Power electronic handbook

Подождите немного. Документ загружается.

1028 B. Karanayil and M. F. Rahman

TDL

LIM

−

(k)

dq*

(k)

ANN

∆w

(k)

REF.

MODEL

∆w

(k)

1/Z

∆w

(k−1)

∆w

(k−1)

1/Z

(k)

CURRENT

CONTROLLED

INDUCTION

MOTOR

ANN

∆w

(k)

∆w

(k−1)

(k)

1/Z

FIGURE 36.28 Adaptive speed control of the induction motor using ANN.

ANN

Flux weakening

Zero

detector

Moving

Average

Filter

Reset

Integrator

Input scaling

Enable /

Reset

ANN Efficiency Optimization System

Output

scaling

∆P

(k)

−1

(k)

∆c(k−1)

∆c (k )

∆C(k )

(z−1)

C(k )

Excitation

flux

C(k )′

C(k )

−1

∆w

(k)

+ z + 1

−1

(k)

FIGURE 36.29 Induction motor efﬁciency optimizer using ANN.

36 ANN Applications in Power Electronics and Electrical Drives 1029

36.4.3 Efﬁciency Optimization in Electric Drives

The efﬁciency improvement of induction motor drives via

ﬂux control can be classiﬁed into three groups: pre-computed

ﬂux programs, real-time computation of losses, and on-line

input–output efﬁciency optimization control. All of these

methods target choosing a value of the motor excitation that

optimizes the motor-converter losses. The main requirement

of an input–output optimization is to achieve the ﬂux opti-

mization in a minimum number of search steps. A constant

search step may take too long if the step is too small, or it

may bypass the minimum power input if the step is too large.

For each mechanical operating point of the motor, it is pos-

sible to ﬁnd a combination of rotor ﬂux linkage and torque

producing current i

at which the dc link power P

to the

drive system is minimum.

One of the possible ANN efﬁciency optimizer reported

is shown in Fig. 36.29. An ANN-based search algorithm is

employed to operate as an efﬁciency optimizer. The inputs to

the system are the dc power fed into the drive system at instant

k, and the change in the control variable at the previous instant

c(k−1). The only output is the actual change in control vari-

able c(k). Appropriate scaling from engineering units to the

normalized interval [−1, 1] are implemented by the input and

output interfaces, input scaling (IS) and output scaling (OS).

The speed signal is used to generate the reference ﬂux C(k)

corresponding to each speed. The mechanical steady-state is

detected by applying a moving average ﬁltering to the speed

Denormalization

Normalization

UP/DOWN

COUNTER

∑

Angle

subnet

Amplitude

subnet

V *

1,1

20,1

1,1

f (V *)

s/2

4,20

(a*)

+WT

s/4

A–ON

= f (V

)* g(a *)+WT

s/4

A-ON

B-ON

C-ON

FIGURE 36.31 Neural network topology (2 × 20 × 4) for PWM wave synthesis.

variation ω

. The ANN efﬁciency optimizer is enabled only

during the mechanical steady-state.

36.5 ANN-based Controls in Power

Converters

A feedforward ANN can implement a non-linear input–output

mapping. A feedforward carrier-based pulse-width modu-

lation (PWM) technique, such as space vector modulator

(SVM), can be looked at as a non-linear mapping where the

command phase voltages are sampled at the input and the cor-

responding pulse-width patterns are established at the output.

Figure 36.30 shows the block diagram of an open-loop V/f-

controlled induction motor drive incorporating the proposed

Space Vector

PWM

(ANN based)

∫

PWM

Inverter

Induction

Motor

= 0

FIGURE 36.30 V/f control of induction motor using ANN-based SVM.

1030 B. Karanayil and M. F. Rahman

ANN-based SVM controller. The command voltage V

∗

(=V

∗

)

is generated from the frequency or speed command, and the

angle command θ

∗

is obtained by integrating the frequency,

as shown. The output of the modulator generates the PWM

patterns for the inverter switches.

