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Digital Signal Processing Solutions for the Switch
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Digital Signal Processing Solutions for the Switch
Digital Signal Processing Solutions for the Switched Reluctance Motor


Literature Number: BPRA058
Texas Instruments Europe
July 1997


4. Control Strategies
4.1 The Switched Reluctance Motor
The Switched Reluctance Motors show promise as potentially low cost electromechanical
energy conversion devices because of their simple mechanical construction. The
advantages of a Switched Reluctance Motor are the production cost, efficiency and the
torque/speed characteristics.
Electric
Motors
AC DC
Brushless DC Sinewave Hysteresis Step
Switched
Reluctance
Synchronous
Reluctance
Asynchronous
Induction
Synchronous
Reluctance
Figure 3: Classification of Electric Motors
The Switched Reluctance Motor is a singly-excited motor with salient poles on both the
stator and the rotor. Only the stator carries windings. The rotor has neither windings nor
magnets and is built up from a stack of steel laminations. One stator phase consists of two
series- connected windings on diametrically opposite poles.
6 Literature Number: BPRA058
The SR motor is an electric motor in which torque is produced by the tendency of its
moveable part to move to a position where the inductance of the excited winding is
maximized. During motor operation, each phase is excited when its inductance is increasing,
and unexcited when its inductance is decreasing.
The air gap being minimum at the aligned position (the position where a pair of rotor poles is
exactly aligned with a stator pole), the magnetic reluctance of the flux flow is at its lowest; it
will be highest at the unaligned position. Thus, when for a given phase the rotor is not
aligned with the stator, the rotor will start to move to align with the excited stator pole.
An easy way to make the rotor turn is to sequentially switch the current from one phase to
the next phase and to synchronize each phase’s excitation as a function of the rotor position.
The direction of rotation is independent of the direction of current flowing through the phase
winding, it only depends on the sequence of the stator winding excitation.
The key to effective control of an SR motor lies in the ability to control the magnitude and the
duration of the current flowing in the stator windings from the produced torque can be
derived as follows:
T
Wc =


q
with Wc di
i = ò f
0
where Wc is called the co-energy, f is the flux-linkage dependent on rotor position and on
current, i is the current flowing in the stator windings, q is the rotor position and T is the
torque produced by the SR motor. The co-energy can be interpreted as follows:
Figure 4: Interpretation of Stored Energy and Co-energy
There are several possible ways to control the SR motor in torque speed and position.
Torque can be controlled by two methods: the current control method or the torque control
method.
Current
Flux Linkage
q rotor position
Wc field co-energy
Wf stored field energy
Digital Signal Processing Solutions for the Switched Reluctance Motor 7
The shaft position information is useful for generating precise firing commands for the power
converter, for the position feedback loop and for the velocity feedback, which can be derived
from the position data.
The different SR motor designs are commonly referenced as the ratio between the number
of stator poles and the number of rotor poles. Typically a 6/8 SR motor has six stator salient
poles (hence it is a three phase motor) and eight rotor salient poles (four pole pairs).
4.2 The Current Control
In this first control method the magnitude of the current flowing into windings is controlled
using a control loop with a current feedback. The current in a motor phase winding is directly
measured with a current/voltage converter or a current sense resistor connected in series
with the phase. The current is compared with a desired value of current, forming an error
signal. The current error is compensated via a control law, such as a PID, and an
appropriate control action is taken. The block diagram below shows that both current and
position feedback are needed for controlling the SR motor. Position feedback is needed to
synchronize the current flow, with respect to the rotor position, in order to generate the
desired motoring torque. Position feedback is also needed to compute the rotor mechanical
speed, which is compared with the desired value of speed.
Figure 5: Speed and Current Control Loop for an SR Motor
SR motor control is often described in terms of “low-speed” and “high-speed” control
strategies. Low-speed operation is typically characterized by the ability to arbitrarily control
the current to any desired value. What is required is that the relationship,
di
dt
dt id > ò
0
t
SR
motor
PID
controller
PWM
strategy
Power
Electronics
PI
controller Icmd error
Speed
reference
Ifb
Speed
Computation
Position feedback Speed
feedback
1/n
n phases
8 Literature Number: BPRA058
is satisfied, where id is the maximum desired motor current and t is the amount of time
available for getting the current out of the motor winding. t is directly related to the speed of
the motor. The expression to use for di dt depends upon the chosen Pulse Width
Modulation strategy and in which states the current driver can be operated.
