Proportional-Derivative Observer-Based Backstepping Control for an Underwater Manipulator

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="397092.fig.0010a" src="https://static.hindawi.com/articles/mpe/volume-2011/397092/figures/397092.fig.0010a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Position tracking errors in PID</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="397092.fig.0010b" src="https://static.hindawi.com/articles/mpe/volume-2011/397092/figures/397092.fig.0010b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Position observer errors in PID</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="397092.fig.0010c" src="https://static.hindawi.com/articles/mpe/volume-2011/397092/figures/397092.fig.0010c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>Position tracking errors in MRC</td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="397092.fig.0010d" src="https://static.hindawi.com/articles/mpe/volume-2011/397092/figures/397092.fig.0010d.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b>Position observer errors in MRC</td></tr></table></td></tr></table>

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</svg>) errors for the circular trajectory in an uncertain and disturbed condition.</table>

Mathematical Problems in Engineering

fig10

Figure 10

Figure 10: Proportional-Derivative Observer-Based Backstepping Control for an Underwater Manipulator 