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is also within the permissible range indicating the ability of the system to regain its

Figure 14 shows the bode plot of the rail car system; the phase margin was found to be 48<sup>o</sup> at a frequency of 20.2 rad/s which signifies significant reduction in the percent overshoot due to the compensation for steady-state error by the deriv-

The control of undesirable vibrations of the rail car system in 6 degrees of freedom was carried out using the PID control system. The initial displacement and vertical acceleration that characterize the performance of the system on encountering rail and load disturbances were minimized with the iterative adjustment of the PID controller according to Nichols-Ziegler tuning rules. In addition, the performance of the control and the rail car system in terms of the input step response, bandwidth, frequency, phase margin and input and output rejections was within the acceptable range. Hence, the PID control system shows significant robustness in providing the required active control for the system, while the rail car system shows improved stability and reduction in vibration under control action of the PID, thus improving ride comfort. However, a single PID may not sufficiently satisfy all the design requirements at the same time resulting in performance trade-off. However, Fuzzy PID or ISA-PID controller can be used to meet the design requirements significantly. This will further improve the performance and robustness of the rail

stability within a second as a result of load or rail disturbances.

ative action of the PID.

Bode plot for the actively controlled rail car.

Noise and Vibration Control - From Theory to Practice

4. Conclusion

Figure 14.

car system.

132

Ilesanmi Afolabi Daniyan\* and Khumbulani Mpofu Department of Industrial Engineering, Tshwane University of Technology, Pretoria, South Africa

\*Address all correspondence to: afolabiilesanmi@yahoo.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
