Transactions on Electrical Engineering, Vol. 3 (2014), No. 1
1
An Accurate Auto-Tuning Procedure for
Encoderless AC Motor Drives in Industrial
Environments
Andreas R. Weber 1), Joachim Weissbacher 2), Gerald Steiner 1), Martin Horn 3)
1)
Institute of Electrical Measurement and Measurement Signal Processing, Graz University of Technology, Austria,
e-mail: andreas.weber@br-automation.com, gerald.steiner@ieee.org
2)
3)
Bernecker + Rainer Industrie Elektronik Ges.m.b.H, Eggelsberg, Austria, e-mail: joachim.weissbacher@brautomation.com
Institute of Smart System-Technologies, Control & Mechatronic Systems Group, Klagenfurt University, Austria,
e-mail: martin.horn@uni-klu.ac.at
Abstract — Modern ac motor drives are based on field
oriented vector control with feedback and feedforward
control units. The feedback control unit for position and
speed consists of two cascaded standard PI-controllers.
These controllers require information of the position and
the derivative of the position, respectively. Typically a shaft
encoder provides this information but more often a position
observer is used instead. The feedforward control unit uses
the set position trajectory in combination with mechanical
parameters and essentially imposes the overall dynamics.
This work presents a new method for self-commissioning of
speed controller, position controller and feedforward
control unit for drives without a shaft encoder. Performance
and feasibility of the proposed method are demonstrated by
experimental results.
Keywords — self-commissioning, feedforward control,
encoderless, sensorless, flux observer, field oriented vector
control, ac motor drives, frequency response measurement,
maximum peak criteria
I. INTRODUCTION
Modern drive technology is often based on field oriented
control structures. A typical controller structure of a field
oriented vector controlled drive is shown in Fig. 1. The
controller structure is composed of three cascaded
controller loops. The innermost is the current controller
loop which is composed of a standard PI-controller with
electromagnetic force (emf) feedforward compensation.
The controller parameters are adjusted automatically by
the knowledge of the electrical motor parameters like
resistances and inductances. Set value for the current
controller (q-direction) is calculated by the superimposed
speed controller whose actual value is given by the time
derivative of the position signal. In order to suppress
noise due to the quantization of the position signal a low
pass filter is used in speed feedback loop. The
corresponding set value of the speed controller is given
by the position controller. Both, position and speed
controller are standard PI-controllers which are only used
as proportional elements. The information of the known
set position trajectory can be used to increase the
performance of the command response. Based on
identified mechanical parameters additive reference
values for speed and quadrature current are calculated in
the feedforward controller unit. The described field
oriented control structure assumes exact information
about the flux position. Typically a shaft encoder is used
to provide the servo drive with this necessary position
information. For lower investment costs, lower
maintenance costs and increased reliability, the shaft
encoder, the necessary cables and evaluation unit are
saved and replaced by an observer. The usage of such an
observer has an impact on the plant and therefore on the
dynamics of the whole system. Since the commissioning
of the current controller and the observer is assumed to be
already completed, the parameters of the speed controller,
position controller and feedforward controller unit have
to be determined.
Goal of this work is to present a method for self-commissioning of these controllers and the feedforward
controller unit which is characterized by simplicity for
the user in terms of tuning parameters.
In contrast to [1] where the mechanical parameters of two
mass systems are identified (parametric model) in order
to design a controller, in this work a nonparametric model
is the basis for the design of the controllers. The
parameters of the feedforward controller unit are
identified by way of a point to point movement and an
offline calculation. The work is organized as follows: In
Section II the basics of the used observer is explained and
compared. In Section III the identification and
determination of feedback and feedforward controller
parameters is shown. In Section IV experimental results
are presented and Section V concludes the article.
Transactions on Electrical Engineering, Vol. 3 (2014), No. 1
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Figure 1: Typical field oriented controller structure with feedforward controller unit
II. ENCODERLESS CONTROL
A. Postion observer based on a flux estimator for a
permanent magnet synchronous motor (PMSM)
The used position observer is a common flux observer in
the stator fixed coordinate system (
). Different
methods of flux observation have been published, and
some examples are reported in [2], [3], [4], [5].
Generally, the observer is estimated by the fundamental
voltage equations.
(1)
(2)
(5)
The problem with the open integration of the observer
structure is avoided with a low pass filter and a feedback
of the estimated flux error vector
multiplied with a
gain factor K. The error vector
is the difference
between the observed flux vector
and a calculated
reference flux vector. So unwanted influences based on
current measurement errors, inadequateness in the voltage
generation (e.g. nonlinear inverter voltage drop) and
uncertain motor parameters are strongly reduced. The
basic structure of the observer is shown in Fig. 2 as signal
flow chart. The performance of the described position
observer is shown in [6] and [7].
Transformed into the flux vector
(3)
(4)
where
is the stator resistance,
the stator inductance,
the measured current vector and
the voltage vector.