The ANN can be conveniently trained off-line with the data

generated by calculation of the SVM algorithm. The ANN has

inherent learning capability that can give improved precision

by interpolation unlike the standard lookup table method.

Figure 36.31 shows such an SVM that can operate during

both undermodulation and overmodulation regions linearly

extending smoothly up to a square wave. The SVM is imple-

mented using two subnets: angle subnet and amplitude subnet.

The subnets use a multiplayer perceptron-type network with

sigmoidal-type transfer function. The bias is not shown in the

ﬁgure. The composite network uses two neurons at the input,

20 neurons in the hidden layer, and four output neurons.

The input signal to the angle subnet is θ

angle which is nor-

malized and then pulse-width functions at unit amplitude are

solved (or mapped) at the output for three phases, as indi-

cated. The amplitude subnet implements the f (V

∗

) function.

The digital words corresponding to the turn-on time are gen-

erated by multiplying the angle subnet output with that of

the amplitude subnet and then adding the T

/4 bias signal,

as shown. The PWM signals are then generated using a sin-

gle timer. The angle subnet is trained with an angle interval

of 2.16

◦

in the range of 0–360

◦

. Due to learning or interpo-

lation capability, both the subnets will operate higher signal

resolution. A sampling interval T

of 50 µs corresponds to a

switching frequency of 20 kHz and a 100 µs that corresponds

to 10 kHz.

Further Reading

1. P. Vas, Artiﬁcial Intelligence-Based Electrical Machines and Drives: appli-

cation of fuzzy, neural, fuzzy-neural and genetic-algorithm – based

techniques, Oxford University Press, New York, 1999.

2. B.K. Bose, Modern Power Electronics and AC Drives, Prentice Hall,

New Jersey, 2002.

3. L. Ben-Brahim, S. Tadakuma, and A. Akdag, “Speed control of induc-

tion motor without rotational transducers,” IEEE Transactions on

Industry Applications, vol.35, no.4, pp. 844–850, July/August 1999.

4. M.G. Simoes and B.K. Bose, “Neural network based estimator of feed-

back signals for a vector controlled induction motor drive,” IEEE

Transactions on Industry Applications, vol.31, pp. 620–629, May/June

1995.

5. K. Funahashi, “On the approximate realization of continuous map-

pings by neural networks,” Neural Networks, vol.2, pp. 183–192,

1989.

6. D.T. Pham and X. Liu, Neural Networks for Identiﬁcation, Prediction

and Control, Springer–Verlag, New York, 1995.

7. M. Wishart and R.G. Harley, “Identiﬁcation and control of induc-

tion machines using artiﬁcial neural networks,” IEEE Transaction on

Industry Applications, vol.31, no.3, pp. 612–619, May/June 1995.

8. K.S. Narendra and K. Parthasarathy, “Identiﬁcation and control of

dynamical systems using neural networks,” IEEE Transactions on

Neural Networks, vol.1, no.1, pp. 4–27, March 1990.

9. J.O. Pinto, B.K. Bose, L.E.B. De Silva, and M.P. Kazmierkowski,

“A Neural-Network based Space-Vector PWM Controller for

Voltage-fed Inverter induction motor drive,” IEEE Transactions

on Industry Applications, vol.36, no.6, pp. 1628–1636, November/

December 2000.

DSP-based Control of Variable

Speed Drives

Hamid A. Toliyat, Ph.D.

Electrical and Computer

Engineering Department, Texas

A&M University, 3128 Tamus,

216g Zachry Engineering Center,

College Station, Texas, USA

Mehdi Abolhassani, Ph.D.

Black & Decker (US) Inc., 701 E

Joppa Rd., TW100, Towson,

Maryland, USA

Peyman Niazi, Ph.D.

Maxtor Co., 333 South St.,

Shrewsbury, Massachusetts, USA

Lei Hao, Ph.D.

