Speed control method for asynchronous motor.
Chioncel, Cristian ; Babescu, Marius ; Chioncel, Petru 等
Abstract: The paper Speed control method for asynchronous motor
presents a method based on the frequency and voltage change that
supplies the stator of an asynchronous motor. Principal the stator of an
asynchronous motor is supplied from an static converter, directly
connected to the grid and the control of the frequency and voltage to
the reference values is realized through the frequency and voltage
controller, that usually are PI or PID controllers.
Key words: asynchronous motor, control algorithm, frequency
control, voltage control
1. INTRODUCTION
To be used in different applications, the ASM must be flexible,
that means it has to adept to electrical drive that are changing their
speed [rpm] and electromagnetic torque, depending on the technical
installation. This can be obtained in automatic control systems when the
motor has the right voltage and frequency to obtain the necessary speed
[rpm] and torque. To realize this request, some control algorithm have
been developed and checked for some numerical applications
The control of the asynchronous machine is studied in many papers
and different publications (Babescu et al, 2005, Abed, et al 2006) where
complex control methods are proposed, with difficult practical
implementation. The proposed method is simpler and presents a high
efficiency.
2. SPEED CONTROL ALGORITHM OF ASYNCRONOUS MACHINE
The control algorithm for ASM realize the speed [rpm] control by:
constant stator flux [[psi].sub.s], constant useful flux [[psi].sub.h]
and constant rotor flux [[psi].sub.r]. By constant stator flux, we
obtain the highest values for the electromagnetic torque, by constant
useful flux with 20% luster, and the lowest values are obtained by
constant rotoric flux, case where the dynamic characteristics are linear
and ideal for rapid controls.
The lowest currents at the same rotation speed are by rotoric
constant flux and the highest, by stator constant flux.
Next we present the proposed control method by constant statoric
flux, when during the application, the speed [rpm] and the
electromagnetic torque is changed.
a. The speed [rpm] will have a reference value, and the
electromagnetic torque has to increase (when the reference speed is
higher that the initial) or to decrease (when the reference speed is
lower that the initial). To change, in steps, the electromagnetic torque
supposes and step change of voltage and frequency.
b. The stator voltage, calculated with
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
and the step modification of the voltage [U.sub.S]([DELTA]y), where
y = [[omega].sub.r] = 2[pi][.sub.r] ([f.sub.r]--frequency of the rotor
currents)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
c. The frequency will change in steps too, [DELTA]y =
[DELTA][[omega].sub.r], changing in steps the rotor pulsation:
y = [[omega].sub.r] [omega] = [[omega].sub.r] + [[omega].sub.m] (3)
or
f + [DELTA]f=([omega]+ [DELTA][omega])/2 [pi] = ([[omega].sub.r] +
[DELTA]y + [[omega].sub.m + [DELTA][[omega].sub.m])/2[pi] (4)
d. The electromagnetic torque depends on y = [[omega].sub.r] as it
results from figure 1.
e. Shaft speed n modifies with An as result of the torque change
with [DELTA][M.sub.elmg]. [omega]+ [DELTA][omega]- [[omega].sub.r] +
[DELTA][[omega].sub.r]) / 2 [pi] = [omega] + [DELTA][omega]-(y +
[DELTA]y) / 2[pi] (5)
f. When the reference value of the speed is reached,
[[omega].sub.r_final], the value for voltage and frequency are:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
The present algorithm is valuable in the general case when the
torque and the speed [rpm] changes, but there are a lot of applications
where one of these parameters (speed, torque) is constant. A control
scheme with three parameters (Alwash, et al., 2003) can be simplified as
shown in figure 2.
So there are technological processes that need a constant speed
([[omega].sub.m]--constant). When the resistant torque, by the shaft of
an ASM increases, the speed will decrease, and through decreasing of the
resistant torque, the speed increase. To keep the speed by the shaft
constant, the electromagnetic torque has to be controlled. This is done
by changing the rotor angular pulsation y = [[omega].sub.r]. This
control algorithm can be corresponding adapted.
In the same way, an algorithm can be adapted when the torque
remains constant and the speed changes.
