 Open Access
 Total Downloads : 395
 Authors : Kavya Sree Chandran, Arun S. Mathew
 Paper ID : IJERTV5IS060438
 Volume & Issue : Volume 05, Issue 06 (June 2016)
 DOI : http://dx.doi.org/10.17577/IJERTV5IS060438
 Published (First Online): 17062016
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Simulation of Stepper Motor using Quasi Square Wave Input
Kavya Sree Chandran
P G Scholar Electrical &Electronics Dept.
Mar Baselios College of Engineering, Thiruvananthapuram ,Kerala, India
AbstractStepper motor is an electromechanical device which converts digital pulses into equivalent mechanical motions. The step motors have advantages like high torque development at low speed and it can start, stop and reverse the direction of travel at high speeds without any loss of steps. In this paper a two phase hybrid stepper motor(HSM) is modeled in matlab/simulink and a quasi square wave is generated and is provided as supply voltage for the two phases. Quasi square wave is generated using H bridge voltage source inverter.
Key words Hybrid stepper motor; quasi square wave; H Bridge.

INTRODUCTION
Arun S Mathew Assistant Professor
Electrical & Electronics Dept Mar Baselios College of Engineering, Thiruvananthapuram, Kerala, India
The organization of this paper can be summarized as follows. The Mathematical model of hybrid stepper motor is explained in Section II. The method by which the quasi square wave input is generated is explained in Section III. The overall system showing the stepper motor supplied with quasi square wave input is included in Section IV.The various simulation results are shown in Section V. Conclusion based on the experimental work is given in Section VI.

MATHEMATICAL MODEL OF HSM
The mathematical model of Stepper motor used is shown below:
Stepper motors have a central gearshaped iron piece
= 1 [
+
sin( )]
surrounded by multiple toothed electromagnets. An external
driver is required to energize the electromagnets. The
= 1 [
cos( )]
working is as follows: first, power is given to one of the electromagnet and it attracts the gear's teeth magnetically
1
towards it.When the next electromagnet is powered, the first
= [ sin() + cos()
one is turned off and the gear rotates to align with the next one and this process continues. This is how the motor shaft
sin(4) ]
turns and each of these rotations are known as a step.
There are three basic types of stepper motors: Permanent magnet(PM), Hybrid and Variable reluctance(VR) stepper motor.Permanent magnet motors have a permanent magnet as the rotor and electromagnets as stator. They operate based on the attraction or repulsion between the rotor and the stator. In variable reluctance motors, a plain iron is used as rotor and they operate in such a way, so that minimum reluctance occurs with minimum gap, and the rotor points are attracted toward the stator magnet poles. Hybrid stepper motors are a combination of PM and VR motors and have maximum power in a small package size.
Positioning systems are powered by different types of electric motors. A special category of electric motors, which areincreasingly used in systems, are hybrid stepper motor. Due the simplicityof construction, command and control, they are used even inother electric drive systems.[1]
Most popular HSM are composed of a stator and two rotors. The motor stator has two control windings, each is placed on two diametrically opposed stator poles. Rotors are spaced axially by a permanent magnet at the periphery, which shows teeth uniform distributed and the first rotor is radially shifted with on tooth [3]
= (1)
where:
ia& ib= currents in phase A and B(Amperes), Ua& Ub= phase voltages (Volt),
Ra,& Rb = phase resistances(ohm), La& Lb=phase inductances(Henry),
km = motor torque constant(Nm/A),
= rotor speed(rad/sec), NR = number of rotor teeth,
= rotor position(radians),
J = rotor inertia(kgm2),
B = viscous friction constant(Nm/rad/sec), MR = load torque
The term kDsin(4NR) represents the detent torque due to permanent rotor magnet interacting with the magnetic material of the stator poles. Detent torque is the torque required to rotate a nonenergized stepper motor.This torque will exist even if the phase current is zero. Typically kD is 5 to 10 percent of the value of kmio, where io is the rated current[2].
The block diagram of the mathematical model described in (1) implemented in Matlab/Simulink is presented in Figure 1.
Fig.1. Matlab/simulink model of stepper motor

