## Info

Incoming angle (deg)

(f) matching error

(e) 0.8m/s ambient flow velocity with 0.8m/s ambient flow velocity

Fig. 11. Comparison results of experiment and simulation with incoming angle

5. Thruster controller

### 5.1 Propeller shaft velocity controller

To obtain the desired thrust force, we need to construct feedback controller with shaft velocity controller. The thruster used in this research only has tachometer for measuring propeller shaft velocity. Hence, firstly, the shaft velocity controller was experimented with open loop and closed loop. Open Loop (Fig. 12(a))

kt kt

K kt where ftref = ftd + kp (ftd - ft) + kr f (ftd - ft) (27)

In Fig. 12, P represents the plant model of thruster and V means the final voltage input to the thruster hardware driver.

5.2 Thrust force controller

The overall thrust force controller is composed as Fig. 13. However, the inverse force map only gives the desired shaft velocity according to the desired force. Hence, for the accurate control, the desired shaft acceleration is required. In this chapter, the filtered derivative algorithm is used for the draw of the desired acceleration signal using the desired velocity input.

### 5.3 Preliminary thruster controller experiments

The Bollard-pull condition was tested with open loop and closed loop controller. The closed loop results (Fig. 14) are normally better than open loop results, but the peak error is larger. This comes from the flexible experimental structure. Hence, if the real systems which dose not have structural flexibility, it is expected that the closed loop performance will be better than open loop performance. As shown in the results, the experimental results are good matching with the model. The force control errors are normally less than 5%.

### 6. Conclusions

In this chapter, a new model of thrust force is proposed. First, the axial flow as a linear combination of the ambient flow and propeller shaft velocity is defined which are both measurable. In contrast to the previous models, the proposed model does not use the axial flow velocity which cannot be measured in real systems, but only uses measurable states, which shows the practical applicability of the proposed model. The quadratic thrust coefficient relation derived using the definition of the axial flow shows good matching with experimental results.

Next, three states, the equi-, anti-, and vague directional states, are defined according to advance ratio and axial flow state. The discontinuities of the thrust coefficient in the non-dimensional plot can be explained by those states. Although they have not been treated previous to this study, the anti- and vague directional states occur frequently when a vehicle stops or reverses direction. The anti- and vague directional states are classified by CAR (Critical Advance Ratio), which can be used to tune the efficiency of the thruster. Finally, the incoming angle effects to the thrust force, which are dominant in turning motions or for omni-directional underwater vehicles, are analyzed and CIA (Critical Incoming Angle) was used to define equi-, anti-, and vague directional regions.

(c) force control error

(c) force control error

(d) force modeling error

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