Torque Ripple Reduction in DTC Induction Motor Drive

3.2.1 Field oriented control (FOC)

The FOC method is implemented based on the analogy of controlling a DC motor. It does not guarantee an exact decoupling of the torque and flux in dynamic and steady state operations. The full information about motor state variable and load torque is required for controlling the IM. The relationship between regulated value and control variables is linear only for constant rotor flux amplitude. The current controllers, coordinate transformations and a PWM algorithm are required. For direct FOC, flux estimator is required. In indirect FOC mechanical speed sensor is needed. This method is very sensitive to rotor time constant.

3.2.2 Direct torque control (DTC)

The DTC is one of the high performance control strategies for the control of AC machine. In a DTC drive applications, flux linkage and electromagnetic torque are controlled directly and independently by the selection of optimum inverter switching modes of operation. To acquire a faster torque output, low inverter switching frequency and low harmonic losses in the model, the selection is made to restrict the flux linkages and electromagnetic torque errors within the respective flux and torque hysteresis bands. The required optimal switching vectors can be selected by using the optimum switching voltage vector look-up table. This can be obtained by simple physical considerations involving the position of the stator-flux linkage space vector, the available switching vectors, and the required torque flux linkage.

The torque is controlled by the stator current component Isqin the classical vector control strategy of FOC according to the Eq. (1)

The motor torque is expressed by rotor flux magnitude Ψrand stator current component Isqas given in the Eq. (2) and this equation is written as:

The Eq. (2) is transformed into the Eq. (3)

whereδis the angle between rotor flux vector and stator current vector and δΨis the angle between rotor and stator flux vectors. The torque value depends on the magnitude of stator and rotor flux as well as the angle δΨ. For FOC methods, the angle δis considered whereas angle δΨis considered for DTC techniques.

The vector diagram of IM is shown in Figure 5.

From the motor voltage Eq. (5) for the omitted voltage drop on the stator resistance, the stator flux can be expressed.

From the mathematical model of IM, the electromagnetic torque equation is given in the Eq. (4)

Taking into consideration the fact that in the cage motor the rotor voltage equals zero and the electromagnetic torque Eq. (4), the following Eq. (5) is derived.

Taking into consideration the output voltage of the inverter in the above Eq. (6) it can be written as

where

The Eq. (7) describes eight voltage vectors which correspond to possible inverter states. These vectors are shown in Figure 6. There are six active vectors U1 to U6 and two zero vectors U0, U7.

It can be seen from the Eq. (7) that the stator flux directly depends on the inverter voltage Eq. (8). By using one of the active voltage vectors the stator flux vector moves to the direction and sense of the voltage vector. Stator flux changes direction for the cycle sequence of the active voltage vectors. Inherently the rotor flux of IM moves slowly but the stator flux could be changed immediately. In DTC methods the angle δΨbetween stator and rotor flux is varied to control the torque. By adjusting the stator voltage, stator flux could be controlled in simple way. The above consideration and equations could be used in the analysis of classical DTC techniques and SVM-DTC methods. In the classical DTC method the control plane is divided for the six sectors shown in Figure 7, that are defined as:

In order to increase magnitude of the stator vector in sector 1, the following voltage vectors U₁ U₂ U₆ are selected. Conversely to decrease, U₃ U₄ U₅ are selected. The stator flux is not changed when any one of the zero vectors U₀ or U₇ is applied. The solving of integration in Eq. (7) is stopped.

To increase the motor torque, the voltage vectors U₂ U₃ U₄ are selected and for decreasing the torque U₁ U₅ U₆ are selected. The switching Table 1 is constructed based on the above considerations.

I. Takahashi and T. Nogouchi proposed the control scheme for Direct torque control and it is block diagram is shown in Figure 8.

The reference signals such as stator flux amplitude Ψscand the electromagnetic torque Mcare compared with the estimated flux amplitudeΨ̂sand electromagnetic torque M̂evalues respectively. The error values such as eΨand torque eMare sent to the hysteresis controllers. The appropriate voltage vector from the switching table is selected by the digitized output variablesdΨ, dMand the stator flux position sectorγssN. The power switches in the inverter are controlled by the pulses S_A, S_B, S_C which are generated form the switching table.

According to the Eq. (15) the torque and flux errors are calculated.

