Robust Adaptive PID Control of Robot Manipulator with Bounded Disturbances

<table>Estimate values of parameters <svg height="13.8875" id="M151" style="vertical-align:-3.9858pt" version="1.1" viewbox="0 0 16.5375 13.8875" width="16.5375" 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,-.012,10.138,13.838)"><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>, <svg height="13.8875" id="M152" style="vertical-align:-3.9858pt" version="1.1" viewbox="0 0 16.5375 13.8875" width="16.5375" 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,-.012,10.138,13.838)"><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>
</svg>, and <svg height="14.0375" id="M153" style="vertical-align:-4.10045pt" version="1.1" viewbox="0 0 16.5375 14.0375" width="16.5375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" id="x1D45D"></path></g>
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Mathematical Problems in Engineering

fig15

Figure 15

Figure 15: Robust Adaptive PID Control of Robot Manipulator with Bounded Disturbances 