As the motor’s speed increases the amount of time t decreases and so it becomes difficult to
regulate the winding current to the desired value. Eventually, a speed is the
current can neither rise nor decay quickly enough in the winding to reach the desired level.
Because of this, it is desirable to get current in and out of the motor’s phase winding while
the phase inductance is still relatively small. Two methods are available to solve the
problem: phase winding switching or advancing the dwell angle (difference between the two
firing angles). Adjusting the dwell angle, so that the phase commutation begins sooner and
ends sooner, offers the advantage of getting the current into the winding while the
inductance is low, and also of having a little more time to get the current out of the winding
before the rotor reaches negative torque region. This principle is depicted in the following
scheme.
Figure 6: Advancing Dwell Angle Strategy according to the Motor Speed
If the rotor position is not precisely available, and when the motor construction permits, it is
possible in high speed mode to switch from the whole phase winding to e half of it. By this
Phase Inductance
Lmax
Lmin
Rotor Position Unaligned
Position
Motoring
Operation
Aligned
Position
Negative Torque
Production Region
Negative Torque
Production Region
Phase Pulsed Signal
at High Speed
Phase Pulsed Signal
at Low Speed
Digital Signal Processing Solutions for the Switched Reluctance Motor 9
means the current rise time constant is divided by two, allowing the desired winding current
to be reached even in the short amount of time before phase’s commutation.
The torque production and the winding current obtained in Low-speed operation thanks to
this current control method are given below:
Figure 7: SR Motor Torque and Current Waveforms with the Current Control Method
Note that even if the phase current is maintained constant the torque produced is not
smooth. The torque ripple is due not only to the control strategy and to the phase
commutation but also to the non-linear relationship between torque and current.
4.3 The Torque Control
Although the above method of controlling the SR motor has many practical applications, a
disadvantage exists. Controlling a constant value of current will result in torque ripple
because of the non-linearity of the relationship between torque and current for a SR motor.
Torque ripple is undesirable because it contributes to the problem of audible noise, it
contributes to vibrations and it introduces torque disturbances which manifest as velocity
errors.
A solution to the problem of torque ripple and torque constant non-linearity in SR motors is
to profile the current such that torque is the controlled variable. Since torque cannot be
controlled directly, due to the lack of adequate torque sensors, this can only be
accomplished using a priori information about the motor’s torque-current-angle
characteristics. Additionally these characteristics must be known fairly accurately in order to
achieve the best results. The torque control strategy is based on following a contour for each
of the phases of the SR motor such that the sum of torque produced by each phase is
constant and equals the desired torque. The desired total torque is calculated from the
velocity loop, and this total torque is split into desired phase torque via shaping function. The
control structure is depicted below.
Phase Current
Ia Ib Ic
Rotor Position
Rotor Position
Produced Torque
10 Literature Number: BPRA058
Figure 8: Speed and Torque Control Loop for an SR Motor
In "low-speed" mode and with a suitable PWM strategy it is possible with this torque control
method to get much smoother torque and an improved current regulation as well as an
improved control of the motor’s velocity. The torque production and the winding current
obtained in Low-speed operation thanks to this torque control method are given below:
Figure 9: SR Motor Torque and Current Waveforms with the Torque Control Method
Some torque ripple will remain if the torque shaping functions do not fully address the torque
non-linearity. Nevertheless, this control structure allows a much smoother torque production
than with the constant winding current control. The torque control method is generally not
Speed
reference PI
controller
PID
controller
PWM
strategy
Power
Electronics
3 phase
SR motor
Phase Current
Ia
Torque
Shaping
Ib
Icmd
Ic
Tcmd
Rotor Position
Ifb
Rotor Position
Speed
Computation
Produced Torque
Position feedback Speed
feedback
1/n
n phases
Digital Signal Processing Solutions for the Switched Reluctance Motor 11
useful for high-speed applications, however, because the torque ripple increases rapidly with
degraded ability to arbitrarily regulate the motor current.
4.4 The PWM Strategies
The selection of Pulse Width Modulation strategy is an important issue in SR motor control
because it dictates how the motor can be controlled. The PWM strategy is also directly
related to the power driver topology. Assuming that each phase of the SR motor can be
independently driven there are three PWM strategies.
