provides stator flux linkage in the stationary reference frame (x and ,B) coordinates as:

Vd

dt Pa =(va-Ria) fZ fo= C V -Ri )dt

ControllerVoltage SI

Sliding Mode

d r

Controller

selection

l

_ 1 r

ALSorque

7; 1 a

(or

Torque

r

Speed

Crque,rS

ia

b

sSpeed

and ~~Flux ~~~~~~~~~~~~~~~~~Secto

Estimator

Where va,

Load

P

(A'

r

va

p

i

w

i

can be

obtained from the

-(vb+vc);

P

(17)

(1 8) ia -(ib + iC); ip=(ib_043 |The estimated stator flux-linkage modulus can be expressed as: Q~ +q# (1 9)

CA

ii) Estimation of Developed Torque The developed electromagnetic torque by the PMSM can be estimated from the stator flux linkages and currents in

Fig.2a Schematic block diagram of sliding mode speed controller A K1

stationary reference (a and ,8 ) frame as:

x

t=

L im it lin e

OP2)2

Where, P is the number of poles.

x

A c tu a

T ra je c to ry o n

t= t1

iii) Estimation of Sector-wise Location of Stator Flux Linkage Vector

s lid in g lin e

Fig.2b Sliding mode state trajectory in phase-plane

If T

vp and

stationary reference frame transformation from three phase voltages and cufrents as:

*

_i

If T

(16)

>

Fig.1 Block Diagram of Sliding Mode Speed Controller Based Direct Torque Controlled PMSM Drive

-

(15)

ref

\f3 and y >O,then Sector--I (21) 0a

If T -T >A|Te| then dTe=1 (14) e e y Vvdc (2 a (38) phase winding currents. The current in the third phase is va b) generated internally in the software from these current values. The dc link voltage is sensed using a Hall effect voltage sensor. The output of the voltage sensor is scaled in the same vdc (2 S S S (39) (39) proportion to give signals in a range of 0 to ± 2V. vb= C dc J(2Sb~Sa~ c) (28)

vd =Rid +P (od 0r (oq

1(O =

modeltequanertions ofefolelowingfirst

requationsgas

as:) tr=a osfo -tSinO

idCos(OrA2t/3).dqSin(OrA2t/3)

,

v =| dc 12-S-)(40) c C 3 ca

Software Implementation ~~~~~~~~~~~~~~B.

The control the sliding controller direct torque algorithm controlled of PMSM drive mode systemspeed is developed ~~~~~~~~~~~for

1304

in the assembly language of DSP ADMC40 1. The rotor position, speed and direction are calculated from the demodulated output of resolver Sin and Cos signals. The error between the reference speed and estimated speed is processed in the sliding mode speed controller and the output of speed controller is used as the reference torque and is limited within a specified value. The estimation algorithm is used to estimate the developed torque of the motor, stator fluxes in stationary reference frame, absolute magnitude of the stator flux, sector wise location of the stator flux linkage. The three level torque and two level flux hysteresis comparators are used to compute the torque and flux errors. Depending upon the error level of these comparators and sector information of stator flux linkage, the table of optimum voltage vector selection is used to select the switching signals for IGBT devices of VSI.

Quadrature axis

v3(010)

V (110) Secto

21

v4(011)

*

ector I \ Sector I

/

Sector 111 ii

Sector III

Sector IV

V1(loo) Direct axis

Sector VI

\#t Sector V

\/

~~~~~V6(101)

v5(001)

Fig.3 Sector of Stator Flux Linkage Space Vector

Single-Phase AC

Single-Phas-

gS---sL---,Sl H

L

SupplAC-DC Converter

S

:vsi

et

c:ud

CircutfoIGBa

bc

V I

l,-> ,

2

l

Gate driver

)

--

7

Sinand ResolSverSgnl PWMPort ~~~~~~~~~~~~~~Co Digital Demodulator Circuit A

Digital

DAC

Storage

DSP

Gate Pulses

A

D

SinC

ADMC-401

co

Vdcse

C

_

ry

Fig.4 Experimental Setup of Sliding Mode Speed Controller based Direct Torque

Controlled PMSM Drive.

Di-crtesystemy |

HyFte-is

Ts =5e-006

Controller

*WeFlu.in

Two

VSI

Flu.

Slidi|g

VVlttg_

Mode

m

Totque