Wavecrest Laboratories, 1613 Star

Batt Drive, Rochester Hills,

Michigam, USA

37.1 Introduction ........................................................................................ 1031

37.2 Variable Speed Control of AC Machines ................................................... 1032

37.3 General Structure of a Three-phase AC Motor Controller ............................ 1032

37.3.1 Pulse Width Modulation Generation • 37.3.2 Analog-to-Digital Conversion Requirements

• 37.3.3 Position Sensing and Encoder Interface Units • 37.3.4 The PI regulator

37.4 DSP-based Control of Permanent Magnet Brushless DC Machines ................ 1037

37.4.1 Mathematical Model of the BLDC Motor • 37.4.2 Torque Generation • 37.4.3 BLDC

Motor Control Topology • 37.4.4 DSP Controller Requirements • 37.4.5 Implementation of

the BLDC Motor Control Algorithm Using LF2407

37.5 DSP-based Control of Permanent Magnet Synchronous Machines................. 1041

37.5.1 Mathematical Model of PMSM • 37.5.2 Mathematical Model of PMSM in Rotor

Reference Frame • 37.5.3 PMSM Control Topology • 37.5.4 DSP Controller Requirements

• 37.5.5 Implementation of the PMSM Algorithm Using the LF2407

37.6 DSP-based Vector Control of Induction Motors......................................... 1046

37.6.1 Induction Motor Field-oriented Control • 37.6.2 DSP Controller Requirements

• 37.6.3 Implementation of Field-oriented Speed Control of Induction Motor

37.1 Introduction

High-performance motor drives are characterized by the need

for smooth rotation down to stall, full control of torque at

stall, and fast accelerations and decelerations. In the past,

variable speed drives employed predominantly dc motors

because of their excellent controllability. However, modern

high-performance motor drive systems are usually based on

three-phase ac motors, such as the ac induction motor (ACIM)

or the permanent magnet synchronous motor (PMSM). These

machines have supplanted the dc motor as the machine of

choice for variety of applications because of their simple robust

construction, low inertia, high power density, high torque

density, and good performance at high speeds of rotation.

The vector-control techniques established for controlling

these ac motors; and most modern high-performance drives

now implement digital closed-loop current control. In such

systems, the achievable closed-loop bandwidths are directly

related to the rate at which the computationally intensive

vector-control algorithms and associated vector rotations can

be implemented in real time. Because of this computational

burden, many high-performance drives now use digital signal

processors (DSPs) to implement the embedded motor- and

vector-control schemes. The DSPs are special microprocessors

used where real-time manipulation of large amounts of digital

data is required in order to implement complicated control

algorithms. The inherent computational power of the DSP

permits very fast cycle times and closed-loop current control

bandwidths to be achieved.

The complete current control scheme for these machines

also requires a high-precision pulse-width modulation (PWM)

voltage-generation scheme and high-resolution analog-to-

digital (A/D) conversion (ADC) for measurement of the

motor currents. In order to maintain a smooth control of

torque to zero speed, rotor position feedback is essential for

modern vector controllers. Therefore, many systems include

rotor-position transducers, such as resolvers and incremental

encoders.

The Texas Instruments TMS320LF2407 DSP Controller

(referred to as the LF2407 in this chapter) is a programmable

digital controller with a C2xx DSP central processing unit

(CPU) as the core processor. The LF2407 contains the DSP

1031

1032 H. A. Toliyat et al.

core processor and useful peripherals integrated onto a sin-

gle piece of silicon. The LF2407 combines the powerful CPU

with on-chip memory and peripherals. With the DSP core

and control-oriented peripherals integrated into a single chip,

users can design very compact and cost-effective digital control

systems.

The LF2407 DSP controller offers 40 million instructions

per second (MIPS) performance. This high processing speed

of the C2xx CPU allows users to compute parameters in real

time rather than look up approximations from tables stored

in memory. This fast performance is well suited for process-

ing control parameters in applications such as notch ﬁlters or

sensorless motor control algorithms where a large amount of

calculations must be computed quickly.

While the “brain” of the LF2407 DSP is the C2xx core,

the LF2407 contains several control-orientated peripherals

onboard (see Fig. 37.1). The peripherals on the LF2407 make

virtually any digital control requirement possible. Their appli-

cations range from analog to digital conversion to pulse width

modulation (PWM) generation. Communication peripherals

make possible the communication with external peripher-

als, personal computers, or other DSP processors. Below is

a graphical listing of the different peripherals onboard the

LF2407 depicted in Fig. 37.1.