With the stator fixed components
and
the
position of the flux vector
and commutation angle
can be calculated via the arcus tangens function.
Figure 2: Signal flow chart of the flux vector estimator
Transactions on Electrical Engineering, Vol. 3 (2014), No. 1
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AC Motors with position or speed observers, which are
based on the fundamental equations, are not applicable at
standstill or very low speed. Due to this fact operation at
certain speed is necessary for identification of the overall
system consisting of mechanics and observer [1], [8].
Since drive controllers are not parameterized yet, a
provisory controller parameterization is necessary.
lowpass as a free design parameter. It should be
mentioned that
should be chosen in this case much
greater than the sum of the small time constants (current
controller loop) and dead times of the servo drive.
Experiments on different mechanical setups showed that
is a reasonable start value for sufficient
suppression of any existing resonances and high
frequency noise.
A. Provisory controller parameterization
B. Identification procedure
In [9] a self-tuning speed control concept for drives with
encoder is presented where a provisory PI speed
controller with low bandwidth is used for performing
experiments for estimation of the frequency response
function (FRF). In contrast to [9] a proportional speed
and position controller parameterized for a nominal value
that equals to the motor inertia (known in the majority of
cases out of datasheets) is used instead of the published
PI speed controller based on the total inertia. The
advantage of the missing integral part in the speed
controller is that in case of a strong deviation of the actual
inertia from its nominal value no unstable speed loop
behavior can occur. Additionally to the given cascaded
controller structure of the used servo drive there is a low
pass (speed filter) in the speed feedback loop in order to
smooth the quantization effects caused through the speed
calculation
With the controller parameters of the previous chapter
and a smooth position trajectory with a sufficiently small
acceleration the drive can be operated at desired constant
speed. The closed loop system is excited with a pseudo
random binary signal (PRBS) as a disturbance signal in
the torque generating component of the stator current [1],
[8]. A PRBS of order
can be generated by
III. AUTOTUNING
(6)
with a filter time constant
and as sample time.
The overall identification structure can be seen in Fig. 3.
(9)
with appropriate coefficients
,
,
where
is also the number of used shift registers.
Useful coefficients for different orders can be found in
discrete time
[11]. The PRBS is periodic with
steps. With a cycle time the necessary measurement
time for one period is given by
(10)
As depicted in Fig. 3, the current (Input) and the
differentiated position signal (Output) of the observer are
used for calculation of the frequency response function.
Therefore a discrete fourier transformation (DFT) of both
input
and output
sequence sampled at
with sample time
is
performed. Element-wise division of the complex
coefficients leads to the desired frequency response
function
(11)
Figure 3: Identification structure
By use of the "Magnitude Optimum" [10] both speed and
position controller gains can be calculated as
(7)
(8)
with
as the motor torque constant,
the known
motor inertia and
the filter time constant of the
at frequencies
. If
exactly one period (
samples) is used after transient
behavior has decayed no windowing technique and
advanced signal processing is necessary to attenuate the
leakage-effect. By use of an efficient fast fourier
transformation (FFT) algorithm for calculation of DFT
the estimation of the FRF can also be implemented on an
embedded system with limited memory and calculation
power. In Fig. 4 a FRF for a typical one mass system is
depicted. As a reference the calculated FRF of the system
with the installed encoder is shown. It can clearly be seen
that at low frequencies both characteristics are very
similar but at higher frequencies (
) a
differentiating behavior of the observer is obvious. The
problem with increasing noise at higher frequencies can
be avoided with the low pass filter (6) in feedback of the
speed loop.
Transactions on Electrical Engineering, Vol. 3 (2014), No. 1
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Figure 4: Comparison of measured FRF (one mass system) with
observer and encoder and a one mass model approximation for low
frequencies
C. Speed controller tuning
Equation (11) can be interpreted as a nonparametric
model of the plant for which the speed controller is
designed in the following. Usually a parametric model is
derived from the measurement data and used for further
calculations. This parameter identification is a
challenging task in view of an automatic procedure.
Therefore a nonparametric model for numerically
calculating the controller parameters is chosen. The open
loop FRF
of the speed controller is a series
connection of the speed filter (6) evaluated at
,
the plant (11) and the controller gain .
(12)
The Maximum Peak Criteria [12]
(13)
is one possible way to formulate the design specifications
in frequency domain in terms of gain margin (GM) and
phase margin (PM) for the closed loop FRF
Figure 5: Proposed tuning algorithm for position and speed controller
(14)
For a given upper bound
a minimum gain and
phase margin of the open loop system is guaranteed. In
this work a value of
resulting in
and
is chosen.
The goal of the proposed tuning algorithm is to find a
maximum value of the gain factor subject to the speed
filter time constant
and condition (13). In Fig. 5
(upper part) the main steps of the algorithm are presented
graphically.