· The single pulse operation
The flux in the Switched Reluctance motor is not constant and so it must be established
from zero every stroke. Each phase must be energized at the turn-on angle and switched
off at the turn-off angle. The difference between the turn-off and the turn-on angle is
called the dwell angle. In single pulse operation the power supply is kept switched on
during the dwell angle and is switched off at the phase commutation angle. As there is no
control of the current and as there is a sharp increase in the rate of change of current, this
PWM strategy is used when the amount of time available to get the desired current is
short. Typically, single pulse operation is used at high mechanical speed with respect to
the turn-on angle determined as a function of speed.
· The chopping voltage strategy
On the other hand, the chopping voltage strategy is useful for controlling the current at
low speeds. This PWM strategy works with a fixed chopping frequency. Where, in the
single pulse operation, the supply voltage was kept switched on during the dwell angle,
the supply voltage in the chopping voltage strategy is chopped at a fixed frequency with a
duty cycle depending on the current error. Thus both the current and the rate of change of
current can be controlled.
The chopping voltage strategy can be separated into two modes: the hard chopping and
the soft chopping strategies. In the hard chopping strategy both phase transistors are
driven by the same pulsed signal: the two transistors are switched on and switched off at
the same time. The power electronics board is then easier to design and is relatively
cheap as it handles only three pulsed signals.
A disadvantage of the hard chopping operation is that it increases the current ripple by a
large factor. The soft chopping strategy allows not only control of the current but a
minimization of the current ripple as well. In this soft chopping mode the low side
transistor is left on during the dwell angle and the high side transistor switches according
to the pulsed signal. In this case, the power electronics board has to handle six PWM
signals.
· The chopping current strategy
The chopping current strategy is a Hysteresis type current regulator in which the power
transistors are switched off and on according to whether the current is greater or less than
a reference current. The error is used directly to control the states of the power
transistors. The hysteresis controller is used to limit the phase current within a preset
hysteresis band. As the supply voltage is fixed, the result is that the switching frequency
varies as the current error varies. The current chopping operation is thus not a fixed
chopping frequency PWM strategy. This PWM method is more commonly implemented in
12 Literature Number: BPRA058
drives where motor speed and load do not vary too much, so that the variation in
switching frequency is small. Here again both hard and soft chopping schemes are
possible.
This chopping current strategy allows a very precise current control – made possible
because the tolerance band width is a design parameter, but acoustic and
electromagnetic noise are difficult to filter because of the varying switching frequency.
4.5 What Defines the Control Fitted to the Application
The choice of the right control is a critical matter for a system design. If the control strategy
is defined properly it provides a better motor performance, lower energy usage, quieter
operation, greater reliability, fewer system components and a better dimensioning of the
power elements.
Here are some helpful variables to describe the system characteristics:
· Motor type (e.g. 4 rotor poles 3 phase Switched Reluctance motor)
· Speed range in rpm
· Speed accuracy range including tolerance
· Sensors or sensorless
· Torque range in Nm
· Efficiency for low and high speed
· Control parameters (e.g. speed or position)
· Drive control type (e.g. PID speed closed loop, real time torque control)
· Operating point for low and high speed in amperes
· Maximum power in W
· Driver type e.g. 3 ind dent phase inverter)
· Maximal phase voltage
· PWM carrier frequency in Hz
· Motor driving strategy
· Protection devices
Digital Signal Processing Solutions for the Switched Reluctance Motor 13
5. Power Electronics Topologies and Position Sensors
The inverter is an important part of a drive system. In this section, two standard inverters for
SR-motors will be proposed and discussed. The proposed inverters are the Miller and the
asymmetric half bridges. The complexity of each inverter type depends on the number of
stator phases.
5.1 Asymmetric Half Bridge Inverter
The asymmetric half bridge inverter is the most used inverter. Each machine phase is
connected to an asymmetric half bridge consisting of two power switches and two diodes.
The figure below illustrates the circuit for a 6/8 SR-motor.
Figure 10: Three Phase SR Motor Asymmetric Half Bridge Inverter
The complete DC voltage can be used to energize and de-energize a machine phase in hard
chopping mode. When a pair of switches are closed a phase will be energized from the
positive DC voltage supply. When both switches are opened, the current commutates from
the switches to the diodes. The voltage across the phase is now the negative DC voltage.