We describe here the fundamental principles behind the

implementation of high-performance controllers for three-

phase ac motors – combining an integrated DSP controller,

LF2407, ﬂexible PWM generation, high-resolution A/D con-

version, and an embedded encoder interface.

37.2 Variable Speed Control of AC

Machines

Efﬁcient variable speed control of three-phase ac machines

requires the generation of a balanced three-phase set of vari-

able voltages with variable frequency. The variable-frequency

supply is typically produced by conversion from dc using

power-semiconductor devices (typically MOSFETs or IGBTs)

as solid-state switches. A commonly used converter conﬁgu-

ration is shown in Fig. 37.2a. It is a two-stage circuit, in which

the ﬁxed-frequency 50 or 60 Hz ac supply is ﬁrst rectiﬁed to

provide the dc link voltage, V

, stored in the dc link capacitor.

This voltage is then supplied to an inverter circuit that gener-

ates the variable-frequency ac power for the motor. The power

switches in the inverter circuit permit the motor terminals to

be connected to either V

or ground.

This mode of operation gives high efﬁciency because, ideally,

the switch has zero loss in both the open and closed positions.

By rapid sequential opening and closing of the six switches

(Fig. 37.2a), a three-phase ac voltage with an average sinusoidal

waveform can be synthesized at the output terminals. The

actual output voltage waveform is a pulse-width modulated

(PWM) high-frequency waveform, as shown in Fig. 37.2b. In

practical inverter circuits using solid-state switches, high-speed

switching of about 20 kHz is possible. Therefore sophisticated

PWM waveforms with fundamental frequencies, nominally

in the range of 0–250 Hz can be generated. The inductive

reactance of the motor increases with frequency. Thus, higher-

order harmonic currents are very small and near-sinusoidal

currents ﬂow in the stator windings. The fundamental voltage

and output frequency of the inverter, as indicated in Fig. 37.2b,

are adjusted by changing the PWM waveform using an appro-

priate controller. When controlling the fundamental output

voltage, the PWM process inevitably modiﬁes the harmonic

content of the output voltage waveform. A proper choice of

modulation strategy can minimize these harmonic voltages

and in result, harmonic losses in the motor.

37.3 General Structure of a Three-phase

AC Motor Controller

Accurate control of any motor-drive process may ultimately

be reduced to the problem of accurate control of both the

torque and speed of the motor. In general, motor speed is

controlled directly by measuring the motor’s speed or posi-

tion using appropriate transducers, and torque is controlled

indirectly by suitable control of the motor-phase currents.

Figure 37.3 shows a block diagram of a typical synchronous

frame current controller for a three-phase motor. The ﬁgure

also shows the proportioning of tasks between software code

modules and the dedicated motor-control peripherals of a

motor controller such as the LF2407. The controller consists of

two proportional-plus-integral-plus-differential (PID) current

regulators that are used to control the motor current vec-

tor in a reference frame that rotates synchronously with the

measured rotor position.

Sometimes it may be desirable to implement a decoupling

between voltage and speed that removes the speed dependen-

cies and associated axes cross coupling from the control loop.

The reference voltage components are then synthesized on the

inverter using a suitable PWM strategy, such as space vector

modulation (SVM). It is also possible to incorporate some

compensation schemes to overcome the distorting effects of

the inverter switching dead time, ﬁnite inverter device on-

state voltages, and dc-link voltage ripple. The two components

of the stator current vector are known as the direct-axis and

quadrature-axis components. The direct-axis current controls

the motor ﬂux and is usually controlled to be zero with

permanent magnet machines. The motor torque may then

be controlled directly by regulation of the quadrature-axis

component. Fast, accurate torque control is essential for high-

performance drives in order to ensure rapid acceleration and

deceleration – and smooth rotation down to zero speed under

all load conditions.

