TORQUE AND SPEED MODES SIMULATION OF A DTC-CONTROLLED INDUCTION MOTOR

Nuno M. Silva1, António P. Martins2, Adriano S. Carvalho2 1 MSc student, Faculdade de Engenharia da Universidade do Porto,

Rua Dr Roberto Frias, 4200-465, Porto, Portugal, - e-mail: pee01003@fe.up.pt 2 Faculdade de Engenharia da Universidade do Porto, Instituto de Sistemas e Robótica,

Rua Dr Roberto Frias, 4200-465, Porto, Portugal, - fax: +351 22 5081443, e-mail: ajm@fe.up.pt

Keywords: Converter control, Induction motor, Direct Torque Control, Simulation

Abstract By the huge advantages associated, induction motors drives are still justifying research and development. This paper presents the work developed in Direct Torque Control (DTC) based drives. With a growing importance in several applications, this method was object of a deep study, either in simulation environment and hardware implementation. The reached results confirm some weaknesses and several strengths, pointing out his worth in strength control, particularly in robotics.

1 Introduction In the past, AC drives were only used in small demanding applications, regardless the advantages of AC motors opposite to DC motors, since the high switching frequency inverters cost was rather competitive.

With the developments in the power electronics area, the vector control methods, which use fast microprocessors and DSP’s, made possible the use of induction motors in typically DC motors dominated areas, since the current components producing torque and flux are decoupled, achieving the system separately excited DC motor similar features.

The Direct Torque Control (DTC) method, developed by German and Japanese researchers [8], [3], allows direct and independent electromagnetic torque and flux control, selecting

an optimal switching vector, making possible fast torque response, low inverter switching frequency and low harmonic losses.

Figure 1 shows the usual block diagram of a DTC controller.

Tref

Gate signals

-

~

Switching logic

++

-

Φref

θφ τ

Tp

*

*

Rs Rs

Φsα

Φsβ

Isα Isβ Vsα Vsβ

++

-

-

+

1, 2, 3 α, β

Motor~

xyx2+y2

ACinput

Φs

Figure 1. Block diagram of a DTC control system.

With DTC it is possible to obtain direct flux and electromagnetic torque control, indirect voltage and current control, sinusoidal current and flux, low torque ripple, superior torque dynamics and hysteresis band dependent inverter switching frequency [5], [2].

Among its main advantages are the absence of: coordinate transformation (which are usually necessary in most vector control drives), modulation specific block, and the absolute position determination.

However, there are some problems during start up and at low speed values, like the difficulty in start up current control and high influence of the motor

Proceedings of the 10th Mediterranean Conferenceon Control and Automation - MED2002Lisbon, Portugal, July 9-12, 2002.

parameters, as well as variable switching frequency and the need of flux and speed estimators.

With the inclusion of a speed estimator in the system, it is possible to obtain gains in hardware complexity reduction and bigger mechanical endurance, making possible the operation in a hostile environment and decreasing the maintenance needs. Simultaneously the noise and motor-load inertia immunity are increased.

However it is necessary to use speed estimation techniques, like: open loop estimators, model reference adaptive systems (MRAS), [6]; Luenberger observers, [7]; Kalman filters, [4]; fuzzy logic estimators, [9] or neural networks, [1].

In this paper, it is introduced the work developed in simulation and experimentation associated to the implementation of a DTC based, DSP controlled drive, of an asynchronous machine, in torque and speed modes.

2 The control process implemented In a voltage source two level three phase inverter, represented in figure 2, and neglecting the switching interval effect (dead-time, snubbers), feeding a three phase, balanced, wye connected load, the voltage measured between the output of each branch and the 0 point can have two values, Vdc or 0 V, given by Equation (1):

dckk VSV ×=0 (1)

being Sk the control signal of k branch, and Vdc the voltage in the DC bus.

S1 S2 S3

1

3n2

Vdc

0 V10 V20 V30

V1n

V3n

V2n

Figure 2. Schematic of a voltage source two level three phase inverter.

The operation may be described by the following manner:

Sk=1 top switch closed, bottom switch opened.

Sk=0 top switch opened, bottom switch closed.

