The Sensorless Speed Controller of Induction Motor in DFOC Model Based on the Voltage and Current

This paper presents the Sensorless Speed control of the Induction Motor (IM) in Direct Field Oriented Control (DFOC) modeling based on the mathematical model of the voltage and current parameter. The rst is DFOC controlled modeling of IM, the second presents sensorless speed controller base on RF-MRAS, the third describes the model of the sensorless speed controller based on measured values directly from the induction motor as the voltage and current. The last is simulation results in the Matlab-Simulink environment. These results indicate that this proposed method can determine accurately, very quickly the speed of the induction motor and can be applied in the practice with high reliability, and low cost.


Introduction
The controller of an induction motor without speed sensors have the advantage of low cost and high reliability, reduction of hardware, working in hostile environments, decreased maintenance requirements.The sensorless speed control method can be classied as follows: 1.The method with machine model such as open loop estimators, Model Reference Adaptive System (MRAS) [1]- [5], observes (Kalman lter, extended Kalman lter) [6]; Luenberger observer [7]; sliding mode observer.
2. Method without machine model is the estimators using intelligence algorithms such as Kalman lter techniques, Neural network, Fuzzy-logic based sensorless control [8]- [12], etc.
The model of reference adaptive system approach [3] is based on the comparison between the outputs of two machine models: the rst one (reference model) does not contain the rotor speed, while the second one (adaptive model) uses the speed to estimate the machine ux.The outputs of the two models are compared to obtain an error signal.The error is the input of a proper adaptation mechanism to generate the estimated speed which is fed back to the adaptive model.This solution requires open-loop integration and drift problems could appear, this aspect is solved using a Low-Pass Filter (LPF) instead of an integrator.The Adaptive-Observers (AO) approach using the Luenberger observer [7] or the Kalman lter [6], gets accurate ux and speed estimates under detuned operating conditions.The key issue of the AO is the computation of their gain matrix to get stability and optimum ltering when both inputs and outputs are corrupted by noise.These solutions are still considered computationally intensive or dicult to tune, so the MRAS modeling is pretty complexity.
The estimators with using intelligence algorithms take much time so it needs a powerful processor such as a digital signal processor (DSP), which also means higher prices.This paper proposes a simple and robust Sensorless speed of Direct Field Oriented Control (DFOC) scheme for low cost applications.
The DFOC model improves motor exploitation (torque, power factor) and the drive eciency.The proposed scheme is based on measured current and voltage of closed-loop DFOC speed controlled modeling.This algorithm is very eective for fast estimation and does not require high speed DSP (It also means reducing costs), but methods using soft-calculated algorithms have a longer response time and require a high-speed DSP and mean that the cost will be higher.The SS-DFOC scheme has been developed and implemented on a low-cost Chip-based controller with the induction motor drive for a primary vacuum pump, fan, etc is used in industrial applications.

THE MODEL OF IM IN DFOC CONTROL STRUCTURE
This part will present the Mathematical Base and speed controlled structure of induction motor with sensorless speed in Direct Field Oriented Control model.

The Mathematical Base of the Induction Motor
The equations of the induction motor model in x − y the coordinates are expressed as follows [10,13]: c 2019 Journal of Advanced Engineering and Computation (JAEC)

The Speed Control Structure of the Induction Motor Drive
From the above equation system, we will construct the SS-DFOC control structure for induction motor drive as below Fig. 1. [1,13].

The Mathematical Equations of RF-MRAS Model
In this model, we only care about the speed of the motor, so the value of the stator resistor is known as given in the simulation (the value of the stator resistor is easily collected by ohm meter).
The signal of error is given by the following expression: where K P > 0, K I > 0.