QUASI SQUARE WAVE GENERATION Modified sine wave or also known as quasi square wave
is given as input to the stepper motor. The Matlab/simulink
set up to generate quasi square wave is shown in figure 2.
It uses an Hbridge bipolar voltage source inverter. The gate pulses used to generate quasi square wave is shown in figure 3.
Fig.2. Hbridge bipolar voltage source inverter for quasi square wave generation.
Fig.3. Gate pulses for the invertTerhe output from the inverter is a quasi square wave
The gate pulses S1&S4 and S2&S3 are the same. Also S2 pulse is 1200 out of phase with that of S1 and this helps to provide a dead time, ie., there is some time where all the MOSFETs are OFF. Initially S1 and S4 will be ON. After turning off S1&S4 and before turning on S2&S3 there will some dead time where noMOSFETs are ON.
which is provided as input to one phase A of the stepper motor. The supply voltage to phase A is denoted as Ua. The supply voltage to phase B, Ub is the inverted version of Ua or in other words it is 1800 out of phase with Ua. The modified sine wave inputs Ua and Ub is shown in Fig.4
IV. OVERALL SYSTEM
The overall system consists of two subsystems. One is quasi square wave generation subsystem and the other is the
IV. OVERALL SYSTEM
The overall system consists of two subsystems. One is quasi square wave generation subsystem and the other is the
Fig. 4 Quasi Square wave input for phase A&B
stepper motor system. Both of the subsystem has been explained in the previous two sections(Section II & III).
Fig.5. Overall system for simulation
The input to stepper motor are Ua, Ub and MR. Ua and Ub are the quasi square wave inputs and Mr is the load torque which is a constant value. The outputs are two phase currents ia & ib, rotor angular velocity, and rotor position,.
V. SIMULATION RESULT
The various parameter values used for simulations are Vdc
= 12V, La = Lb = 12mH, Ra = Rb = 11, B = 0.025 Nm/rad/s, NR = 50, J = 1.125*104 kgm2, km = 0.22 Nm/A, Mr = 0.07, kd
= 0.022 Nm[1].
The various simulation results are shown in the following figures. Figure 6&7 shows the phase current waveforms. On examining phase current waveform we can see that it is almost same as the supply voltage waveform. The current in phase B is 1800 out of phase with that of current in phase A, similar to phase A&B voltages.
The variation of speed of motor is illustrated in figure 8. Motor speed varies uniformly in each step. Initially speed increases from zero and reaches a maximum value, then speed decreases and settles to zero when it attains steady state, this constitutes one step.
The complete 3600 rotation of rotor in shown in figure 9.
The angle of rotation increases in each step.
Fig.6. Current in phase A
Fig.7. Current in phase B
Fig.8. Angular velocity of the motor
Fig.9. Variation of theta
IV. CONCLUSION
This paper presents the simulation of stpper motor using quasi square wave input. A two phase hybrid stepper motor is modeled in matlab/simulink and a quasi square wave is generated and is provided as supply voltage for the two phases. Quasi square wave or modified sine wave is generated using H bridge voltage source inverter. The generated quasi square is provided as input to phase A and the inverted version is applied to phase B. The simulation results obtained were satisfactory.
REFERENCES

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M. Zibri and J.Chiasson, Position Control of a PM Stepper Motor by Exact Linearization, IEEE Transactions on Automatic Control, Vol. 36, No. 5, May 1991.

A. Morar, Comanda inteligent a acionrilor electrice cu motoare pascu pas, Editura Mediamira, Cluj Napoca, 2007.

Dr. Qais S. AL Sabbagh and Ali Sabah Mahdi, Pulse Width Modulation for High Performance Hybrid Stepper Motor, Journal of Engineering, No. 4, Vol. 16, Dec 2010.

George Mihalache, Gheorghe Livint and Vasile Horga, A New Method for Modeling and Control of Hybrid Stepper Motors, ISSN 1453 7397, 2014.

Shrddha Baldha, Jimit Shukla and Kuldip Tarpara, Design and Simulation of TwoPhase Hybrid Stepper Motor with Current Tracking, International Journal of Advance Engineering and Research Development (IJAERD), 2015.