Assuming that the n point is a virtual neutral, the line-neutral voltage may be evaluated; Vkn, Equation (2):

⋅−−=

⋅−−=

⋅−−=

dcn

dcn

dcn

VSSSV

VSSSV

VSSSV

)2(31

)2(31

)2(31

2133

3122

3211

(2)

The application of the Clarke transformation allows the attainment of a generic vector expression, Equation (3):

)(32

32

21 nnn VaVaVjVVV ++=+= βα (3)

where 32π

=j

ea .

Using the measured inverter output currents and voltages, the motor flux is estimated, and then the electromagnetic torque is estimated.

In this set of operations it becomes specially important the stator flux estimation. In this application, it has been implemented an open loop estimator, with the flux calculated by stator voltage integration, and considering the stator losses, Equation (4).

( )∫ −=Φ dtIRU ssss (4)

Being p the number of pole pairs, the electromagnetic torque is determined by the following expression, Equation (5):

( )*Im ssem IpT ⋅Φ⋅= (5)

2.1 Electromagnetic torque control mode

The electromagnetic value resulting from the previous stage is then compared with the electromagnetic torque reference, using the three level hysteresis comparator, represented in figure 3. In this manner, the result may be increase,

decrease or maintain the torque, depending on the comparator output.

Tref

Tτ

+

-

1

0-1

Figure 3. Three level hysteresis comparator: τ=1⇒ increase torque; τ=0⇒ maintain torque; τ=-1⇒ decrease torque.

In a similar way, the flux value will be compared with a flux reference, but using a two level hysteresis comparator, shown in figure 4. The result will be used to increase or decrease the flux.

Φref

φ+

-

1

0Φ

Figure 4. Two level hysteresis comparator: φ= 1 ⇒ increase flux; φ= 0 ⇒ decrease flux.

An important factor in these operations is the hysteresis band of the two comparators. A narrow window will give a better current flux waveforms but will also increase the inverter switching frequency.

For the switching vector selection it is necessary to know the angular sector in which the actual flux is located. The actual position can be determined by Equation (6), from the orthogonal flux components:

Φ

Φ=θ

α

β

s

sarctg (6)

The θ angle returned by Equation (6) determines the sector where the flux is, (figure 5).

The combination of the comparators outputs and the sector is then applied to an optimal switching table (Table 1) which will give the voltage vector to be applied to the inverter.

30o

90o

150o

210o

270o

330o

θ1

θ2θ3

θ4

θ5 θ6

Figure 5. (α, β) plane division in six angular sectors.

τ φ θ1 θ2 θ3 θ4 θ5 θ6

+1 1 V2 V3 V4 V5 V6 V1

0 1 V7 V0 V7 V0 V7 V0

-1 1 V6 V1 V2 V3 V4 V5

+1 0 V3 V4 V5 V6 V1 V2

0 0 V0 V7 V0 V7 V0 V7

-1 0 V5 V6 V1 V2 V3 V4

Table 1: Optimal switching selection table.

In figure 6 it is represented the relative positions of the stator and rotor fluxes and the stator current vectors. From figure 6, and as can be seen in figure 7, the next applied voltage vector, will cause a displacement in the stator flux vector in order to reach the results determined by the comparators.

x

y

Φr

Φs

Is

γ

ω

Figure 6. Stator and rotor fluxes and stator current vectors.

According to the stator flux vector position, it is applied the voltage vector that satisfies the table entries requirements.

Considering the situation presented in figure 6, if it is wanted a torque increase and flux maintenance it

should be applied voltage vector V3, as it will be the one that will cause the bigger displacement of the stator flux vector in the direct direction.

V1

V2V3

V5 V6

V4

α

β

θ1

θ2

30º

90º

150º

210º

270º

330º

θ3

θ4

θ5 θ6

Φs

Figure 7. Possible voltage vectors to be applied to a stator flux vector.

Instead, vector V6 would cause a bigger displacement in the inverse direction. Every time the torque is out of the hysteresis bounds a null vector is applied (V0 or V7).

2.2 Speed control mode

It is also possible to implement a speed controller in closed loop using the DTC method. For that, it becomes essential to know the rotor mechanical speed. To meet this requirement it has been developed a rotor speed estimation algorithm.

