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This paper is concerned with a framework which unifies direct torque control space vector modulation (DTC-SVM) and variable structure control (VSC). The result is a hybrid VSC-DTC-SVM controller design which eliminates several major limitations of the two individual controls and retains merits of both controllers. It has been shown that obtained control laws are very sensitive to variations of the stator resistance, the rotor resistance, and the mutual inductance. This paper discusses the performances of adaptive controllers of VSC-DTC-SVM monitored induction motor drive in a wide speed range and even in the presence of parameters uncertainties and mismatching disturbances. Better estimations of the stator resistance, the rotor resistance, and the mutual inductance yield improvements of induction motor performances using VSC-DTC-SVM, thereby facilitating torque ripple minimization. Simulation results verified the performances of the proposed approach.

Many fascinating and challenging subjects of induction machine control have been developed in order to provide a fast dynamic response of torque and reduction of the complexity of field oriented algorithms. Among several approaches used to control induction motors (IM) is the direct torque control (DTC), which has significantly improved the drive performances when compared to the vector control. The DTC was first proposed by Takahashi and Noguchi and by Depenbrock et al. in the mid of 1980 [

Recently, many research efforts have been carried out to reduce the torque ripples and harmonics and to improve the uncontrolled commutation frequency. In fact, in order to reduce the level of torque and flux ripples, several researchers have proposed the use of multilevel inverters [

It should also be noted that the stator resistance, the rotor resistance, and the mutual inductance changes can significantly degrade the performances of a DTC-SVM induction motor, since the stator resistance is required for stator flux estimation and the rotor resistance and the mutual inductance are required for torque estimation in the basic configuration of DTC-SVM. A lot of researches have proposed nonlinear control laws with parameter estimations [

Within this approach, this paper proposes a DTC-SVM scheme using sliding mode controllers-based parameters estimator for induction motor drives. The effects of the stator resistance, the rotor resistance, and the mutual inductance variations on performances of VSC-DTC-SVM drives are investigated. Moreover, the expected responses to such a variation in terms of electromagnetic torque, stator flux, and stator current are confirmed through simulation results. Sensitivities of the DTC-SVM to temperature variations, leading to stator and rotor resistances changes, and to variations on the magnetic permeability of the stator and rotor cores, are eliminated by online estimation of stator and rotor resistances and mutual inductance. The proposed VSC-DTC-SVM control algorithm based on parameters estimator is verified by simulation results.

While stochastic systems are very sensitive to external disturbances [

The dynamic behavior of an induction machine is described in terms of space variables as follows:

Relationships between currents and flux are

The machine speed results from the following differential equation:

In a voltage fed three phases, the switching commands of each inverter leg are complementary. So for each leg, a logic state

The voltage vector of the three-phase voltage inverters is represented as follows:

The DTC strategy is built upon the direct control of stator flux and electromagnetic torque through stator voltage vector selection. This strategy presents the advantage of a very simple control scheme of stator flux and torque by two hysteresis controllers, which give the input voltage of the motor by selecting the appropriate voltage vectors of the inverter through a look-up-table in order to keep stator flux and torque within the limits of two hysteresis bands.

The basic equation governing induction motor operation stator flux is given by

Electromagnetic torque in an induction motor is given by

It can be concluded from (

However, the basic DTC approach causes large torque and flux ripples, accompanied by acoustical noise, due to the uncontrolled switching frequency [

The direct torque control based on space vector modulation (DTC-SVM) preserves DTC transient merits, furthermore, it produces better quality of the steady state performances in a wide speed range [

When this method is employed, the hysteresis controllers and the look-up tables present in DTC are replaced by PI controllers and a space vector modulator, thus achieving a fixed switching frequency and reducing considerably the switching losses as well as torque and current ripples.

The linear PI controllers and a space vector modulator are investigated by [

Sliding mode (SM) control is well known as variable structure control (VSC) [

The objectives of the sliding mode control consist of the following steps [

Design the switching function

Then, a choice of the sliding surface

with

Determine a switching control strategy as

In order to decide a system trajectory, the equivalent control

Thus, one can choose for the controller the following expression:

and the equivalent control can be designed as follows. When the system remains on the sliding surface, we have

The proposed variable structure controllers will be designed to provide the fast and accurate torque and flux control laws which replace the traditional hysteresis comparators used in conventional DTC strategy. The sliding surface is chosen as

While the stator flux remains constant, it has been shown that the transmittance binding the torque

Considering (

Sliding mode loop of the speed control.