37 DSP-based Control of Variable Speed Drives 1033

XTAL1/CLKIN

XTAL2

PLLV

CCA

PLLF2

PLLF

SSA

REFHI

ADCIN08-ADCIN15

CCA

ADCIN00-ADCIN07

SCIRXD/IOPA1

SPISIMO/IOPC2

XINT2/ADCSOC/IOPD0

SCITXD/IOPA0

REFLO

Port A(0-7) IOPA[0:7]

SPICLK/IOPC4

SPISTE/IOPC5

SPISOMI/IOPC3

Port E(0-7) IOPE[0:7]

Port F(0-6) IOPF[0:6]

Port C(0-7) IOPC[0:7]

Port D(0)IOPD[0]

Port B(0-7) IOPB[0:7]

TDO

TDI

CANRX/IOPC7

TRST

CANTX/IOPC6

EMU1

PDPINTB

TCK

EMU0

TMS

CAP5/QEP4/IOPF0

CAP4/QEP3/IOPE7

PWM7/IOPE1

PWM8/IOPE2

CAP6/IOPF1

PWM10/IOPE4

PWM9/IOPE3

PWM11/IOPE5

PWM12/IOPE6

T4PWM/T4CMP/IOPF3

T3PWM/T3CMP/IOPF2

TDIRB/IOPF4

TCLKINB/IOPF5

DARAM (B0)

256 Words

DARAM (B1)

256 Words

DARAM (B2)

32 Words

C2xx

DSP

core

PLL clock

10-Bit ADC

(with twin

autosequencer)

CLKOUT/IOPE0

XINT1/IOPA2

BIO/IOPC1

MP/MC

W/R / IOPC0

TMS2

A0-A15

D0-D15

TP1

TP2

BOOT EN/XF

READY

STRB

R/W

PS, DS, IS

VIS OE

ENA 144

CAP3/IOPA5

PWM1/IOPA6

CAP1/QEP1/IOPA3

CAP2/QEP2/IOPA4

PDPINTA

PWM5/IOPB2

PWM6/IOPB3

PWM3/IOPB0

PWM4/IOPB1

PWM2/IOPA7

T2PWM/T2CMP/IOPB5

T1PWM/T1CMP/IOPB4

TCLKINA/IOPB7

TDIRA/IOPB6

(3.3V)

CCP

(5V)

SARAM (2K Words)

Flash/ROM

(32K Words

:4K/12K/12K/4K)

External memory interface

SCI

SPI

Digital I/O

(shared with other pins)

CAN

JTAG port

Indicates optional modules in the 240x family. The memory size and peripheral selection

of these modules change for different 240xA devices

Event manager B

- 3 Capture Inputs

- 6 Compare/PWM Outputs

- 2 GP Timers/PWM

Event manager A

- 3 Capture Inputs

- 6 Compare/PWM Outputs

- 2 GP Timers/PWM

FIGURE 37.1 Graphical overview of DSP core and peripherals on the LF2407. (Courtesy of Texas Instruments)

The actual direct and quadrature current components are

obtained by ﬁrst measuring the motor phase currents with

suitable current-sensing transducers and converting them to

digital, using an on-chip ADC system. It is usually sufﬁcient

to simultaneously sample just two of the motor line cur-

rents: since the sum of the three currents is zero, the third

current can, when necessary, be deduced from simultane-

ous measurements of the other two currents The controller

software makes use of mathematical vector transformations,

known as Park Transformations that ensure that the three-

phase set of currents applied to the motor is synchronized

to the actual rotation of the motor shaft, under all oper-

ating conditions. This synchronism ensures that the motor

always produces the optimal torque per ampere – i.e. operates

at optimal efﬁciency. The vector rotations require real-time

calculation of the sine and cosine of the measured rotor

1034 H. A. Toliyat et al.

(b)

(a)

FUNDAMENTAL

MOTOR

PHASE

VOLTAGE

RECTIFIER

INVERTER

THREE-

PHASE

60Hz

MAINS

DESIRED FREQUENCY

DESIRED

AMPLITUDE

FIGURE 37.2 (a) Typical conﬁguration of power converter used to drive three-phase ac motors and (b) typical PWM waveforms in the generation

of a variable-voltage, variable-frequency supply for the motor.