The RF-MRAS Model
The block structure of the model of reference adaptive system (RF-MRAS) with the adaptation method of the speed estimation is shown in Fig. 2. [3,13].
Integrate the two sides of ( 14) and (15) we have with ψ sα (0) = 0, ψ sβ (0) = 0, substitution of Equations ( 16) and (17) into Equations ( 12) and ( 13) separately, we obtain the following equations: The above integral equations may be written in the following concise forms. where Equations ( 20) and ( 21) are functions of the rotor speed, we can rewrite as c 2019 Journal of Advanced Engineering and Computation (JAEC) with From ( 23) and ( 24) we calculate the angular velocity as follows: However, we cannot use them to estimate the rotor speed directly because the sinusoidal variables D β and Q α may equal zero.In order to avoid division by zero, we can change as follows: squaring equations ( 23) and ( 24) adding the resulting equations.
Take the square root of both sides, we obtain the expression as: When the magnitude of the sinusoidal variables is larger than zero, the rotor speed may be estimated by: .
(29) However, the above formula gives only the absolute value of the angular velocity.We need to identify its sign with the following inference: From (4.21) we have: The last formula uses to calculate the angular velocity as follows: In addition, we need to use the low pass lters at the input of the signals: v sα , v sβ , i sα , i sβ and the output of signal: w 0 to eliminate the noise that can aect the accuracy of the estimated velocity.
The applications in real, the desired pass-band frequency is 100 Hz (628.3 rad/s), we need ve Analog Filter Blocks.
The blocks have the following feature: Design method: Butterworth, Filter type: Low-pass, Filter order =1, Pass-band cut frequency (rad/s) = 628.3rad/s Now, we build the speed estimation model as shown in Fig. 3.

The Machine Model
From equation (31) we proved.Now, we construct a model of estimation of speed as follows:

SIMULATION RESULTS
The induction motor is used for simulation in MATLAB-SIMULINK has the following basic parameters: P = 0.735 kW, U dc =270 V, P p = 2, R S =2.1 Ω, R r =2.51 Ω, L m = 0.129 H, L S = 0.137 H, L r = 0.137 H, J=0.043 kg.m 2 .
In this section, we will simulate three dierent speed levels: 100 rpm, 60 rpm and -40 rpm for both methods.The following gures show the response of the estimated speed with the RF-RAS model, the error between the estimated speed and the actual speed (see Figs. 4-6).In case we do not use a low-pass lter, the response we get is as follows: (see Fig. 8) In case we use the low-pass lter in the model, the response we get is as shown below: (see Figs. From the above simulation results, we nd that when there is no low-pass lter, the response of the speed is ripple (Fig. 8.) but when using a low-pass lter the accuracy of the MM is good at many dierent speeds (Fig. 9.), at the speed is near zero, the error is still quite large [1] and [9].Comparing the MM method to the RF-MRAS model, we nd that its characteristics are approximately equal.
In addition, we also obtain the response of the stator current and rotor ux during the operation as follows: (see Figs. 11-12)   With the response of the current and ux at 1.2 seconds, the speed of the induction motor changing direction leads to a sudden change in its response.This paper presents a method; for estimating the speed of an induction motor; based on a machine model (MM).It achieves accuracy at many dierent speed levels, but it is limited at near zero speed.Its characteristics are compared to the RF-MRAS model, its advantage is that convergence time is faster than RF-MRAS model because it calculates directly the current and voltage measured from the induction motor.RF-MRAS model is adaptive so they time to converge.Also on the hardware, it does not need a high speed DSP as intelligent estimation methods: Genetic Algorithm (GA), Articial Neural Network (ANN) [8] and [9], Fuzzy logic [10] etc and thus reduces the cost of implementation.They can be applied in places where no need to operate at near zero speed such as fans, pumps, etc or other applications using V/Hz technology in the past.

vP
sx , v sy Components of stator voltage in [x, y] system i sx , i sy Components of stator current in [x, y] system i rx , i ry Components of stator current in [x, y] system The number of poles P = P/2 The number of pole pairs v sα , v sβ Component of stator voltage in [α − β] system i sα , i sβ Component of stator current in [α − β] system ψ Rα , ψ Rβ Component of rotor ux in [α − β] system ψRα , ψRβ Component of estimated rotor ux in [α − β] system

Fig. 3 :
Fig. 3: The schemes of Speed Estimation base on Machine Model.

5. 1 .
Estimate Speed of IM base on RF-MRAS Model

Fig. 10 :
Fig. 10: The dierence between real speed and MM estimated speed.