Transfer matrix method for multibody systems (MS-TMM) is a rife method to multi-rigid-flexible-body systems dynamics model deduction due to that there are no needs to establish the global dynamics equations of the system. Its basic idea is transferring a state vector between the body input(s) and output(s); this idea is close to the linear theories in control analysis and design. In this paper, three controllers’ parameters tuning techniques for the proposed system model using MS-TMM are utilized; one technique is applied to get the stability regions via the frequency response of MS-TMM derived model. Another technique considers a classical PID controller design through the analysis of step input response of the system, and the last technique can be applied in both time and frequency domains if the model has a known mathematical model. A car suspension system is considered to represent modeling and tuning problems. In-depth study of MS-TMM with control techniques and defining the controllers’ parameters stability regions provide an opportunity to formulate a relationship between MS-TMM and control design for novel control applications due to the powerful strength of MS-TMM dealing with more complex problems of the controlled multibody systems. 1. Introduction With the increments of complexity of multibody systems and the development of their design and control methods, the need for more elegant formulations of the equations of motion becomes an issue of paramount importance. Many methods and theories for developing the model of the multibody system dynamics and control are presented for such reasons. In transfer matrix method for multibody systems (MS-TMM) there are two cases to deal with control element, one is to express the control force with state of system of previous time such as the delay control, and the second is that the control force is relative to present state of system, such as real-time control systems. Rui et al. have trials to develop new controlled systems depending on deriving the dynamics equations using MS-TMM [1, 2]. Bestle et al. reformulated the car suspension system using MS-TMM as similar as classical control theory’s structural diagram [3]. Proportional-Integration-Differentiation (PID) controller is prevalent in industry applications. Reference [4] indicated that more than 90% of feedback control loops are based on PID control and [5] indicated that more than 97% of regulatory controllers utilize the PID algorithm. But the tuning of the controller gains is a problem because many industrial models suffer some burdens such as
References
[1]
X.-T. Rui, B. He, B. Rong, G.-P. Wang, and Y.-Q. Lu, “Discrete time transfer matrix method for dynamics of a multi-rigid- flexible-body system moving in plane,” Proceedings of the Institution of Mechanical Engineers K, vol. 223, no. 1, pp. 23–42, 2009.
[2]
B. Rong, X. Rui, G. Wang, and F. Yang, “Discrete time transfer matrix method for dynamics of multibody system with real-time control,” Journal of Sound and Vibration, vol. 329, no. 6, pp. 627–643, 2010.
[3]
D. Bestle, “Application of the transfer matrix method to control problems,” in Proceedings of the Thematic Conference, Multibody Dynamics, Zagreb, Croatia, 2013.
[4]
S. Yamato and I. Hashimoto, “Present status and future needs the view from Japanese industry,” in Proceedings of the 4th International Conference on Chemical Process Control, Y. Arkun and W. H. Ray, Eds., Padre Island, Tex, USA, 1991.
[5]
C. C. Yu, Auto Tuning of PID Controllers, Springer, 2nd edition, 2006.
[6]
G. J. Suva, A. Datta, and S. P. Bhattacharyya, “New results on the synthesis of PID controllers,” IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 241–252, 2002.
[7]
J. G. Ziegler and N. B. Nichols, “Optimum settings for automatic controllers,” Journal of Dynamic Systems, Measurement, and Control, vol. 115, no. 2, pp. 220–222, 1993.
[8]
T. S. Schei, “A method for closed loop automatic tuning of PID controllers,” Automatica, vol. 28, no. 3, pp. 587–591, 1992.
[9]
B. D. Tyreus and W. L. Luyben, “Tuning PI controllers for integrator/dead time processes,” Industrial and Engineering Chemistry Research, vol. 31, no. 11, pp. 2625–2628, 1992.
[10]
K. J. Astrom and T. Hagglund, PID Controllers: Theory, Design and Tuning, Instrument Society of America, Research Triangle Park, NC, USA, 2nd edition, 1995.
[11]
M. Shamsuzzoha and S. Skogestad, “The setpoint overshoot method: a simple and fast closed-loop approach for PID tuning,” Journal of Process Control, vol. 20, no. 10, pp. 1220–1234, 2010.
[12]
M. Shamsuzzoha, M. Lee, and H. Seki, “Closed-loop PI/PID controller tuning for stable and unstable processes,” in Proceedings of the American Control Conference, pp. 2368–2373, Montreal, Canada, 2012.
[13]
A. J. Barr and J. L. Ray, “Control of an active suspension using fuzzy logic,” in Proceedings of the 5th IEEE International Conference on Fuzzy Systems, pp. 42–48, September 1996.
[14]
M. Cai, H. Liu, P. Du, J. Guo, and H. Chang, “Suspension dynamics simulation based on simulink,” in Proceedings of the International Conference on Electric Information and Control Engineering, pp. 2715–2718, April 2011.
[15]
N. Changizi and M. Rouhani, “Comparing PID and fuzzy logic control a quarter-car suspension system,” The Journal of Mathematics and Computer Science, vol. 2, no. 3, pp. 559–564, 2011.
[16]
K. J. ？str？m and T. H？gglund, “The future of PID control,” Control Engineering Practice, vol. 9, no. 11, pp. 1163–1175, 2001.
[17]
N. Tan, I. Kaya, C. Yeroglu, and D. P. Atherton, “Computation of stabilizing PI and PID controllers using the stability boundary locus,” Energy Conversion and Management, vol. 47, no. 18-19, pp. 3045–3058, 2006.
[18]
J. Y. Wong, Theory of Ground Vehicles, John Wiley & Sons, New York, NY, USA, 1988.
[19]
J. Zhihong, E. Zhang, L. Zhonghua, J. Jing, and Z. Fan, “Simulation and experiment research on human riding comfort for vehicle vibration in dynamic environment,” in Proceedings of the 9th International Conference on Computer-Aided Industrial Design and Conceptual Design: Multicultural Creation and Design, pp. 175–181, November 2008.