3. COMPUTING RESULTS OF THE PRESENTED ALGORITHM FOR AN ASM
The simulation results, obtained through Maple implementation
(Ross, 2004) are obtained for an ASM, with the following nominal
parameters:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The initial conditions are:
* Stator [flux.sub.s] [[psi].sub.s] = 1,2[Wb],
* n(0) = 2866,2 [rpm] or [[omega].sub.m](0)=300[rad / s].
* Electromagnetic torque [M.sub.elmg] = 2.56Nm.
From the electromagnetic torque (7), we obtain the value of
[[omega].sub.r][right arrow][[omega].sub.r] = 14 rad / s.
Computing the pulsation,
[omega] = [[omega].sub.m] + [[omega].sub.r] = 300 + 14 =
314[rad/sec] (8)
we obtain the frequency value
f = [omega] / 2[pi] = [[omega].sub.r] / 2[pi] + n = 50Hz (9)
and the voltage value, from relation (6). It is:
U([infinity]) = 391 [V] (10)
for the initial conditions.
The final conditions are:
* stator flux [[psi].sub.s] = 1,2[Wb],
* n(0) = 2589,2 [rpm] or [[omega].sub.m](0) = 271 [rad / s] ,
* Electromagnetic torque [M.sub.elmg] = 5.3Nm.
From the electromagnetic torque, we obtain the value of
[[omega].sub.r_final]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
Computing the pulsation,
[omega] = [[omega].sub.m] + [[omega].sub.r_final] = 301[rad / sec]
(12)
we obtain the frequency value
f = [omega] / 2[pi] = [[omega].sub.r] / 2[pi] + n - 48Hz (13)
and the voltage value U(8) = 389[V] for the final condition.
The obtained results are similar to those with more complex control
methods (Quang & Schoenfeld, 2005)
4. CONCLUSIONS
The presented computing method for ASM speed control represents a
modern solution for the automatic control for many electrical drive
systems meet in practice. Through the proposed algorithm, the voltage
and frequency for the motor supplier are in concordance with the
technological supplies. The control components are the usual once used
for ASM: static converter (rectifier, intermediary circuit, and
inverter) and PI or PID controllers that can be implemented in
analogical or digital form.
The numerical simulation of the system of differential equations,
that describes the ASM mathematical model, the movement equation and the
parameter of the PI controllers, show a good response of the system by a
change of speed [rpm] and electromagnetic torque. A precise
visualization is realized using time-frequency representations (Gillich
et al., 2007).
When the parameter of the two PI controllers are changed, once
changing the Ti time constant by the frequency controller and once
modifying the Ti time constant in both PI controllers, will drive to
different results, that will be analyzed in a next step, by constant
stator, useful and rotor flux.
5. REFERENCES
Abed, K.; Nebti, K. & Benalla H . (2006) A Speed Sensorless
Control for Triphase Induction Machine using Indirect Field-Oriented
Control Scheme, Conference of Applied Simulation and Modelling, ,
Rhodes, Greece
Alwash, S.R.; Al-Chalabi, L.A. & Mansi, S.H. (2003) Improved
Fuzzy Logic Parameters for a 3-Phase Induction Motor Speed Control,
Conference of Applied Simulation and Modelling, Marbella, Spain
Babescu, M & Paunescu, D. (2005) Analiza matematica a dinamicii
ma[degrees]inilor electrice (Mathematical analyze of the dynamic
behavior of electric machines), Ed. Politehnica, Timisoara
Gillich, G.R.; Samoilescu, G.; Berinde, F. & Chioncel, C.
(2007) Determinarea experimentala a caracteristicii de rigiditate si a
modulului de elasticitate a cauciucului utilizand reprezentarea
timp-frecventa (Experimental determination of the dynamic rigidity and
Young modulus for rubber using time-frequency representations), Revista
Materiale Plastice, 44 (1), page numbers 18-21
Quang, Ph. & Schoenfeld, R. (2005) Dynamische Stromregelung zur
Drehmeomenteinpregung in Drehsttromantrieben mit Pulswechslerichter
(Dynamic current control for pulsation in alternative machines), Journal
Electrical Engineering, Spinger, Berlin, page numbers 317-323
Ross, C.C. (2004) Differential Equations. An Introduction with
Mathematica, Springer Verlag Berlin