Direct Adaptive Fuzzy Sliding Mode Control with Variable Universe Fuzzy Switching Term for a Class of MIMO Nonlinear Systems

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="543039.fig.004a" src="https://static.hindawi.com/articles/mpe/volume-2012/543039/figures/543039.fig.004a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Control effort of <svg height="12.7" id="M368" style="vertical-align:-3.9858pt" version="1.1" viewbox="0 0 14.8 12.7" width="14.8" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,8.413,12.638)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="543039.fig.004b" src="https://static.hindawi.com/articles/mpe/volume-2012/543039/figures/543039.fig.004b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Control effort of <svg height="12.7" id="M369" style="vertical-align:-3.9858pt" version="1.1" viewbox="0 0 14.8 12.7" width="14.8" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M474 429q-19 -69 -47 -222l-65 -347q-8 -49 0 -60t49 -16l26 -3l-4 -26l-246 -12l4 25l17 3q37 6 50 20.5t23 60.5l67 321h-2q-65 -79 -150 -138q-69 -47 -104 -47q-28 0 -48.5 32t-20.5 81q0 78 35 148t90 117q67 57 161 77q23 5 58 5q43 0 90 -15zM387 387
q-30 16 -75 16q-58 0 -92 -27q-49 -39 -78.5 -112t-29.5 -136q0 -34 8.5 -52.5t21.5 -18.5q40 0 109.5 63.5t103.5 115.5q16 53 32 151z" id="x1D45E"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.413,12.638)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
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<table>Control input torques of robotic manipulators.</table>

Mathematical Problems in Engineering

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Figure 4

Figure 4: Direct Adaptive Fuzzy Sliding Mode Control with Variable Universe Fuzzy Switching Term for a Class of MIMO Nonlinear Systems 