Scalar speed control of induction motors with difference frequency

Speed monitoring of electric motors has attracted the attention of many researchers from past to present. Induction Motor (IM), which is one of the electric motor types, falls behind the nominal speed in different loads. This study was conducted to increase the speed control performance of IM. In the study, speed control of IMs was realized by Difference Frequency (DF). The Scalar Control (SC) method was used in IM speed control. In order to increase the performance of SC, the frequency information received from IM was compared with the reference frequency. The resulting DF was applied to the system input again. For the performance analysis of the study; SC, PI + SC and DF + SC methods were compared. The results obtained from the study simulated in Matlab software show that the proposed method can be used in speed control.


INTRODUCTION
Induction Motors (IM) are preferred in industrial areas due to advantages such as simple structure, low cost, low maintenance requirements and high efficiency [1] - [5].This situation reveals the need for use of IMs at different speeds.However, the nonlinear dynamic model, the time varying parameters and external load torque of these motors makes the speed control quite complicated [6] - [9].In this context, it is expected from the control system that to have proper behavior of location and speed at transient and steady state, to respond well to the variable speed, not to be affected by changes in the disruptive input parameter such as an external force (load torque) [1], [10], [11].Speed control of IMs is carried out in two distinct ways: scalar and vector [12], [13].Considering the industrial application; Scalar Control (SC) method is being used because of simple structure, easy application and low cost [14].SC method is performed by maintaining Voltage / frequency (V / f) rate constant.The goal here is to keep constant the motor torque desired to be operated at different speeds.However, when IMs operated at low speed, torque production is reduced due to the reduction of internal voltage drop and dynamic performance of the motor decreases due to disruptive influences such as external load conditions [15] - [18].Therefore, SC method is used in conjunction with additional control methods such as Proportional-Integral-Derivative (PID) [19] - [21].However, parameter sensitivity of the PID controls is fairly weak.If the system controller coefficients are set well, system can be controlled in a good way.However, any changes in system parameters affect the performance of the controller negatively.In this case, the PID control coefficients will need to readjust [19], [22].In addition to classical methods of control, many methods have been suggested [23] - [25].These; Kalman filter [26], field orientation [27], [28], position [29], adaptive [30], finite elements [31], finite differences [32], logic [33], state feedback [34], stator voltage [35], observer-based [36], matrix theory [37], shift mode [38], digital signal processor [39], sensor-sensor-less [40], robust [41] control, etc.When the studies in recent years are examined, it is understood that intelligent audit methods Artificial Neural Network (ANN), Fuzzy Logic (FL), Genetic Algorithm (GA) etc. and these methods are used together with classical methods.In addition to the abovementioned methods, we observed that control methods such as ANN, FL, GA are used [42] - [45].Referring to the literature, it is observed that intelligent control systems which can be used instead of the PID have been developed [46], [47].These methods show the desired performance in the nonlinear case in system [48].Also, the control performance system is less affected from parameter variations [49] - [51].The aim of this study is not to reveal the positive and negative aspects of the known methods, but to reveal a different solution method.The purpose of this study is to improve the performance of the SC method utilized in speed control of IMs without the need for additional controller.The motor that controls to be carried are required to reach the reference speed at idle and load.Therefore, Difference Frequency (DF) + SC method is recommended in control of IMs.

MATERIAL AND METHOD 2.1. Mathematical Expressions of IMs
In terms of ease of simulation biaxial mathematical expressions of IMs are used.These statements are [4], [52], [53]; The stator voltage equations of dq axis: Rotor voltage equations of dq axis: Here; Stator and rotor flux given in these equations (Matrix expression): Flux equations in the air gap: The equation of torque generated by the motor: The equation of electrical torque generated by the motor:

Mathematical Expressions of SC
SC simulation was performed with the angle and amplitude ratio obtained by calculating from the reference frequency entered into the system.Reference voltage equations are given below for three phases [12].Here, SC simulation will be carried out with the angle and amplitude ratio obtained by calculating from the reference frequency entered into the system.Current, torque and speed graphics will be obtained by running the motor at idle and load [54].Here, PI sets the control input, reduces errors, and will work to achieve the desired reference frequency value.Current, torque and speed graphics will be obtained by running the motor at idle and load.

