# Speed control method for asynchronous motor.

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