In this paper, an adaptive controller is investigated for a class of uncertain single-input-single-output nonlinear systems preceded by an unknown backlash-type hysteresis nonlinearity, which is modeled by a differential equation. Backstepping design procedure is employed to construct the control input and adaptation laws. A new algorithm is designed to reduce the computational burden compared with previous work for unknown backlash-type hysteresis. Based on Lyapunov stability theory, all the signals in the closed-loop system are bounded, and the system output can track the reference signal to a bounded compact set. An example for hard disk drives with hysteresis friction nonlinearity is given to verify the feasibility of the proposed approach.
BoulkrouneAM’saadM (2012) Fuzzy adaptive observer- based projective synchronization for nonlinear systems with input nonlinearity. Journal of Vibration and Control18: 437–450.
2.
BusawonKDeLJAche-DazaS (2001) A controller design for a special class of nonlinear systems. Applied Mathematics Letters14: 499–505.
3.
ChenWSLiJM (2008) Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics38: 258–266.
4.
ChenMGeSSRenBB (2011) Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica47: 452–465.
5.
ChoHBaiE (1998) Convergence results for an adaptive dead zone inverse. International Journal of Adaptive Control and Signal Processing12: 451–466.
6.
KanellakopoulosIKokotovicPVMorseAS (1991) Systematic design of adaptive controllers for linearizable systems. IEEE Transactions on Automatic Control36: 1241–1253.
7.
KrsticMKanellakopoulosLKokotovicPV (1995) Nonlinear and Adaptive Control Design, New York: Wiley-Interscience.
8.
LiHYuJHiltonC (2012) Adaptive sliding mode control for nonlinear active suspension systems using T-S fuzzy model. IEEE Transactions on Industrial Electronics. DOI: 10.1109/TIE.2012.2202354, in press.
9.
LiZJ (2008) Adaptive neural-fuzzy control of uncertain constrained multiple coordinated nonholonomic mobile manipulators. Engineering Applications of Artificial Intelligence21: 985–1000.
10.
LiZJGeSSAdamsM (2008) Adaptive robust output-feedback motion/force control of electrically driven nonholonomic mobile manipulators. IEEE Transactions on Control Systems Technology16: 1308–1315.
11.
LiZJLiJXKangY (2010) Adaptive robust coordinated control of multiple mobile manipulators interacting with rigid environments. Automatica46: 2028–2034.
12.
LiZJCaoXQDingN (2011) Adaptive fuzzy control for synchronization of nonlinear teleoperators with stochastic time-varying communication delays. IEEE Transactions on Fuzzy Systems19: 745–757.
13.
LiuYJWangW (2012) Adaptive output feedback control of uncertain nonlinear systems based on dynamic surface control technique. International Journal of Robust and Nonlinear Control22: 945–958.
14.
NgocP (2012) On exponential stability of nonlinear differential systems with time-varying delay. Applied Mathematics Letters25: 1208–1213.
15.
RenBBGeSSSuCY (2009) Adaptive neural control for a class of uncertain nonlinear systems in pure-feedback form with hysteresis input. IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics39: 431–443.
16.
SanPPRenBBGeSS (2011) Adaptive neural network control of hard disk drives with hysteresis friction nonlinearity. IEEE Transactions on Control Systems Technology19: 351–358.
17.
SuCYStepanenkoYSvobodaJ (2000) Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis. IEEE Transactions on Automatic Control45: 2427–2432.
18.
SuCYWangQQChenXK (2005) Adaptive variable structure control of a class of nonlinear systems with unknown Prandtl-Ishlinskii hysteresis. IEEE Transactions on Automatic Control50: 2069–2074.
19.
TaoGKokotovicPV (1995) Adaptive control of systems with unknown output backlash. IEEE Transactions on Automatic Control40: 326–330.
20.
TongSCHeXLZhangHG (2009) A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control. IEEE Transactions on Fuzzy Systems17: 1059 1069.
21.
TongSCLiuCLLiYM (2010) Fuzzy adaptive decentralized control for large-scale nonlinear systems with dynamical uncertainties. IEEE Transactions on Fuzzy Systems18: 845–861.
22.
WangXSSuCYHongH (2004) Robust adaptive control of a class of nonlinear systems with unknown dead-zone. Automatica40: 407–413.
23.
YangCGGeSSXiangC (2008) Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Transactions on Neural Networks19: 873–886.
24.
YangCGGeSSLeeTH (2009) Output feedback adaptive control of a class of nonlinear discrete-time systems with unknown control directions. Automatica45: 270–276.
25.
YangCGGaneshGAlbu-SchaefferA (2011) Human like adaptation of force and impedance in stable and unstable tasks. IEEE Transactions on Robotics27: 918–930.
26.
YaoJJWangCG (2012) Model reference adaptive control for a hydraulic underwater manipulator. Journal of Vibration and Control18: 893–902.
27.
YaoJJWangXCHuSH (2011) Adaptive neural network-based adaptive inverse control for an electro-hydraulic servo system. Journal of Vibration and Control17: 2007–2014.
28.
ZhouJWenCZhangY (2004) Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis. IEEE Transactions on Automatic Control49: 1751–1757.
29.
ZhouJZhangCJWenCY (2007) Robust adaptive output control of uncertain nonlinear plants with unknown backlash nonlinearity. IEEE Transactions on Automatic Control52: 503–509.
30.
ZhouQShiPLuJ (2011) Adaptive output feedback fuzzy tracking control for a class of nonlinear systems. IEEE Transactions on Fuzzy Systems19: 972–982.