Consider the following

The slip angular reference speed

The synthesis of the sliding mode controller of the stator flux consists of these following stages.

The choice of the sliding surface is given by (see Figure

Sliding mode loop of the flux control.

Similarly to the last case, and imposing

The new structure of this control approach is given by the block diagram of Figure

Block diagram of DTC-SVM with sliding mode controllers.

The sensitivity of the DTC-SVM to (i) variations on the magnetic permeability of the stator and rotor cores and (ii) variations on the rotor resistance, which can vary with time and operating conditions, can be removed by an online estimation of the mutual inductance and rotor resistance. The adaptive VSC of the speed can be derived based on the mutual inductance and rotor resistance estimations using the

The following slip angular reference speed control law stabilizes the speed loop:

Consider the following function:

The time derivative of the

Thereby, (

One of the main problems of the DTC of induction motor drives is the variation of the stator resistance, which could change up to 1.5–1.7 times of its nominal value. It is affected mainly by the change in motor temperature and stator frequency variation. This variation decreases the performances of the drive by introducing errors in the estimated magnitude and position of the stator flux vector [

The following stator voltage control laws stabilize the flux loop:

Considering the following function:

The time derivative of the

The induction motor has the following ratings: 220 V, 10 kW, and 1470 rpm at 50 Hz. Its parameters are

The above induction motor parameters have been determined from stator resistance measurement, no load test and blocked rotor test of an induction motor [

The induction motor is coupled to a load whose torque is proportional to the speed, such that

The rotor flux reference was constant,

The drive has been subjected to the following speed and torque profiles:

The speed increases from 0 s to 1 s to reach the nominal speed

Then the speed will be stabilized at

After that, a linear and rapid decrease of the speed to

Finally, the speed will be stabilized at

Figure

Transient behavior of the induction motor under DTC-SVM using sliding mode controllers, without parameters variations.

Figure

a linear decrease on the mutual inductance applied starting from

a linear increase of the rotor resistance from 0.5 s to 0.7 s,

and a linear increase of the stator resistance from 1.3 s to 1.4 s.

Transient behavior of the induction motor under DTC-SVM using sliding mode controllers without parameters estimation, with parameters variations

Computer simulations have been performed to determine the observer sensitivity to motor parameters changes. We have considered the stator resistance, the rotor resistance, and the mutual inductance which take shapes described above.

Figure

Transient behavior of the induction motor under DTC-SVM using sliding mode controllers with parameters estimation, with parameters variations

The obtained results can be illustrated as

Referring to Figures

Referring to Figures

Referring to Figures

The curves relating to VSC-DTC-SVM approach, with the adaptive estimators show the effectiveness of the proposed controllers. These curves prove the robustness of the proposed parameter estimators in the case of parametric variations.

Figure

Figure

In order to have real estimations of the stator and rotor resistances and the mutual inductances, we have added a saturation function on these estimations. In fact, stator resistance and rotor resistance cannot be less than their values at cold. Moreover, they have no meaning if they become larger than three times of these values. However, the mutual inductance cannot be larger than its value at rest, and its value has no meaning if it becomes smaller than the quarter of its value at rest. Then we have:

where

Evolution of estimated stator resistance

The present work has been dedicated to the study of a framework unifying direct torque control space vector modulation (DTC-SVM) and variable structure control (VSC). The result, which is a hybrid VSC-DTC-SVM controller design, eliminates limitations of the two individual controls. It retains merits of both controllers.

Moreover, The present paper has been devoted to the analysis of effects of the stator resistance, the rotor resistance, and the mutual inductance variations on the performances of the VSC-DTC-SVM induction motor drive system. Based on Lyapunov theory, on line estimations of these parameters have been carried out to improve performances of the proposed approach. Regarding the induction motor, simulation results dealing with performances of the adaptive VSC-DTC-SVM approach dedicated to speed drives have been presented and discussed.

The presented work can be easily applied to stochastic systems. In fact, sliding mode control is insensitive to external disturbances. However, the application of this work can be extended to other classes of complex systems, such as time delay systems, hybrid systems, and so forth.

The authors declare that there is no conflict of interests regarding the publication of this paper.