These asymmetric half bridges permit soft switching operation as well, thus obtaining a zero
voltage freewheeling state: the phase is energized from the positive DC voltage and deenergized
at zero voltage. No restriction exists to prevent energizing two phases at the
same time, thus achieving a higher torque.
The disadvantage of this inverter is the high number of power semiconductor elements as
each half bridge needs two switches and two diodes.
5.2 Miller Inverter
The Miller inverter optimizes the number of power devices, using only one main power
switch and one main diode for all phases together plus one more switch-diode pair per
phase. The scheme of the Miller inverter shows Figure 11
A B C
Vcc
Gnd
14 Literature Number: BPRA058
Figure 11: Three Phase SR Motor Miller Inverter
The features of the Miller inverter are:
· Hard and Soft chopping operation are possible.
· The number of power semiconductor devices is minimized. For a three phase SR-motor
only four switches and four diodes are necessary. However the power specification of the
main switch and main diode is much more higher than the phase switches or diodes and
so is the cost.
The main disadvantage of the Miller inverter is that the phases can’t be energized
independently.
5.3 Shaft Position Sensors
The position information is used to generate precise firing commands for the power
converter, ensuring drive stability and fast dynamic response. In servo applications, position
feedback is also used in the position feedback loop. Velocity feedback can be derived from
the position data, thus eliminating a separate velocity transducer for the speed control loop.
Two common types of position sensors are used: the incremental sensors and Hall effect
sensor.
· The incremental sensors use optically coded disks with either single track or quadrature
resolution to produce a series of square wave pulses. Position is determined by counting
the number of pulses from a known reference position. Quadrature encoders are direction
sensitive and so do not produce false data due to any vibration when the shaft begins
rotation. The Quadrature Encoder Pulse unit of the TMS320C24x DSP handles encoders
output lines and can provide 1,2 or 4 times the encoder resolution. Speed information is
available by counting the number of pulses within a fixed time period.
· The Hall effect sensors provide non-overlapping signals giving a 15° (6/8 Switched
Reluctance motor configuration) or 30° (6/4 SR motor configuration) wide position range.
The signals can be wired to the C24x DSP Input Capture pins, thus speed information is
available by measuring the time interval between two Input Captures. The time interval is
automatically stored by the TMS320C24x in a specific register at each Input Capture.
From speed information it is numerically possible to get the precise position information
needed for sharp firing commands.
A
Vcc
Gnd
B C
Digital Signal Processing Solutions for the Switched Reluctance Motor 15
6. Enhanced Motor Control
In the above classical Switched Reluctance Motor operation, torque is developed by the
tendency of the magnetic circuit to adopt a configuration of minimum reluctance. The
conduction angle for a phase is controlled and synchronized with rotor position, which is
usually provided by a direct sensor. In the following chapters several methods are presented
to improve the SR motor control quality and to reduce the overall drive cost by suppressing
the position sensor.
6.1 Control Strategies Based on Sensing Inductance
As the direct rotor position sensors do not provide any information on the electrical
characteristics of the machine, because position sensors are insensitive to inductance profile
variation with rotor angle, and as the torque production is not dependent on the
instantaneous rotor position but on the rate of change of co-energy with rotor position
(T i
dL
d
= 1
2
2
q
) it appears that a desired instantaneous torque can be obtained from
instantaneous inductance information rather than rotor position. The figure below depicts the
use of inductance for direct commutation.
Figure 12: Use of Inductance for Direct Commutation
Since there is at least one idle phase in a SRM the inductance of that phase can be sensed
for the purpose of commutation control. The phase inductance of the idle phase is estimated
from the measurements of the motor terminal voltages and currents. The commutation
instants of the active coil are expressed in terms of the phase inductance value of the idle
phase: Lon and Loff. The commutator compares the instantaneous supplied coil inductance
L with the values Lon and Loff and commutates the corresponding coil current.
Speed
reference
Speed
feedback Speed
Calc.
PWM
Strategy
Power
Converter
SRM Torque
Shaping
PI T
Inductance
Based
Calculator
I
Lon
Loff
Inductance
Sensor
16 Literature Number: BPRA058
6.2 Methods of Sensing Inductance
The fundamental types of inductance sensors are based on the following principles.
· Phase pulsing: a voltage pulse V is applied to an unenergized SRM phase by the drive
converter for a period of time DT and the change in coil current DI is measured. The
inductance is obtained from L V
T
I
= D
D
.