VOLTAGE

DECOUPLING

PARK

SVM

NON-

IDEALITY

CORRECTION

ADC

SYSTEM

ENCODER

FEEDBACK

SIGNALS

ENCODER

INTERFACE

UNIT

FWM

GENERATION

UNIT

MOTOR

CURRENT

FEEDBACK

PWM

OUTPUTS

MOTOR CONTROL

PERIPHERALS

DSP SOFTWARE

PID

PARK

3−>2

TRANSFORM

ROTOR

POSITION

−

−j

FIGURE 37.3 Conﬁguration of typical control system for three-phase ac motor.

37 DSP-based Control of Variable Speed Drives 1035

angle, plus a number of multiply-and-accumulate operations.

The overall control-loop bandwidth depends on the speed

of implementation of the closed-loop control calculations –

and the resulting computation of new duty-cycle values. The

inherent fast computational capability of the 40-MIPS, 16-bit

ﬁxed-point DSP core makes it the ideal computational engine

for these embedded motor-control applications.

37.3.1 Pulse Width Modulation Generation

In typical ac motor-controller design, both hardware and soft-

ware considerations are involved in the process of generating

the PWM signals that are ultimately used to turn on or off

the power devices in the three-phase inverter. In typical digi-

tal control environments, the controller generates a regularly

timed interrupt at the PWM switching frequency (nominally

10–20 kHz). In the interrupt service routine, the controller

software computes new duty-cycle values for the PWM signals

used to drive each of the three legs of the inverter. The com-

puted duty cycles depend on both the measured state of the

motor (torque and speed) and the desired operating state. The

duty cycles are adjusted on a cycle-by-cycle basis in order to

make the actual operating state of the motor follow the desired

trajectory.

Once the desired duty cycle values have been computed by

the processor, a dedicated hardware PWM generator is needed

to ensure that the PWM signals are produced over the next

PWM and controller cycle. The PWM generation unit typically

consists of an appropriate number of timers and comparators

that are capable of producing very accurately timed signals.

Typically, 10-to-12 bit performance in the generation of the

PWM timing waveforms is desirable.

Figure 37.4 shows a typical PWM waveform for a single leg

inverter. In general, there is a small delay required between

turning off one power device like A-phase lower device and

turning on the complementary power device A-phase upper

device. This dead-time is required to ensure the device being

turned off has sufﬁcient time to regain its blocking capability

before the other device is turned on. Otherwise a short circuit

of the dc voltage could result.

CONTROL PERIOD CONTROL PERIOD CONTROL PERIOD

20015010050

CONTROLLER

INTERRUPTS

DUTY CYCLE, D1 DUTY CYCLE, D2 DUTY CYCLE, D3

NN + 1N + 2

TIME

µs

FIGURE 37.4 Typical PWM waveforms for a single inverter leg.

In LF2407, the compare units have been used to generate the

PWM signals. The PWM output signal is high when the output

of current PI regulation matches the value of T1CNT and is

set to low when the timer underﬂow occurs. The switch-states

are controlled by the ACTR register. In order to minimize the

switching losses, the lower switches are always kept on and

the upper switches are chopped on/off to regulate the phase

current.

37.3.2 Analog-to-Digital Conversion

Requirements

For control of high-performance motor drives, fast, high-

accuracy, simultaneous-sampling A/D conversion of the mea-

sured current values is required. The drives have a rated

operation range – a certain power level that they can sus-

tain continuously, with an acceptable temperature rise in the

motor and power converter. They also have a peak rating – the

ability to handle a current far in excess of the rated current for

short periods of time. This allows a large torque to be applied

transiently, to accelerate or decelerate the drive very quickly,

and then to revert to the continuous range for normal oper-

ation. This also means that in the normal operating mode of

the drive, only a small percentage of the total input range is

being used.

