In addition, increasing K increases the undamped natural frequency ω n (i.e., the magnitude of the pole), and hence the speed of response of the system increases. Use of the root locus in the design of a second-order system. Also, the tuning parameters of the FOPID K p, K i, K D, λ, and δ are equal, as illustrated in Table 9.įigure 5.2. This means that the change of the performance indices has no influence on the tuning process. The time responses of height of the car body ( X or d1), height of the tire body ( Y or d2), and deflection ( X– Y or d1– d2) as shown in Fig. The simulation result shows that the FOPID has IAE, ISE, and ITAE error criteria that are noticeably lower than the same values for the case of AWPSO-PID. In this part, Model 2 of the car active suspension system has been verified with the FOPID tuning based on GA controller using five variables K p, K i, K D, λ, and δ. On the other hand, the time response of the car body height ( X) has a small percentage overshoot in the case of the ITAE tuning index compared with the other two indices IAE and ISE. The time response of the deflection ( X– Y ) yields a small percentage overshoot in the case of applying the ITAE tuning performance index compared with the other two indices IAE and ISE. The model was tested with the PI controller, but it did not yield good results. In addition, in the case of AWPSO, the minimum settling time and overshoot have been achieved with the ITAE performance index. However, in the case of conventional PID with Zeigler and Nichols, it is about 4 s. In the case of AWPSO, the settling time for IAE, ISE, and ITAE performance indices is less than 1.5 s. The simulation results using the AWPSO algorithm are better than the simulation results where the PID controller has been tuned with the Zeigler and Nichols approach ( Aboelela et al., 2015b). The obtained results of applying the PID and FOPID controllers on the car active suspension system can be summarized as follows. Aboelela, Rania Helmy Mansour Hennas, in Fractional Order Systems, 2018 7.4 Summary for Model 2 Simulation
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