Let consider a first example as depicted in figure 8; in this simulation we want to control d near zero and z near -2 meter with 30 times counter duration. We use a reasonable amount of dive planes to do the job. Assumption: 4o dive planes when pitch angle deviates to 5o from zero, the AUV reaches a depth of -2 meter with 0.32 meter deviation. Therefore, we assume all terms in Q ^0 and R ^0, except: qu = (4/57.2958)-2=205.21, q44 = (5/57.2958)-2= 131.31, and r11= (0.32)-2=9.76, simulation result as illustrated in figure 8 using solid line. To overcome undershoot and overshoot in the runtime simulation, after duration of t = 4 seconds PC2 send new weighting matrices to the PC1 to change a pitch angle deviates to 5o with 0.02 meter deviation at -2 meter depth: qn=(4/57.2958)-2= 205.21, q44 = (5/57.2958)-2=131.31, r11= (0.02)-2=2500, simulation result as illustrated in figure 8 using dash line. The time response of both controller are equal for t < 4 seconds because of all parameters are same, by intervention from PC2 to PC1 when t > 4 seconds, the new control parameters are apply during runtime, then it could be seen that time response is improved significantly,
Fig. 8. Online Overshoot &Undershoot Suppression after 4 seconds 4.2 Simulation condition 2
Similar to the previous simulation, PC1 running the controller gain and system matrix with assuming all terms in Q ^0 and R ^0, except: qu = 205.21, q44 = 131.31, and Vu = 400, as illustrated in Figure 9 using solid line. To reduce the rise time duration in the runtime simulation, when t = 2 seconds PC2 send a new weighting matrices to the PC1 to change a pitch angle deviates to 10° from zero with 0.02 meter deviation at -5 meter depth: qu = 205.21, q44= 23.83, and Vu = 2500, as illustrated in figure 9 using dash line. In this case, a settling time response also improved easily during runtime when t > 2 seconds. It could be seen that time response is improve significantly.
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