At the other end of the scale, in order to achieve the smooth

and accurate rotations desired in these machines, it is wise to

compensate for small offsets and non-linearities such as core

saturation and parameter detuning. In any current-sensor elec-

tronics, the analog signal processing is often subject to gain

and offset errors. Gain mismatches, for example, can exist

between the current-measuring systems for different wind-

ings. These effects combine to produce undesirable oscillations

in the torque. To meet both of these conﬂicting resolution

requirements, modern motor-drives use 10-bit A/D convert-

ers, depending on the cost/performance trade-off required by

the application.

The bandwidth of the system is essentially limited by the

amount of time it takes to input information and then per-

form the calculations. The A/D converters that take many

1036 H. A. Toliyat et al.

microseconds to convert can produce intolerable delays in

the system. A delay in a closed-loop system will degrade the

achievable bandwidth of the system, and bandwidth is one of

the most important ﬁgures of merit in these high-performance

drives. Therefore, fast analog-to-digital conversion is a neces-

sity for these applications.

A third important characteristic of the A/D converter used

in these applications is timing. In addition to high resolu-

tion and fast conversion, simultaneous sampling is needed. In

any three-phase motor, it is necessary to measure the currents

in the three windings of the motor at exactly the same time

in order to get an instantaneous “snapshot” of the torque in

the machine. Any time skew (time delay between the mea-

surements of the different currents) is an error factor that is

artiﬁcially inserted by the means of measurement. Such a non-

ideality translates directly into a ripple of the torque – a very

undesirable characteristic.

The analog-to-digital converter (ADC) on the LF2407 allows

the DSP to sample analog or “real-world” voltage signals. The

output of the ADC is an integer number which represents the

voltage level sampled. The integer number may be used for

calculations in an algorithm. The resolution of the ADC is

10 bits, meaning that the ADC will generate a 10-bit number

for every conversion it performs. However, the ADC stores the

conversion results in registers that are 16-bit wide. The 10 most

signiﬁcant bits are the ADC result, while the least signiﬁcant

bits (LSBs) are ﬁlled with “0”s. There are a total of 16 input

channels to the single input ADC. The control logic of the ADC

consists of auto-sequencers, which control the sampling of the

16 input channels to the ADC. The auto-sequencers not only

control which channels (input channels) will be sampled by

the ADC, but also the order of the channels that the ADC per-

forms conversions on. The two 8-conversion auto-sequencers

can operate independently or cascade together as a “virtual”

16-conversion ADC.

37.3.3 Position Sensing and Encoder Interface

Units

Usually the motor position is measured through the use of an

encoder mounted on the rotor shaft. The incremental encoder

produces a pair of quadrature outputs (A and B), each with a

large number of pulses per revolution of the motor shaft. For

a typical encoder with 1024 lines, both signals produce 1024

pulses per revolution. Using a dedicated quadrature counter,

it is possible to count both the rising and falling edges of both

the A and B signals so that one revolution of the rotor shaft

may be divided into 4096 different values. In other words,

a 1024 line encoder allows the measurement of rotor posi-

tion to 12-bit resolution. The direction of rotation may also

be inferred from the relative phasing of quadrature signals

A and B.

Figure 37.5 shows the structure of an optical encoder. It con-

sists of a light source, a radially slotted disk, and photoelectric

Light

Sensors

(a)

(b)

FIGURE 37.5 The structure of an encoder.

sensors. The disk rotates with the rotor. The two photosensors

detect the light passing through the slots in the disk. When

the light is hidden, a logic “0” is generated by the sensors.

When the light passes through the slots of the disk, a logic

“1” is produced. These logic signals are shown in Fig. 37.5. By

counting the number of pulses, the motor speed can be calcu-

lated. The direction of rotation can be determined by detecting

the leading signal between signals A and B.

This is all very well, but there is an increasing class of cost-

sensitive motor drive applications with lower performance

demands that can afford neither the cost nor the space require-

ments of the rotor position transducer. In these cases, the same

motor-control algorithms can be implemented with estimated

rather than measured rotor position.