3.2.3 Problems in conventional DTC

Despite its simplicity and robustness, the conventional DTC control has major drawback. The use of hysteresis controllers causes high ripples in the flux and electromagnetic torque at low speeds. It results in undesirable mechanical vibrations and acoustic noise, and subsequently leads to degradation of the machine performances. Thus the variable switching frequency and current distortions could detoriate the quality of the output power. The negligence in the calculation of stator resistance leads to problems at low speed. Moreover, the practical implementation of nonlinear components of the hysteresis type needs low sampling period. Many DTC strategies are developed based on the principle of instantaneous torque and stator flux regulation in order to rectify the drawbacks of classical DTC. The direct determination of the inverter control signals from the switching table is implemented [9].

4.1.1 Modification in switching tables

The modifications are carried out in the DTC- basic switching table with the objective of improving starting and overload conditions which enable all the voltage vectors are applied in appropriate sequence. They are implemented by two methods namely 1. Six sector table and 2. Twelve sector table respectively. The zero voltage vectors are selected from the switching Table 1 during starting and very low speed conditions and results in flux level reduction due to the drop in stator resistance [11].

4.1.2 Dither signal injection

Feedback signals should not be delayed in order to maintain maximum possible switching frequency. Due the presence of isolation amplifier, Hall effect transducer and other components, the delay is made inevitably. By introducing the dither signal at very high frequency, the effect due to delay could be compensated. Normally these dither signals are triangular waves at double or triple the sampling frequency of the system. This dithering technique minimizes the torque ripple to 30% compared to conventional DTC method [14].

The frequency of the dither signal is selected well above the cutoff frequency of the system so that its presence could not be detected in the output. When the system parameters are not exactly known and not alterable, the method of instantaneous injection of dither signal is robust to noise in measurements. The inherent delay in signal transduction, data acquisition system and computation leads to low switching frequency which would result in increased torque and flux ripples. The dithering signal injection is implemented to improve the switching frequency of inverter. The appropriate magnitude and frequency of dither signals which are injected in torque and flux errors could minimize torque ripples and acoustic noise level in the drive [15].

4.1.3 Deadbeat control

In the inverter operation to avoid a short circuit in the DC-link, only one switch is turned on at a time. During the transistor switching signals, a delay time must be inserted and as a result the transistors stops to conduct. The dead-time TD is presented for the transistors T₁, T₂ for the two control signals SA+, SA- respectively. Most of the transistors take 1-3 μs duration of dead-time. The safe operation of the inverter is guaranteed by this delay time but it results into a serious distortion in the output voltage. Consequently there is a loss of control momentarily, where a deviation in output voltage from the reference voltage is observed. It is repeated for every switching cycle, so it has significant impact on the control of the inverter and this is known as dead-time effect. The inverter has nonlinear characteristics due to the dead-time and voltage drop on the switching devices. So the compensation algorithms are required in the control strategies [8] as shown in Figure 10.

The dead-beat DTC scheme is based on the technique, forcing the magnitude of torque and stator flux to attain their reference values in one sampling period. It is achieved by synthesizing a suitable stator voltage vector applied from Space Vector Modulation (SVM). In this approach the changes in the magnitude of torque and flux over one sampling period are calculated from the motor equations. To get the command value of stator voltage vector in stationary coordinates, a quadratic equation is solved [11].

The flux estimation is crucial part in the sensor less control strategies. The algorithm used for this is sensitive on the calculation accuracy of the inverter output voltage. From the switching signals, the voltages are reconstructed. Figure 11 shows the DTC control with modification of flux error status block [13] dead-time compensation algorithm is significant in this SVM-DTC method [8].

The torque and flux ripple are reduced when the switching frequency of the inverter is maintained constant and greater than the sampling frequency [11].

4.1.4 SVM-DTC

The main difference between classical DTC and DTC-SVM (Figure 12) control methods lies in which the control algorithm is being used for the calculations. Based on the instantaneous values, the classical DTC algorithm directly calculates the digital control signals for the inverter. In the DTC-SVM methods control algorithm calculations are based on averaged values whereas the switching signals for the inverter are calculated by space vector modulator. Based on voltage model, the flux estimator with reference flux is selected for the implementation DTC-SVM control structure in sensor less mode of operation [8].

4.1.4.3 Proposed artificial intelligent schemes for DTC-SVM

The Space Vector PWM (SVPWM) is a technique used for solving the switching losses in the power converter. The SVPWM is operated in a symmetrical way, so the switching state of each sector is predefined. In this proposed scheme, the initial values to the DTC controller have been fixed based on the induction motor rating. Then the estimation of DTC parameters is found and it is fed to the reference to the Hybrid Asymmetric Space Vector PWM (HASVPWM) controller.

