This paper proposes a new approach for adaptive sliding mode controller (ASMC) designs. The goal is to obtain robust, smooth, and fast transient performance for nonlinear systems with finite uncertainties of unknown bounds and limited available inputs so that the phenomena of the slow response and the gain overestimation in most ASMC designs can be greatly improved. Sufficient and necessary conditions for the existence of a sliding mode in the ASMC designs are discussed. Based on the sufficient conditions, we introduce an integral/exponential adaptation law targeting the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously speeding up the system response to the uncertainties. An illustrative example and numerical simulations are performed to convey the discussed results.
BhatSBernsteinD (2000) Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization38(3): 751–766.
2.
ChenX (2006) Adaptive sliding mode control for discrete-time multi-input multi-output systems. IEEE Transactions on Automatic Control1(42): 427–435.
3.
CongBChenZLiuX (2012) On adaptive sliding mode control without switching gain overestimation. International Journal of Robust and Nonlinear Control1(1): 1–17.
4.
FallahaCSaadMKanaanH. (2011) Sliding-mode robot control with exponential reaching law. IEEE Transactions on Industrial Electronics58(2): 600–610.
5.
FeiJXinMJuanW (2012) Adaptive fuzzy sliding mode control using adaptive sliding gain for MEMS gyroscope. Transactions of the Institute of Measurement and Control35(4): 551–558.
6.
GaoWHungJ (1993) Variable structure control of nonlinear systems: A new approach. IEEE Transactions on Industrial Electronics40(1): 45–55.
7.
HuangYKuoTChangS (2008) Adaptive sliding-mode control for nonlinear systems with uncertain parameters. IEEE Transactions on Systems, Man and Cybernetics–Part B: Cybernetics38(2): 534–539.
8.
HungJYGaoWHungJC (1993) Variable structure control: A survey. IEEE Transactions on Industrial Electronics40(1): 2–22.
LeeHUtkinV (2007) Chattering suppression methods in sliding mode control systems. Annual Reviews in Control31(1): 179–188.
11.
LevantA (2001) Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence. IEEE Transactions on Automatic Control46(9): 1447–1451.
12.
LevantA (2007) Principles of two-sliding mode design. Automatica43(43): 576–586.
13.
LiPZhengZQ (2012) Robust adaptive second-order sliding-mode control with fast transient performance. IET Control Theory and Applications6(2): 305–312.
14.
LiYXuQ (2010) Adaptive sliding model control with perturbation estimation and PID sliding surface for motion tracking of a piezo-driven micromanipulator. IEEE Transactions on Control Systems Technology18(4): 798–810.
15.
MahmoodabadiMTaherkhorsandiMTalebipourM. (2014) Adaptive robust PID control subject to supervisory decoupled sliding mode control based upon genetic algorithm optimization. Transactions of the Institute of Measurement and Control70(1): 1–10.
16.
MazinanAKazemiMShirzadH (2013) An efficient robust adaptive sliding mode control approach with its application to secure communications in the presence of uncertainties, external disturbance and unknown parameters. Transactions of the Institute of Measurement and Control36(2): 164–174.
17.
PaiMC (2013) Observer-based adaptive sliding mode control for robust tracking and mode following. International Journal of Control, Automation, and Systems11(2): 225–232.
18.
PlestanFShtesselYBrégeaultV. (2010) New methodologies for adaptive sliding mode control. International Journal of Control83(9): 1907–1919.
19.
PolyakovAPoznyakA (2009) Reaching time estimation for “Super-Twisting” second order sliding mode controller via Lyapunov function designing. IEEE Transactions on Automatic Control54(8): 1951–1955.
20.
ShtesselYShkolnilovIBrownM (2003) An asymptotic second-order smooth sliding mode control. Asian Journal of Control5(4): 498–504.
UtkinV (1992) Sliding Modes in Control and Optimization. Berlin: Springer-Verlag.
23.
UtkinVPoznyakA (2013a) Adaptive sliding mode control with application to super-twist algorithm: Equivalent control method. Automatica1(49): 39–47.
24.
UtkinVPoznyakA (2013b) Advances in Sliding Mode Control – Concept, Theory and Implementation. New York, NY: Springer.
25.
WheelerGSuCYStepanenkoY (1998) A sliding mode controller with improved adaptation laws for the upper bounds on the norm of uncertainties. Automatica34(12): 1657–1661.
26.
YangSKeS (2000) Performance evaluation of a velocity observer for accurate velocity estimation of servo motor drives. IEEE Transactions on Industry Applications36(1): 98–104.
27.
YoungKUtkinVOzgunerU (1999) A control engineer’s guide to sliding mode control. IEEE Transactions on Control Systems Technology7(3): 328–342.
28.
YuSYuXShirinzadehB. (2005) Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica41: 1957–1964.
29.
ZhuJKhayatiK (2014a) Adaptive sliding mode control with smooth switching gain. In: IEEE Canadian conference on electrical and computer engineering, Toronto, Canada.
30.
ZhuJKhayatiK (2014b) New algorithms of adaptive switching gain for sliding mode control: Part I – ideal case. In: IEEE second international conference on control, decision and information technologies, Metz, France.
31.
ZhuJKhayatiK (2014c) On adaptive sliding mode control switching gain comments and alternative design. In: Canadian Society for Mechanical Engineering international congress, Toronto, Canada.