The DSP core is quite capable of computing rotor posi-

tion using sophisticated rotor-position estimation algorithms,

such as extended Kalman estimators that extract estimates of

the rotor position from measurements of the motor voltages

and currents. These estimators rely on the real-time compu-

tation of a sufﬁciently accurate model of the motor in the

DSP. In general, these sensorless algorithms can be made to

work as well as the sensored algorithms at medium to high-

speeds of rotation. But as the speed of the motor decreases,

the extraction of reliable speed-dependent information from

voltage and current measurements becomes more difﬁcult.

In general, sensorless motor control is applicable princi-

pally to applications such as compressors, fans and pumps,

where continuous operation at zero or low speeds is not

required.

37.3.4 The PI regulator

An electrical drive based on the ﬁeld-orientated control (FOC)

needs two constants as control parameters: the torque com-

ponent reference i

e∗

and the ﬂux component reference i

e∗

The classical PI regulator is well suited to regulate the torque

and ﬂux feedback to the desired values. This is because it is

able to reach constant references by correctly setting both the

proportional term (K

) and the integral term (K

), which are,

respectively, responsible for the error sensibility and for the

steady-state error. The numerical expression of the PI regulator

37 DSP-based Control of Variable Speed Drives 1037

1/Z

ref

fbk

FIGURE 37.6 Classical PI regulator structure in discrete domain.

1/Z

ref

fbk

–

FIGURE 37.7 Numerical PI regulator with correction.

is as follows:

(k)

= K

(k)

k−1



n=0

(n)

(37.1)

which is represented in Fig. 37.6.

During normal operation, large reference value variations

or disturbances may occur, that result in the saturation and

overﬂow of the regulator variables and output. To solve this

problem, one solution is to add a correction of the integral

component as depicted in Fig. 37.7.

The constants K

, K

, proportional, integral, and integral

correction components, are selected based on the sampling

period and on the motor parameters. After deﬁning the DSP-

controlled motor drives requirements, in the following, we

describe the digital control algorithms for permanent magnet

motors and induction motors.

37.4 DSP-based Control of Permanent

Magnet Brushless DC Machines

Permanent magnet alternating current (PMAC) motors are

synchronous motors that have permanent magnets mounted

on the rotor and poly-phase, usually three-phase, armature

windings located on the stator. Since the ﬁeld is provided by

the permanent magnets, the PMAC motor has higher efﬁciency

than induction or switched reluctance motors. The advantages

of PMAC motors, combined with a rapidly decreasing cost

of permanent magnets, have led to their widespread use in

many variable speed drives such as robotic actuators, com-

puter disk drives, appliances, automotive applications, and air

conditioning (HVAC) equipment.

In general, PMAC motors are categorized into two types.

The ﬁrst type of motor is referred to as PM synchronous

0 20 40 60 80 100 120 140 160 180

−40

−30

−20

−10

Rotor Position (deg)

Back-EMF (V)

A B C

(a)

0 20 40 60 80 100 120 140 160 180

−50

−40

−30

−20

−10

Rotor Position (deg)

Back-EMF (V)

A C

(b)

FIGURE 37.8 The back-EMF of PMAC motors: (a) three-phase back-

EMF of PMSM and (b) three-phase back-EMF of BLDC motors.

motor (PMSM). These motors produce a sinusoidal back-

EMF, shown in Fig. 37.8a, and should be supplied with

sinusoidal current/voltage. The PMSM’s electronic control and

drive system uses continuous rotor position feedback and

PWM to supply the motor with the sinusoidal voltage or cur-

rent. With this, constant torque is produced with very little

ripple.

The second type of PMAC motor has a trapezoidal back-

EMF and is referred to as the brushless DC (BLDC) motor.

The back-EMF of the BLDC motor is shown in Fig. 37.8b. The

BLDC motor requires that quasi-rectangular-shaped currents

are fed into the machine. Alternatively, the voltage may be

applied to the motor every 120

◦

, with a current limit to hold

the currents within the motor’s capabilities.

37.4.1 Mathematical Model of the BLDC Motor

The phase variables are used to model the BLDC motor due to

its non-sinusoidal back-EMF and phase current. The terminal