**5. Simulation and Analysis**

In this section, we conduct comparative simulations to verify the effectiveness of the proposed SIFOFLC algorithm for AUV motion control. The optimized controllers expressed in Table 3 are applied and the target trajectory of AUV does not change.

Figure 13 shows the trajectory of AUV under SIFOFLC and the state of the response is depicted in Figure 14. Simulation results reveal that the trajectory tracking is accurate and rapid with SIFOFLC. Actually, the steady state error of depth is within 0.01 m in 6.5 s and gradually decreases to approximately 0.002 m in 7 s. Correspondingly, the maximum error of yaw angle is 2.5◦ and it gradually decreases to 0.01◦ in 13 s. The cruise speed maintains 1.54 m/s and the peak overshoot of pitch angle is 10◦.

Figures 15 and 16 respectively illustrate the angular velocity of an AUV using FOPID controller and T-S FLC. Furthermore, the oscillation and settling times of angular velocity, the ITAE index of track error and the optimal fitness value are all presented in Table 4. The responses with SIFOFLC algorithm have much shorter settling times and steady state errors. Compared with the SIFOFLC, the control performance obtained via the FOPID controller and T-S FLC requires a much longer settling time, and they also oscillate considerably in the beginning, which may lead to an unstable performance of the controlled system. Simulation results clearly reveal the superior stability and transient control performance of the proposed SIFOFLC.

**Figure 13.** Comparison of desired trajectory and actual trajectory with SIFOFLC.

**Figure 14.** State response of AUV with SIFOFLC.

**Figure 15.** Angular velocity curves with FOPID.

**Figure 16.** Angular velocity curves with T-S FLC.


**Table 4.** Quantitative analysis of system performance.
