SPEED SENSORLESS VECTOR CONTROL OF INDUCTION MACHINE BASED ON THE MRAS THEORY

PRAJAPAT K.K.¹*, LAL V.N.²*, SHUCHI SHUKLA³*, SRIVASTAVA R.K.⁴*
¹Department of Electrical Engineering, Sri Balaji College of Engg. & Tech., Jaipur (Raj.), India
²Department of Electrical Engineering, Institute of Technology, Banaras Hindu University, Varanasi India -221005
³Department of Electrical Engineering, Sri Balaji College of Engg. & Tech., Jaipur (Raj.), India
⁴Department of Electrical Engineering, Institute of Technology, Banaras Hindu University, Varanasi India -221005
* Corresponding Author : rksrivastava.eee@itbhu.ac.in

Received : 21-08-2011     Accepted : 22-09-2011     Published : 01-12-2011
Volume : 2     Issue : 2       Pages : 30 - 36
J Electron Electr Eng 2.2 (2011):30-36

This work describes a model-reference adaptive system (MRAS) for the speed estimation of induction motor from terminal voltages and currents. The estimated speed is used as feedback in a vector control system, thus achieving good bandwidth for speed control without the use of shaft-mounted sensors. This technique uses for controlling induction Motor using Vector control. Simulation has been done in Matlab software. In MATLAB, Due to Embedded Legacy C source code can be verified through simulation with this legacy code as controller and plant model in simulink block diagram. In vector control, accuracy of internal parameter such as resister of motor armature and inductance affects control performance. Internal parameters are used, for example, feed-forward compensator of current controller and parameters of observer model in position Sensorless. Production-quality code suitable for implementation with good readability, customization and performance, can be generated by combining add-on tool of RTW, RTW Embedded Coder.

MRAS, Embedded Legacy C source code, feed-forward compensator, RTW, RTW Embedded Coder

In recent years, the control of high-performance induction motor drives for general industry applications and production automation has received widespread research interests. Many schemes have been proposed for the control of induction motor drives, among which the field oriented control [1,2] , or vector control, has been accepted as one of the most effective methods. In following table1 summarizes the control technique advantages and disadvantages [3] .

Some of the solutions provided for different development phases are listed in [Fig-1] . In vector control, accuracy of internal parameter such as resistance of motor armature and inductance affects control performance. Internal parameters are used, for example, feed-forward compensator of current controller and parameters of observer model in position sensorless.

The dynamic equivalent circuits in literature [1] are shown.

A model-reference adaptive system (MRAS) for the estimation of induction motor speed from measured terminal voltages and currents [3] The estimated speed is used as feedback in a vector control system, thus achieving moderate bandwidth speed control without the use of shaft-mounted transducers [4] . This technique is less complex and more stable than previous MRAS tacholess drives. Different speed sensorless estimation is shown in [Fig-4] .

It is important to determine accurate flux vector in induction motor. Some of the methods to detect flux vector include direct detection, where magnetic sensor by hall element is used, and indirect detection, where slip angular frequency is added to the detected rotating angular velocity. In [Fig-5] and [Fig-6] , model that estimates flux vector and rotating angle using flux observer.

Internal model of coordinate transform is shown in [Fig-7] . In [Fig-8] Current controller is PI control loop with feed forward compensator considered in synchronously Rotating co-ordinate system. This model compensates, by feed forward, no stationary term of power Supply frequency ω obtained from electric formula of motor’s analogous circuit in orthogonal two axis rotating coordinate system.
Adaptive observer is constructed by two-phase fixed coordinate system. Modeling of adaptive Observer is described in the next Topic.

Modeling of Adaptive Flux Observe State-space expression of induction motor in orthogonal two axes fixed coordinate system can be expressed in the equation below [4] :



&space;i_{\alpha&space;\,&space;s}&space;\:&space;i_{\beta&space;\,&space;s}\:&space;\lambda&space;_{\alpha&space;\,&space;r}\:&space;\lambda&space;_{\beta&space;\,&space;r}\right&space;] title="Where\: x=\left [ i_{\alpha \, s} \: i_{\beta \, s}\: \lambda _{\alpha \, r}\: \lambda _{\beta \, r}\right ]" />

&space;\nu_{\alpha&space;s}&space;\;&space;\nu_{\beta&space;s}\right&space;] title="\nu_{s}=\left [ \nu_{\alpha s} \; \nu_{\beta s}\right ]i_{s}=\left [ i_{\alpha s} \; i_{\beta s}\right ]" />



&space;(1/\sigma&space;Ls)I\;&space;02\times&space;2&space;\right&space;] title="B=\left [ (1/\sigma Ls)I\; 02\times 2 \right ]T [] 02\times 2]" />







Where, H is observer gain, ^ is estimation value, e is current error e=îs-is [4,5] .



Then, parameter adjusting law of estimation electric angular velocity ωr are provided by the following equation using size of outer product of current error vector, e, and estimation flux [5] :



Observer gain H is designed in a way to ensure adaptability of control system consisting of adaptive observer and induction motor, i.e. limt->∞ e=0 Assuming that terms other than velocity estimation value is true value, equation concerning current error, e, can be expressed as below from formulas (1) and (2). It can be obtained by subtracting (1) from (2) and define matrix Bω by separating term of ω from system matrix. Its complete derivation is omitted here [5,6] .





