Abstract

In this paper optimal second order sliding mode controller for uncertain systems by using integral sliding surface is proposed. The optimal controller is designed based on linear quadratic regulator (LQR) method for nominal model of the system. In optimal control method, the LQR is combined with sliding mode control to obtain equivalent control and switching control. The sliding mode controller is designed using integral sliding surface to obtain the value of switching control and to equivalent control values are obtained using LQR technique. It is observed that LQR and integral sliding mode control method are more efficient compare to other conventional techniques. Stabilization of inverted pendulum system is done using the sliding mode control approach. The system of inverted pendulum is used in state space approach. The main advantages of this method is that disturbance rejection, insensitivity to parameter variations and implementation issues are addressed easily using proposed controller stabilization of inverted system. The simulation result conform an advantage of the designed optimal sliding mode control approach in terms of output responses and stabilization of the system.

References

• Madhulika Das , Chitralekha Mahanta” Optimal second order sliding mode control for linear uncertain systems,” ISA. Trans proceeding sliding mode control.
• I. J. Nagrath, M.Gopal control system Engg. International publication fifth edition
• Utkin V. “Sliding modes in control and optimization”,. Berlin: Springer-Verlag; 1992.
• Utkin V. “Variable structure systems with sliding modes”, .IEEE Trans Autom Control 1977;22(2):212-22.
• XuR,Özgüner Ü. “Optimal sliding mode control for linear systems”, .In :IEEE proceedings on variable structure systems.2006.p.143–8.
• young KD,Özgüner Ü. “Sliding- mode design for robust linear optimal control”,Automatica1997;33(7):1313–23.
• Laghrouche S, Plestan F ,Glumineau A. Higher order sliding mode control based on integral sliding mode”.Automatica2007;43(3):531–7.
• Feng Y,Han X, Wang Y ,Yu X. Second order terminal sliding mode control of uncertain multivariablesystems.IntJControl2007;80(6):856–62.
• Hung J, Gao W, Hung J .Variable structure control :a survey. IEEE Trans Ind Electron 1993;40(1):2–22.
• Pang H-P, Yang Q. Optimal sliding mode output tracking control for linear systems with uncertainties.In:2010international conference on machine learning and cybernetics (ICMLC), vol.2,2010.p.942–6.
• Dong R, Gao H-W ,Pan Q-X .Optimal sliding mode control for nonlinear systems with uncertainties In:IEEEproceedingsoncontrolanddecision,2011.p. 2098–103.
• Schmitendorf W. Barmish B. Robust asymptotic tracking for linear systems with unknown parameters .Automatica1986;22(3):355–60
• Marino R, Tomei P.Global adaptive output-feedback control of nonlinear systems, Part i: linear parameterization. IEEE Trans Automatic Control1993;38(1): 17–32.
• .