**3.5. Disturbance estimation and integral control**

Full-ordered observers effectively estimated constant and sinusoidal disturbance currents and proved useful in the control designs for feedforward control, but furthermore reduced-ordered observer were applied in cases where disturbances were forces and moments and feedforward control was not used. Integral control was used instead to drive steady-state error to zero where sufficiently large time-constants were used for the integrator, i.e. the fifth pole in the pole placement control must be less negative than the other poles.

#### **3.6. Fully assembled system demonstration**

In light of all these results, a fully assembled control system was used to navigate the proper mathematical models of the *Phoenix* autonomous submersible vehicle through a simulated 200 m 500 m minefield in the presence of unknown ocean currents. The field was populated randomly with 30+ mines, and vehicle successfully traversed the minefield in the presence of an unknown 0.5 m/s current with a miss distance from the nearest mine not less than 5 m, navigating from the starting point to pass within 0.5 m of a commanded en route point at sea, and then return to the start point. The outer loop controller used line-of-sight guidance to provide heading commands to the inner loop, and the inner loop controller was an outputfeedback heading controller. Two control strategies both proved effective: Linear-quadratic Gaussian, and approximate optimal pole-placement by *rule of thumb*. In the linear-quadratic Gaussian case, both the controller gains and observer gains were selected by optimization of the respective matrix Riccati equation. **Figure 23** displays the completed maneuver where each dot displays the location of a randomly placed mine. Full state feedback was achieved with state observers via the certainly equivalence principle and the states were utilized in a proportional-derivative-integral feedback control architecture. Detailed outputs and figures of merit are plotted in **Figures 24**–**28** including performance of a second transit of the minefield for validation purposes.

**Figure 23.** Navigation through simulated field of 30 randomly placed mines in 0.5 m/s current with linear quadratic Gaussian PID controller and full-state observer.

Autonomous Underwater Vehicle Guidance, Navigation, and Control http://dx.doi.org/10.5772/intechopen.80316 25

**Figure 24.** Continuous distance (m) to closest mine with linear quadratic Gaussian optimized *PID* controller and *full-state* observer versus time (s).

**Figure 25.** Linear quadratic (Gaussian) optimal observer convergence with actual value in light-pink near zero, while estimates are depicted oscillating in blue, (a) state *ν*, (b) state *r*.

**Figure 26.** Linear quadratic (Gaussian) optimal observer convergence, (a) state *ψ*, (b) command tracking (radians) versus time (s).

**Figure 27.** Linear quadratic (Gaussian) optimal observer convergence of *y*, (c) state *y*, (d) state.

**Figure 28.** Validation trajectory through simulated field of 30 randomly placed mines in 0.5 m/s current with linear quadratic Gaussian optimized *PI* controller and *reduced-ordered* observer, (a) second trajectory (results validation), (b) heading command tracking.