Where



&space;I/\varepsilon&space;-1&space;\right&space;] title="I4:4\times 4-unit \: matrix,\: \: B\omega =\left [ I/\varepsilon -1 \right ]^{T}" />

Then, consider feedback system comprising linear time-invariant block G(s) and nonlinear time Variation block similar to the Fig. below. Applying Popov’s hyper stability [5,6] , the following needs to be satisfied to ensure stability, limt->∞ e=0
Linear time-invariant block G(s) is SPR (Strictly Positive Real).
Input, v1, and output, w1, of nonlinear time variation block satisfy Popov’s equation [5-7] for all time t1>t0.



It is possible to prove that (2) is satisfied by using (5). Optimal feedback gain H obtained from the only solution of Riccati equation is applied to make G(s) SPR as a condition of (1).

H=PCTR^-1 (6)

Riccati equation: PAT+AP-PCTR^-1CP+BWQBWT = 0 (7)

Where, P: Solution of Riccati equation, Q, R: Weight matrix.
The weight matrices are Q=1, R=y I, respectively (however, y is a small positive number).

Parameters of motor and each matrix of state-space expression are defined in program (M-file) of MATLAB language, (7) is solved using the Control System Toolbox, and optimal feedback is obtained.
{H,P,E} = Iqe(A, Bw, C, Q, R)

[Fig-11] on the next page indicates model of the overall system .Reference voltage from CPU subsystem is compared with carrier wave with PWM Generator block provided in SimPowerSystems and generates six PWM pulses. The mechanism switches each gate of IGBT of three arm bridge circuit block (Block name: Universal Bridge), and drive connected induction motor block.

Reference speed 1000 rpm to 500 and torque change 1N-m to 50 N-m
[Fig-12] shows simulation results from 0 to 1.5 seconds. 0 to 0.5 seconds show velocity step response when velocity reference value is changed from 0(rpm) to 1000 (rpm), 0.5 to 1.0 show velocity step response of 1000 (rpm) to 500 (rpm), and 1.0 to 1.5 show torque step response when external load torque is changed from 1(N) to 50(N). Voltage between inverter UVs, armature current, rotating velocity, and transient response of torque are simulated.
When reference speed signal 1000rpm and load torque 1N-m.
In [Fig-13] , speed peak shoot is 1425 rpm and steady state speed 1050 rpm get in .3 sec. Stator transient current overshoot up to 100A and study state current 34.21A. We can see that reference speed tracking very fast for low load condition. In [Fig-14] torque speed curve is shown speed transient is less as compare to old references.

When reference speed signal 1000rpm and load torque 50N
In [Fig-15] speed peak shoot is 1400 rpm and steady state speed 1010 rpm get in .3 sec. Stator transient current overshoot up to 150A and study state current 43.233A. We can also see that reference speed tracking very fast for high load condition. In [Fig-16] torque speed curve is shown speed transient is less as compare to old references.

In [Fig-17] machine start with start .speed changes from 1000 rpm to -1000 rpm .we can seen in soft start machine speed transient is low it acquired simultaneous -1000 rpm with linearly decrease speed .speed peak shoot is 1090.2 rpm and -1092.4 rpm.
Steady state speed 1010-rpm get in .31 sec. Stator transient current overshoot up to 35A and study state current 25.233A in positive direction. We can see that reference speed is varied linearly than dynamic response of machine very good. In [Fig-18] torque speed curve shown how speed is move 1000rpm to -1000rpm.

[Fig-20] I_a and I_b is shown, circle represent that ia and ib are 90°. [Fig-21] is a bode diagram of linear time-invariant block G(s) drawn with the LTI Viewer of the Control System Toolbox. From the phase diagram, it can see that weight factor of (8) y=1, y=0.006, are within ± 90° across the whole frequency range, and they are stable.

It presents position-Sensorless vector control simulation by observer using optimal feedback gain as an example of process from algorithm design to logic verification, by using MATLAB/Simulink. Result in simulation verifies that MRAS technique with vector control give good dynamic responses with change of reference speed. This work can extend by following way:
Generation of vector control PWM signal using PC/laptop installed with D-SPACE and MATLAB simulation environment. Make virtual instrument kit for controlling machine using DSPACE controller Desk. Use above simulation for controlling induction machine in real time system. Verify result with Real time Workshop [Fig-22] .

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	Fig. 1- Controller development process and related optional tools
	Fig. 2- Dynamic Equivalent Circuit on a Stationary Reference Frame [1]
	Fig. 3- Dynamic Equivalent Circuit on an Arbitrary Reference Frame Rotating at ωa [1]
	Fig. 4- Speed sensorless estimation Techniques
	Fig. 5- Position sensorless vector control configuration
	Fig. 6- Modelling of controller part
	Fig. 7- Internal model of current controller subsystem
	Fig. 8- State-space expression of observer in [Fig-9] can be expressed in the equation below [4] :
	Fig. 9- Current error block feedback system [7]
	Fig. 10- Complete simulink model for MRAS based vector control of Induction Motor
	Fig. 11- Motor rotating velocity [rpm] , and torque [Nm]
	Fig. 14- Stator voltage, stator current, speed, torque vs. time
	Fig. 15- Torque-Speed curve for t=1.5sec
	Fig. 16- Rotor speed and reference signal 1000 to -1000
	Fig. 17- Torque and speed upto t=1.8
	Fig. 18- Stator voltage, stator current, speed, torque vs. time
	Fig. 19- Plot of Ia and Ib
	FIG. 20- G(s) responses of different value of y
	Fig. 21- Hardware implimentation of vector control using mras of induction machine
	Table 1- Comparison of different methods for speed control of induction machine
	Fig. 12- Stator voltage, stator current, speed, torque vs. time
	Fig. 13- Torque-Speed curve up to t=1.5sec