DF+SC method
IM simulation model of DF+SC method (The proposed method) is shown in Figure 3. Here, DF will be performed by adding the difference between the frequency obtained from motor speed and reference frequency to SC input.Current, torque and speed graphics will be obtained by running the motor at idle and load [55].Also, it is understood that the motor torque graph is at the desired value.However, when speed graphs examined it is understood that the SC method could not be successful by the motor load torque increases.But DF+SC gave the same results with PI+SC method and it is observed that this method is successful at speed control.The second simulation test input information is given in Table 2 and simulation test results are shown in Figure 5.The motor current, torque and speed graphs is given Figure 5 (a), respectively.Consequences are 10 Hz and 0 Nm in Figure 5 (a), 10 Hz and 0.25 Nm in Figure 5 (b), 10 Hz and 0.5 Nm in Figure 5 (c).It is seen that the motor current is equal to each other in these three simulation tests.Also, it is understood that the motor torque graph is at the desired value.However, when speed graphs examined it is understood that the SC method could not be successful by the motor load torque increases.But DF+SC gave about the same results with PI+SC method and it is observed that this method is successful at speed control.The third simulation test input information is given in Table 3 and simulation test results are shown in Figure 6.The motor current, torque and speed graphs is given Figure 6 (a), respectively.Consequences are 15 Hz and 0 Nm in Figure 6 (a), 15 Hz and 0.25 Nm in Figure 6 (b), 15 Hz and 0.5 Nm in Figure 6 (c).It is seen that the motor current is equal in these three simulation tests.Also, it is understood that the motor torque graph is at the desired value at SC and DF+SC methods but it is not at the desired value at PI+SC method.When speed graphs examined it is understood that SC and PI+SC methods could not be successful by the motor load torque increases.For this simulation test, it is observed that DF+SC method is successful at speed control.The fourth simulation test input information is given in Table 4 and simulation test results are shown in Figure 7.

Table 2. The second simulation tests input information
The motor current, torque and speed graphs is given Figure 7   shows that the motor operates at a constant speed.It is understood that the motor has 0%, 0.25% and 0.51% speed error respectively when operating at 0, 0.25 and 0.5 Nm load torque.

CONCLUSION
In this study, IM' Scalar Speed Control with Difference Frequency were performed.The results obtained from this study can be listed as follows.
 SC: It shows desired performance in all speed during idling.When working in load, at low speeds it does not show the desired performance.The desired control results are obtained when working at high speed in idle and load [17].
 PI+SC: Coefficients determined for PI controller shows desired performance in specific speed ranges.Nevertheless, while the range of speed and torque changes it does not demonstrate the required performance [19], [22].
 DF+SC: This proposed method indicates the desired control performance in each case tested.
 The obtained results indicate that the proposed method will contribute speed control operations done in industrial areas.
When considering developments in this area, much more work can be made.

2 . 4 .
Methods for Control of IMs 2.4.1.SC method IM simulation model of SC method is shown in Figure 1.

Figure 1 .
Figure 1.Simulation of SC Method

Figure 3 .
The first simulation test results

Figure 4 .
The second simulation test results

Figure 5 .
The third simulation test results (a), respectively.Consequences are 50 Hz and 0 Nm in Figure 7 (a), 50 Hz and 0.25 Nm in Figure 7 (b), 50 Hz and 0.5 Nm in Figure 7 (c).It is seen that the motor current is equal in these three simulation tests.When examining torque graphs in three methods, it is seen that the desired result is obtained by SC and DF+SC methods.When speed graphs examined it is understood that SC and DF+SC methods are successful by the motor running at idle and load but PI+SC control is not successful.

Table 4 .Figure 6 .
Figure 8 is presented for a better understanding of the performance of the proposed method.A frequency of 25 Hz was applied to the IM.The results obtained from different load moments are shown on the same graph and the traceability of the results has been increased.In Figure8(a) shows the torque graph, (b) the velocity graph.Figure8 (b)shows that the motor operates at a constant speed.It is understood that the motor has 0%, 0.25% and 0.51% speed error respectively when operating at 0, 0.25 and 0.5 Nm load torque.

Figure 8 .
Performance analysis of motor at constant speed and different load moments

Table 3 .
The third simulation tests input information