· Frequency modulation: inductance information is encoded in a frequency-modulated
signal using a low voltage analog circuit.
· Phase modulation: a low alternating voltage is applied to an unenergized phase of the
SRM and the phase angle difference between the input voltage and the resulting current
is detected. The inductance is given by L
R = tan f
w
where f is the phase angle.
· Amplitude modulation: a low level alternating voltage is applied to an unenergized phase
and the amplitude of the resulting current is mapped to the coil inductance. The
inductance can be expressed as L
V
I
R m
m
= - 1 2
2
2
w
where Vm is the voltage amplitude of
the input alternating voltage, Im is the current amplitude and R is the resistance in the
circuit.
· Self voltage technique: the inductance of the active phase is estimated in real time from
measurements of the active phase current and phase flux. If I0 is the current in the active
phase linking a flux Y0 then the phase inductance is given by L
I 0
0
0
=
Y
.
6.3 SRM Sensorless Operation Based on Flux/Current Characteristics
The rotor position can be calculated from the magnetic characteristics provided that y (or L)
and I can be measured. Some flux/current based sensorless methods are given below.
· The Waveform detection technique relies on monitoring the phase current rise and fall
times due to change in the incremental phase inductance which varies as a function of
current and rotor position.
· The State Observer method based on terminal measurements of voltage and currents
used as inputs of a digitized electromagnetic model of the SR machine.
7. An Example Studied
An example is given below of the implementation and realization of a Switched Reluctance
motor controlled in speed and connected to an alternating supply voltage. Few results are
given.
Digital Signal Processing Solutions for the Switched Reluctance Motor 17
7.1 Power Electronics
Below is a complete drive system including the load that may be non-linear.
TMS320C240
DSP
controller
Rectifier Input
Filter
Auxiliary
Supply
Inverter
Position
Sensor
Output
Input
Voltage
Figure 13: Three Phase Switched Reluctance Motor Driver
The input filter provides several functions, protection of the hardware (by fuse and voltage
transient suppresser) and, to match the EMC standards, an EMI filter and a power factor
correction (PFC) are implemented. The PFC may be active or passive; in se it is
entirely handled by the DSP. This block is directly connected to the voltage supply.
To achieve a continuous voltage from the alternating input signal, a single-phase input
bridge with tank capacitor is needed, represented as the rectifier block
To generate the phase voltages with variable amplitude and frequency to supply the 3 SR
motor phase signals to the motor, a 3-phase inverter is used, based on MOSFET
technology.
The system is controlled by the TMS320C240 DSP. The inputs are three Hall effect sensors
to detect the shaft position, and a resistor sensor on the line (IBUS ) to measure the phase
currents. The controller uses a serial link to communicate. The auxiliary supply feeds the
inverter driver and the logic circuitry.
7.2 The Control Strategy
The control uses a fixed frequency (set on 20kHz) symmetrical Pulse Width Modulation. The
power electronics board is designed to support voltage chopping in hard-chopping mode.
The motor design and the control electronics support the switching of the phase inductance
value in order to achieve torque regulation in high speed operation. The chosen control
strategy is current control with commutation angle information given by a position sensor.
The speed and current controllers are all implemented using a standard PI regulator block.
The braking action is done by delaying the phase winding firing angle. The rotor position is
given by three Hall effect sensors wired on the Input Capture and the phase current
information is given by three current/voltage transformers.
18 Literature Number: BPRA058
7.3 Software Implementation
The proposed control scheme is implemented on the TMS320C240. All the control routines
are implemented using assembler language with fixed precision numerical representation.
The control algorithm is synchronized by the DSP PWM Timer that generates interrupts on
its Period Signal. These interrupts start current conversion on the line determined in the
Capture interrupts. The current conversion result is put into the current loop to generate new
pulsed signals. The current loop frequency thus equals the PWM timer frequency, that is to
say, 20 kHz. The Capture Interrupts synchronize the supplied phase with the rotor position.
The speed is controlled once every few current control cycles and is computed from the time
interval between two interrupts coming from the position sensor.
Phase current measurements need sampling of the inverter DC current during the 20 kHz
PWM period. This is performed by driving the A/D conversion through another interrupt
(PWM period interrupt) and the result is received through an end-of-conversion interrupt.


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