Traditional PWM techniques consist of two signals called carrier signal and reference signal for generating the PWM pulses. If any distortions in the reference signal (i.e error signal) may produce miscellaneous pulses, which will affect the performance of the converter. But SVPWM technique is purely based on estimating the voltage magnitude and its angle for pulse generation. In this, three phase voltages Vabc are converted into Vd,Vq and V0 using abc-dq0 theory. This method will make the estimation of the sector angle and voltage magnitude easier. In traditional SVPWM, each sector denotes 60⁰ angles and totally it has six sector and two reference vector in its implementation. Even though the estimation is done for every sector accuracy of generating the pulses is lagging due to the higher range of sector angle and minimum switching sectors. For an example, if estimated sector angle is 55⁰, then the switching pattern in sector 1 is selected for the PWM generation. But V₂ vector is also having different switching pattern and that may also well suited for the same estimated sector angle 55⁰. In order avoid such difficult situations, a HASVPWM is used for controlling the DTC drive which reduces torque ripples, switching losses and improved power quality.

The implementation of HASVPWM is similar to the SVPWM technique. In general, three phase Voltage source inverters (VSI) have eight distinct switching losses, where state 1 to 6 are active states, 0 and 7 are inactive switching states. In HASVPWM, asymmetric voltage vectors are represented as Vni, Vnj and Vnk where n = 1,2,3,4,5,6 and four quadrants. HASVPWM has two non-zero vectors (V1 and V2) and two zero vectors (V0 and V24) in each vector will be used for the vector 15⁰.Hence this HASVPWM have 24 sectors and it is shown in Figure 13.

Major portion in HASVPWM is to removal of mismatching pulses which will be done by comparing the HASVPWM pulses with the traditional SVPWM pulse. The mismatching pulses are removed by calculating its rise time (T_r) and fall time (T_f) of the mismatching pulses with magnitude. Then the same magnitude of pulse with same instant is added. For mismatching pulse removal. This logic avoids the mismatching pulses in the output and reduce the switching losses in the VSI based DTC drive. In this proposed system, intelligent control methods such as Fuzzy Logic Control (FLC) and Artificial Neural Network (ANN) are utilized to find the suitable sector for continuous operation. They are also efficient than the classical control techniques which are utilized to find suitable sector for the continuous operation.

4.1.4.3.1 Fuzzy logic controller for HASVPWM

The proposed hybridization process is performed by the combination of continuous ASVPWM and fuzzy operated Discontinuous ASVPWM technique. Finally, the mismatching pulses of both PWM techniques are applied to control the inverter. Pulse mismatching technique helps to reduce the active region of the switch and achieve the optimal input pulse to the inverter. Pulse mismatching technique helps to reduce the active region of the switch and achieve the optimal input pulse to the inverter. The optimal hybrid pulse reduces transition time of inverter switch and improves operating performance of the inverter. The Fuzzy rules help to select the optimal switching sector for discontinuous modulation. If there is more number of sectors in the hexagon, it allows more degrees of freedom which help to find the optimal reference voltage and angle. The Fuzzy logic system describes to what degree the rule applies, while the conclusion assigns a fuzzy function to each of one or more output variables. These Fuzzy Expert Systems allow more than one conclusion per rule.

The linguistic labels are divided into five groups. They are: NB-Negative Big; NS- Negative Small; ZE-zero; PS-Positive Small; PB-Positive Big. Each of the inputs and the output contain membership functions with all these five linguistics.

The set of rules in a fuzzy expert system is given in Table 3 and corresponding input and membership function values are indicated in Figure 8.

CE\E	NB	NS	ZE	PS	PB
NB	NB	NB	NS	NS	ZE
NS	NB	NS	NS	ZE	PS
ZE	NS	NS	ZE	PS	PS
PS	NS	ZE	PS	PS	PB
PB	ZE	PS	PS	PB	PB

Table 3.

Fuzzy Logic Rules to select suitable sector in HASVPWM.

The simulation model of DTC with HASVPWM scheme is developed using MATLAB software Simulink tool. The fuzzified inputs and defuzzified outputs are shown in Figures 14–16 respectively. Consider a case, when the sector angle estimated from the SVPWM calculation as shown in Figure 14 is equal to −165⁰, it means negative big (NB) as mentioned in Table 3. And change in the sector angle at the next instant is about −110⁰, it represent the negative small (NS). Then the corresponding fuzzy output is NB, which is mentioned in Figure 16.

