A Rotor Flux and Speed Observer for Sensorless Single-Phase Induction Motor Applications

<table>Stator currents of the no-load SPIM and their estimated values during a step variation from 10 Hz to 50 Hz in the stator frequency (computational simulation): (a) auxiliary winding <svg height="15.475" id="M103" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 16.612499 15.475" width="16.612499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q16 0 76 48z" id="x1D456"></path></g>
<g transform="matrix(.012,-0,0,-.012,4.7,15.275)"><path d="M352 391q0 -31 -27 -44q-14 -7 -24 6q-39 48 -84 48q-23 0 -39.5 -15t-16.5 -40q0 -43 73 -90q49 -32 70 -58t21 -57q0 -58 -62 -105.5t-129 -47.5q-40 0 -75.5 25t-35.5 52q0 28 32 46q7 4 15 3t11 -6q19 -31 48.5 -50.5t54.5 -19.5q34 0 54 19.5t20 42.5q0 43 -65 81
q-97 56 -97 123q0 50 51 96q19 17 58 32.5t62 15.5q37 0 61 -18t24 -39z" id="x1D460"></path></g><g transform="matrix(.012,-0,0,-.012,9.162,15.275)"><path d="M545 106q-67 -118 -134 -118q-24 0 -40 37.5t-30 129.5h-2q-47 -72 -103 -119.5t-108 -47.5q-47 0 -76 45.5t-29 119.5q0 113 85 204t174 91q47 0 70 -33.5t43 -119.5h3q32 47 80 140l55 13l10 -9q-47 -80 -138 -201q17 -99 27.5 -136t22.5 -37q23 0 69 61zM333 204
q-14 98 -31 149.5t-50 51.5q-49 0 -94 -70t-45 -164q0 -55 15.5 -86t40.5 -31q70 0 164 150z" id="x1D6FC"></path></g>
</svg>, (b) details of <svg height="15.475" id="M104" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 16.612499 15.475" width="16.612499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.2)"><use xlink:href="#x1D456"></use></g>
<g transform="matrix(.012,-0,0,-.012,4.7,15.275)"><use xlink:href="#x1D460"></use></g><g transform="matrix(.012,-0,0,-.012,9.162,15.275)"><use xlink:href="#x1D6FC"></use></g>
</svg>, (c) main winding <svg height="18.450001" id="M105" style="vertical-align:-5.76984pt" version="1.1" viewbox="0 0 16.762501 18.450001" width="16.762501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.2)"><use xlink:href="#x1D456"></use></g>
<g transform="matrix(.012,-0,0,-.012,4.7,15.275)"><use xlink:href="#x1D460"></use></g><g transform="matrix(.012,-0,0,-.012,9.162,15.275)"><path d="M558 587q0 -32 -14 -61t-40 -53.5t-48.5 -41t-54.5 -36.5q144 -51 144 -174q0 -55 -43.5 -108t-104.5 -87q-77 -42 -131 -42q-31 0 -54 20t-31 47l11 18q48 -29 108 -29q79 0 119.5 43t40.5 109t-44.5 107.5t-119.5 50.5l22 47q34 1 65 21q96 61 96 157q0 42 -24 67.5
t-62 25.5q-24 0 -43.5 -9t-35 -29.5t-27 -44t-22.5 -63t-19.5 -75.5t-18.5 -91q-57 -294 -68 -380q-26 -190 -35 -200q-26 -31 -97 -37l-4 26q19 9 48 170l77 413q23 121 52.5 187.5t83.5 114.5q70 62 148 62q51 0 88.5 -34t37.5 -91z" id="x1D6FD"></path></g>
</svg>, (d) details of <svg height="18.450001" id="M106" style="vertical-align:-5.76984pt" version="1.1" viewbox="0 0 16.762501 18.450001" width="16.762501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.2)"><use xlink:href="#x1D456"></use></g>
<g transform="matrix(.012,-0,0,-.012,4.7,15.275)"><use xlink:href="#x1D460"></use></g><g transform="matrix(.012,-0,0,-.012,9.162,15.275)"><use xlink:href="#x1D6FD"></use></g>
</svg>.</table>

International Journal of Rotating Machinery

fig5

Figure 5

Figure 5: A Rotor Flux and Speed Observer for Sensorless Single-Phase Induction Motor Applications 