An Improved Optimal Sliding Mode Control for Structural Stability

In this paper, the modified optimal sliding mode control with a proposed method to design a sliding surface is presented. Because of the inability of the previous approach of the sliding mode method to design a bounded and suitable input, the new variation is proposed in the sliding manifold to obviate problems in a structural system. Although the sliding mode control is a powerful method to reject disturbances and noises, the chattering problem is not good for actuators. To decrease the chattering phenomena, the optimal control is added to the sliding mode control. Not only the proposed method can decline the intense variations in the inputs of the system but also it can produce the efficient responses respect to the sliding mode control and optimal control that are shown by performing some numerical simulations.

• Leila Fatemi
• Morteza Moradi
• Azadeh Mansouri

• Structural Control
• optimal control
• optimal sliding mode controller
• modified sliding surface.

[1] O. A. Nishitani, et al, " Semi-active structural control with variable
friction dampers", Proceeding of the American Control Conference,
California, 1999, pp. 1017-1021.
[2] R. Guclu, " Sliding mode and PID control of a structural system
against earthquake", Mathematical and Computer Modeling, Vol. 44,
2006, pp. 210-217.
[3] C. L. Lee, et al, " Optimal design theories and applications of tuned
mass dampers", Engineering Structures, Vol. 28, 2006, pp. 43-53.
[4] S. Chakraborty, B. K. Roy, " Reliabilty based optimum design of
tuned mass damper in seismic vibration control of structures with
bounded uncertain parameters", Probabilistic Engineering
Mechanics, Vol. 26, 2011, pp. 215-221.
[5] J. M. Sloss, et al. "Optimal control of structural dynamic systems in
one space dimension using a maximum principle", Journal of
Vibration Control, Vol 11, 2005, pp. 245-261.
[6] S. G. Wang, et at, " Simulation of the robust control for uncertain
structural system against earthquake", Proceeding of the 4th World
Congress on Intelligent Control and Application, China, 2002, pp.
1681-1686.
[7] G. E. Stavroulakis, et al, " Robust active control against wind-induced
structural vibrations", Journal ofWind Engineering and Industrial
Aerodynamics, Vol. 94, 2006, pp. 895-907.
[8] R. Xu, " Optimal sliding mode control and stabilization of
underactuated systems", Dissertations, Ohio State University, 2007.
[9] C. Pukdeboon, A. S. I. Zinober, " Optimal sliding mode controllers
for attitude tracking of spacecraft", 18th IEEE International
Conference on Control Applications, Saint Petersburg, 2009, pp.
1708-1713.