4.1.4.3.2 Artificial neural network controller for HASVPWM

The DTC control can also be achieved with HASVPWM using Artificial Neural Network (ANN) control. ANN is nonlinear model that is easy to use and understand compared to statistical methods like Fuzzy logic. Compare with Fuzzy Logic, ANN has an ability to learn from the previous trained data. Hence, the major advantage of ANN is to train a system with large amount of data sets. The output performance will depend upon the trained parameters and the data set relevant to the training data. In this proposed scheme, ANN is used to estimate the suitable sector of HASVPWM.

ANN is used to determine the sector number for the estimated value of θe. There are total of 24 sectors, each sector of 15 degree. Again three layers of neurons are used but with a 5–4-1 feed forward configuration as shown in Figure 17. The Input layer is of log sigmoid transfer function, hidden layer is of hyperbolic tangent sigmoid function and the output layer is of linear transfer function. Levenberg -Marquardt back propagation based training method is used for train the neurons. As soon as the training procedure is over, the neural network gives almost the same output pattern for the same or nearby values of input. This tendency of the neural networks which approximates the output for new input i.e. angle theta since sector selection is purely based on theta.

The following Figure 17 shows the structure of Neural Network (NN) which is utilized in the proposed ANN controller for DTC-SVM scheme for induction motor.

The Step by step procedure for NN Algorithm is given below:

Step 1: Initialize the input weight for each neuron.

Step 2: Apply the training dataset to the network. Here X is the input to the Network and Y₁, Y₂ and Y₃ are the output of the network.

Step 3: Adjust the weights of all neurons.

Step 4: Determine Sector Angle for SVPWM.

Compare with Fuzzy logic control, ANN control in HASVPWM is able to identify the suitable voltage vector and its angle for minimizing the torque ripple and PEC losses and THD, maximizing DTC capabilities under various operating conditions like speed reversal, loading conditions etc. The effectiveness of ANN-HASVPWM in DTC scheme is predicted by comparing ANN with the Fuzzy based HASVPWM scheme. The results for ANN based HASVPWM scheme to DTC controller under the same loading conditions, it shows that torques ripple, switching loss and harmonic content reduction is expected. The comparative simulation results are clearly presented and shown in Table 4.

Control strategies	Torque ripple factor (%)
Proposed FLC controller for HASVPWM FOR DTC-SVM scheme	5.1
Proposed ANN controller for HASVPWM FOR DTC-SVM scheme	4.5

Table 4.

Comparison of control strategies in induction motor.

4.1.4.3.3 Simulation results and discussion

The two proposed schemes namely 1.Fuzzy Logic Controller (FLC) for DTC-SVM and 2.Artificial Neural Network (ANN) controller for DTC-SVM respectively for IM. Has been simulated using MATLAB version R2009a and the results are compared and shown in Table 4. Both of the proposed scheme methods uses HASVPWM. The parameters of IM used in the simulation are given in the appendix.

The torque ripple can be calculated by using the relation.

Torque Ripple Factor=Peak to Peak torque/Rated torqueE16

The simulation results of FLC for DTC-SVM of IM with HASVPWM is shown in Figures 18 and 19.The simulation results of ANN for DTC-SVM of IM with HASVPWM is shown in Figures 20 and 21.

From Figure 19 (Torque ripple waveform) it is inferred that the torque ripples oscillates from 9.5 Nm (Minimum) to 10.1 Nm (maximum) for the given Reference torque of 10 Nm.

Torque Ripple factor (%) as per Eq. 23 is given by = ((10.01–9.5)/10) × 100 = 0.51/10×100 = 5.1.

From Figure 21 (Torque ripple waveform) it is inferred that the torque ripples oscillates from 9.55 Nm (Minimum) to 10 Nm (maximum) for the given Reference torque of 10 Nm.

Torque Ripple factor (%) as per Eq. 23 is given by = ((10–9.55)/10) × 100 = 0.45/10×100 = 4.5.

Figure 22 shows the comparison of Torque Ripple of FLC and ANN based DTC-SVM of IM with HASVPWM at 1000 rpm.

It is clear that variation in Torque ripples shown in Table 4 is less in case of ANN and they can achieve a minimum torque ripple than other control techniques. It has been viewed that the discussed control strategy has helped in reducing the torque ripples. Thus, by using FLC and ANN based controller for DTC of IM, the ripples are reduced completely.