Electricity: motive power systems – Induction motor systems
Reexamination Certificate
2000-09-29
2002-03-19
Nappi, Robert E. (Department: 2837)
Electricity: motive power systems
Induction motor systems
C318S609000, C318S727000, C318S825000, C388S906000
Reexamination Certificate
active
06359416
ABSTRACT:
CROSS-REFERENCE TO RELATED APPLICATIONS
Not applicable.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not applicable.
BACKGROUND OF THE INVENTION
The present invention relates to synchronous frame current regulators and more specifically to an adaptive predictive current regulator that increases system bandwith while maintaining current overshoot within an acceptable range.
In virtually any control environment the goal is to cause a specific result instantaneously when a specific command signal is provided. While the stated goal is simple, the solution for achieving the stated goal often is much more complex as hardware required to facilitate instantaneous results often have unknown or variable characteristics and hardware controlling systems often cause processing delays that are difficult to eliminate.
One area of the controls industry in which precise control is particularly important is in motor control or control of other inductive type machines. In these cases often even a slight delay in system control can result in loss of motor control, motor and control system damage or expedited degradation. For this reason many motor control systems include several different control or feedback loops that compare command signals to resulting signals to generate error signals and then adjust the command signals as a function of the error signals in an effort to eliminate the control error.
To this end vector motor drives include a current regulator as an innermost control loop with other control loops nested around the current regulator. Because other loops are nested around the current regulator any error generated by the current regulator can be exacerbated by the other loops. For this reason the current regulator typically needs to be extremely accurate and highly responsive.
As well known in the controls industry, most vector drives perform current regulation on electrical reference frame variables to ensure zero steady state error. Electrical reference frame variable regulators are commonly referred to in the motor control industry as synchronous frame current regulators (SFCRs).
Referring to
FIG. 1
, a typical SFCR in the sampled data and continuous domain system
10
is illustrated that includes a plurality of blocks that together model an inductive load and associated control system. All of the events and calculations in
FIG. 1
occur inside a microprocessor or within other motor drive or motor hardware controlled by the processor. Nevertheless, system
10
is represented as discrete events and calculations in order to generate transfer functions and current predicting equations that must be understood for a thorough understanding of the present invention.
System
10
includes first and second summers
12
,
14
, respectively, a proportional-integral (PI) compensator
16
, a unit sample delay
18
, a zero order hold (ZOH)
20
, a pulse width modulator (PWM) gain block
22
, a plant “effect” model or block
24
and a sampler
26
.
First summer
12
receives each of a current command signal i*(z) and a sampled current signal i(z) and subtracts the sampled signal from the command signal to generate a current error signal Er. Pi compensator
16
receives error signal Er and steps that signal up as a function of a PI gain factor Kpi thereby generating a voltage adjustment signal V(z). The PI compensator
16
function can be expressed as:
k
pi
(
z
-
δ
c
)
z
-
1
Eq. 1
Second summer
14
receives the voltage adjustment signal V(z) and a voltage feedforward signal Vff(z) from another control loop sampler (not illustrated) and adds the received signals to generate an adjusted voltage signal V(z)′.
The unit sample delay
18
and the ZOH
20
are provided in system
10
to represent the finite update rate of practical conventional control loop configurations.
Voltages having specific amplitudes and frequencies are generated using PWM inverters. As well known in the motor controls industry a PWM inverter typically includes a plurality of switching devices that alternately link positive and negative DC buses to output lines thereby causing a series of positive and negative voltage pulses on the output lines. The average of the voltage pulses over a PWM cycle causes an alternating voltage at the output. Where a load is linked to the output the alternating voltage causes an alternating current across the load. PWM block
22
represents the gain effects of a conventional PWM inverter as represented by a gain factor Kpwm. The effect of block
22
is to modify the received signal by factor Kpwm. The output of block
22
is provided to plant block
24
.
Every plant or load linked to PWM inverter outputs has some effect on the current provided to the plant. For example, where the plant is inductive (e.g., in the case of an induction motor), current provided to the plant cannot change immediately and therefore, even where an inverter is controlled to cutoff voltage to the plant, the inductive plant will still draw some current from the inverter. In general, the effect of a plant on received current is a function of both load resistance r
s
and load inductance L and can be expressed in the continuous domain by the equation:
1
r
s
1
+
s
τ
Eq. 2
where &tgr; equals a load time constant L/rs. Thus, “plant effect” is modeled as illustrated in block
24
and current i(t) represents the current provided to the plant via a PWM inverter.
Referring to
FIGS. 1 and 1
a
, system
10
can be represented in the z-domain as two gain blocks G
comp
(z) and G
plant
(z). In
FIGS. 1
a
and
1
similarly numbered components are identical.
Sampler
26
links the plant current i(z) to first summer
12
and samples the plant current i(z) at intervals T, providing a new sampled current i(t) every T interval.
Referring still to
FIG. 1
, the positions of the feedforward sampler (i.e., providing Vff(z)) and feedback sampler
26
result in an explicit transfer function between the current command i*(z) and current feedback i(z) such that the overall system gain G(s) can be expressed as: G(s)=G
comp
(z)*G
plant
(z). It is customary to set the proportional and integral gains of the PI compensator so as to cancel the dominant dynamics (i.e., the pole) of the plant, which are typically the slowest dynamic in a practical control system. If such a pole-zero cancellation is assumed, the current regulator/R-L load reduces to a second order system with an open loop transfer function G(z) expressed as:
G
(
z
)
=
K
pi
K
PWM
(
1
-
ⅇ
-
T
/
τ
)
/
r
s
z
(
z
-
1
)
=
i
(
z
)
i
*
(
z
)
Eq. 3
Thus, the closed loop transfer function of system
10
in
FIG. 1
has two poles at locations governed by the PI compensator gain Kpi. As compensator gain Kpi is increased the poles in Equation 3 depart from the real axis, an occurrence that indicates an undesirable oscillatory characteristic.
As well known in the motor controls industry oscillation problems are exacerbated as the system operating bandwidth is increased. When the operating bandwidth includes relatively high frequencies overshoot is increased. Thus, one solution for dealing with second order system overshoot and resulting oscillations is to reduce the system operating bandwidth. Unfortunately, when bandwidth is reduced response time is increased (i.e., settling time is increased).
Another solution for dealing with oscillations in a second order system is to provide a predictor that acts as a unit sample advance in the current feedback loop. A unit sample advance
28
in the feedback loop is illustrated in
FIG. 2
where block
30
represents blocks
16
,
18
,
20
,
22
and
24
and summer
14
from FIG.
1
. The open loop gain G
p
(z) of the current regulator in
FIG. 2
can be expressed as:
G
p
(
z
)
=
K
pi
K
PWM
(
1
-
ⅇ
-
T
/
τ
)
/
r
s
(
z
-
1
)
Eq. 4
Thus, the current regulator
10
′ of
FIG. 2
operates as a first order system cascaded with a unit sample delay, thereby decoupling the dynamics of the computation delay from those of PI compensator
16
Kerkman Russel J
Rao Aakash Vishalraj K.
Schlegel David W.
Gerasimow Alexander M.
Jaskolski Michael A.
Leykin Rita
Nappi Robert E.
Rockwell Automation Technologies Inc.
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