Transactions on Electrical Engineering, Vol. 3 (2014), No. 1
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D. Position controller tuning
The identification of the position controller parameter
is based on the calculated FRF of the closed speed loop
and an integrator from actual speed to
actual position. Similar to Sec. III-C a gain factor of the
position controller can be calculated for the open position
loop FRF
(15)
as depticted in Fig. 5 (lower part).
E. Feedforward controller tuning
Since the positioning profile is usually known in advance,
this fact can be used to improve the tracking behavior of
the drive by means of speed and torque feedforward
(feedforward controller unit). Whereas the speed
reference is calculated by simply differentiating the
position
the torque reference
is based on a
simple one mass system with static and dynamic friction
and can be calculated as:
(19)
In contrast to [13] where the identification of the
feedforward parameters is carried out online, here the
optimization is done offline in the rest time task. This has
the advantage of less computation effort in the cyclic
task.
IV. APPLICATION RESULTS
The used motor is a three phase permanent magnet
synchronous motor (PMSM) from B&R connected with
an extra flywheel (
). The motor is fed
by a B&R ACOPOS 8V1090.00-2 servo drive. Motor and
servo drive parameters are described in the Appendix.
The identified FRF of the speed controller plant is shown
in Fig. 6
(17)
(16)
It should be mentioned that the calculated feedforward
torque has to be transformed into an equivalent current by
(17)
with the motor torque constant
(see Fig. 1). To
identify the parameters
and
movements with acceleration, constant speed and
deceleration phases (speed trapezoidal) are necessary.
Since the position and speed controller are already
parameterized only the characteristics of the trajectory
(distance, speed, acceleration) have to be determined.
Usually the maximum distance is given by the hardware
limits of the mechanics and the maximum speed by the
nominal speed of the motor. The acceleration can be
) which is
calculated via an estimated inertia (
based on a one mass approximation of the measured FRF
(see Fig. 4) for small :
(18)
The set speed, set acceleration and resulting current
signal for this excitation profile are used for identifying
by solving the
the parameters
optimization problem:
Figure 6: Comparison of measured FRF of the two mass system with
observer and encoder
and represents a typical two mass system with a
resonance frequency at
, an anti-resonance
frequency at
and an approximated mass moment
of inertia of
. The parameters
identified with the presented method for the speed an
position controller are given in Tab. I.
Table I: Controller Parameters
In Fig. 7 the FRF of the plant with observer, open and
closed speed loop is shown. Fig. 8 represents the FRF of
the position controller plant (closed speed loop in series
with an integrator) as well as the open and closed position
loop FRF. In the upper part of Fig. 9, the speed profile for
the feedforward parameter identification is shown. In the
Transactions on Electrical Engineering, Vol. 3 (2014), No. 1
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identified parameter set is listed in Tab. II. By means of a
typical positioning profile the performance improvement
with the identified parameters is demonstrated.
Table II: Feedforward Parameters
Figure 7: Calculated FRF for speed controller tuning
The profile includes an acceleration phase from standstill,
a constant speed phase and a deceleration phase to
standstill. Note that the used observer can not be used in
standstill, so an open loop current vector control is used
for the region from standstill to
. In this area the
position controller error is forced to zero. Fig. 10 shows
the reference position, reference speed and position error
of a point to point movement with and without
feedforward control. The acceleration and deceleration
are set to a value that the necessary torque is half of the
nominal torque of the motor. The occurred position error
is described in units per revolution (1000 Units per
revolution). The improvement with feedforward control is
more than sufficient for a motor and servo combination
without shaft encoder and can be useful for a lot of
industrial applications.
Figure 8: Calculated FRF for position controller tuning
Figure 9: Speed profile (top) and measured vs. identified torque
(bottom)
lower part the necessary measured torque for the given
profile and the identified torque are depicted. The
Figure 10: Position profile (top), speed profile (middle) and position
error for a point to point movement with and without feedforward
control (bottom)
Transactions on Electrical Engineering, Vol. 3 (2014), No. 1
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V. CONCLUSION
This paper presents an acccurate method for
parameterizing the position controller, speed controller
and feedforward control unit in a field oriented controller
structure without the position information of a shaft
encoder. The need for an accurate position information
and the possibility to observe this information via a flux
observer are discussed. The structure of this position
observer is described. A method to identify the FRF of
the plant in combination with the position observer is
shown. With the described maximum peak criteria the
controller gains are determined. Furthermore a procedure
for identifying the feedforward controller parameters is
shown. Finally the performance and the feasibility of the
proposed solution are demonstrated by means of a typical
movement profile in industrial drive technology.
VI. APPENDIX
MOTOR: PMSM, B&R 8LSA36.E0030D200-0, NUMBER
OF POLE-PAIRS = 2, RATED VOLTAGE = 400V, RATED
CURRENT = 1.9A, RATED SPEED = 3000MIN , RATED
TORQUE = 2.7NM
INVERTER: B&R ACOPOS 8V1090.00-2, RATED
VOLTAGE = 3X400-480V, RATED CURRENT = 8.8A,
WWW.BR-AUTOMATION.COM
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