Between several options, as referred earlier in this paper, there are open loop estimators, neural network and fuzzy logic based models and observers. However, due to methods complexity and to the implementation available means, an open loop estimator have been chosen.

In the presented application, the rotor flux is calculated from Equation (7):

( ) ryrxsssm

rr jILLL

Φ+Φ=σ−Φ=Φ (7)

where, Lm is the magnetizing inductance, Lr the rotor inductance, Ls the stator inductance and σ the leakage factor, calculated according to Equation (8):

))(( mrms

mLLLL

L++

=σ (8)

Afterwards, with the measured stator currents, it is obtained the electrical motor frequency. At last, the electrical speed is calculated by the following expression, Equation (9):

Φ−ω=ω

2r

erer

TRp (9)

This method has some error sources, since beyond using motor parameters that may have errors, there are still the flux and electrical angular speed calculations as the more complex quantities.

In the speed mode operation, the estimated speed is compared with the speed reference. The error is applied to speed controller, which supplies an electromagnetic torque reference.

3 Simulation

3.1 Simulation platform

Using the per phase equivalent circuit of a three phase induction motor, with the parameters presented in Table 2 (obtained with a set of essays according to the IEEE 112 Standard) it was implemented a control algorithm in the simulation software package “SABER”.

U 220/380 V Xm 22,92 Ω

I 18.5/11.5 A Xs 1,7 Ω

P 4 kW Xr 1,7 Ω

Cos ϕ 0.78 Rs 1,48 Ω

Poles 4 Rr 1,05 Ω

Table 2: Motor parameters.

The implementation was made considering the subsequent experimental validation in a hardware platform composed of diode rectifier and a MOSFET three phase inverter, being the control algorithm accomplished with a TMS320F240 digital signal processor.

The control algorithm has been implemented using a C function, which simulates the microcontroller, and the remainder components with the simulator blocks. In this way, the migration to the hardware system is made easier.

3.2 Simulation results After the algorithm implementation it were made several essays in order to evaluate the controller behavior, either in torque control mode, either in speed control mode.

3.2.1 Torque control mode In the essay presented in figure 8, in a first instant the electromagnetic torque and the flux references have been kept constant, being the load torque varied later. Afterwards, an electromagnetic torque reference step is applied, being the torque and flux kept constant.

Figure 8. Electromagnetic torque and flux behavior, with load torque applied.

As can be seen in figure 8, the system behavior is good, even in extreme conditions like the overload regime, in which the system has been submitted between instants t=0.25 s and t=0.375 s, tracking, even so, the supplied electromagnetic torque reference. The observed ripple in both electromagnetic torque and flux is due to the use of hysteresis controllers.

In figure 9, it can be seen an excellent response to an electromagnetic torque step, being fast (tr=500 µs) and without overshoot.

3.2.2 Speed control mode The speed controller essay was made supplying a speed reference of ω=300 rad/s (approximately

twice the nominal speed), having the motor no load coupled to the shaft.

Figure 9. Electromagnetic torque step response.

In this case, it is possible to verify an error of approximately 15 rad/s between real and measured speeds (figure 10). This error is due to the used speed estimation method.

Figure 10. Estimated and measured speed.

In figure 11 it is possible to observe both the controller generated electromagnetic torque and flux references, as well as the field weakening action.

4 Conclusions Is this paper it has been presented an implementation of the DTC control method associated with a three phase induction motor. Two control modes have been implemented, the electromagnetic torque mode and the speed control mode.

Figure 11. Field weakening mode operation.

Although the existence of a not so interesting behavior in the speed control mode, the results as torque controller were excellent. In fact, due to the speed estimator inferior performance, the speed controller mode has a less interesting behavior, inserting a significant error, implying a new speed estimation system implementation with higher precision.

However, the torque controller simulation results were very good verifying, as expected, an excellent torque control response, either in steady-state or transient regime. The good results continued steadily even when the system was submitted to the most demanding essays, like overload operation.

5 Acknowledgement The work presented in this paper was partially funded by FCT (Fundação para a Ciência e a Tecnologia), under POSI (Programa Operacional Sociedade de Informação) of QCA III (Quadro Comunitário de Apoio).

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