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.003a" src="https://static.hindawi.com/articles/mpe/volume-2011/397092/figures/397092.fig.003a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Tracking errors in PID</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="397092.fig.003b" src="https://static.hindawi.com/articles/mpe/volume-2011/397092/figures/397092.fig.003b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Observer errors in PID</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="397092.fig.003c" src="https://static.hindawi.com/articles/mpe/volume-2011/397092/figures/397092.fig.003c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>Tracking errors in MRC</td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="397092.fig.003d" src="https://static.hindawi.com/articles/mpe/volume-2011/397092/figures/397092.fig.003d.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b>Observer errors in MRC</td></tr></table></td></tr></table>

<table>Time trajectories of the joint position errors for the straight line trajectory in an ideal condition.</table>

Mathematical Problems in Engineering

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Figure 3

Figure 3: Proportional-Derivative Observer-Based Backstepping Control for an Underwater Manipulator 