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    The selection of the fuzzy system parameters and gains k1, η1, andη2, which achieve the desired transient response, were based ontrial and error. The selection was compromised between the responseand the limitation of the control effort. In this study, k1=3.75,η1=15, η2=0.1, pup=150 bar, and plow=122 bar, and the initialvalue of θ0=[1, 0.67, 0.33, 0, −0.33, −0.67, −1]T. The experimentalresults of the total test with the three control strategies HST, non-switching, and switching, according to the three missing profiles,are shown in Figs. 17, 18, and 19, respectively. Obviously, the perfor-mance of the system in any control scheme was acceptable.Fig. 17a, b, and c shows the experimental results of the HST, non-switching, and switching strategies for the 10-mode schedule, respec-tively. The figures show that the pressures (p1,p2), displacements ofthe pump/motors (P1,PM2), and the states of the directional controlvalve (V11,V12) in each strategy definitely differed from the others,but the outputs (ω) were not dramatically different. Fig. 17a showsthe characteristics of a traditional flow coupling system, where thepressure is completely dependent on the load. The pressure increasedfrom the 20th second to the 30th second then decreased when thespeed of the flywheel was nearly constant. From the 43rd second,the brake system displacement u1 decreased and the pressure in thereturn line increased. In this strategy, u2 was constant at 0.8. Thespeed of the flywheel was controlled by adjusting u1 with anAFSMC. The experimental results of the non-switching mode of thesystem were shown in Fig. 17b. To drive the load, the flywheel inthe test bench system, the secondary unit PM2 operated as a hydraulicmotor. During this time, the displacement of PM2 was positive andthe potential energy of fluid stored in HA1 was transformed to the ki-netic energy of the load. To brake or decelerate the load PM2 was con-trolled to revert its displacement into negative region and it operatedas a hydraulic pump. The fluid from large size and low pressure accu-mulator HA2 was pumped to high pressure accumulator HA1 via PM2. As a result, the pressure in HA1 increased while the pump P1 wasdeactivated. In this test, the hydraulic brake systemwas not activated.The torque at PM2 shaft functioned as a braking torque to deceleratethe load. The kinetic energy of the load was transformed to the poten-tial energy of the fluid in HA1 so the system in the non-switchingmode could generate the braking energy. Specifically, u1 is only 1 or0 and is independent of ω in Fig. 17b. From the 20th second to the30th second, u2 increased to increase ω and decreased to keep ω con-stant. From the 43rd second to the 51st second, the regenerativebrake was applied by reverting u2 into the negative region and ω de-creased to zero. Meanwhile, the pressure in the accumulator in-creased even though u1=0, and energy recovery was achieved. Inthis scheme, u2 increased whenever the speed increased and p2 wasalways low. Unlike in the non-switching control scheme, p2 increasedfrom the 43rd second to the 51st second in the switching schememethod. Fig. 17c shows that u2 was only in the interval [0 1], whichimplied that the fluid was not reverted.Fig. 17d shows the analyzed energy utilization of the system. Thepower rate of the system for the 10-mode schedule was about6 kW, and the required brake power was about 3 kW. The energy re-quired to complete the schedule in 140 s was estimated at about120 kJ, and approximately 60 kJ of the flywheel's kinetic energy wasable to be recuperated. Fromthemeasurement of the supplied energyfrom the test bench, we found that the supplied energies were 160 kJ,145 kJ, and 145 kJ for the three control strategies, respectively. Thusthe switching scheme saved about 10% more than did the HSTscheme.Fig. 18a, b, and c shows the experimental results of the system forthe three control strategies for the modified 10-mode schedule. Thisschedule had a higher acceleration and deceleration than those ofthe 10-mode schedule, and the cycle time was 70 s. Here, the u2softhe non-switching and switching schemes were greater than that inFig. 17. Fig. 18d shows that the rate required for the driving and brak-ing powers for this profile were about 18 kW and 4.5 kW, respective-ly. The calculated energy was 100 kJ, the recoverable energy was65 kJ, and the measured supplied energies were 121 kJ, 100 kJ, and95 kJ for the HST, non-switching, and switching control schemes, re-spectively. Thus the switching control schemes saved about 20%more than did the HST control scheme. Fig. 19a, b, and c shows the experimental results of the system forthe three control strategies with the highway schedule. Fig. 19bshows that u2 was positive even though there was twice the amountof deceleration from the 20th second to the 120th second of theschedule. Fig. 19c shows that the system using the switching controlscheme was able to operate well in that condition by reverting u2into the negative region. If the pump/motor was only able to operatein the positive region, the adaption control of V12 based on the cur-rent speed should be developed to avoid the above situation.Fig. 19d shows that the rates required for the driving and brakingpowers for this profile were about 5 kW and 2.5 kW, respectively.The calculated energy was 167 kJ, the recoverable energy was 70 kJ,and the measured supplied energies were 205 kJ, 185 kJ, and 184 kJfor the three control strategies, respectively.
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