This article presents a new control scheme for H systems with symmetric dead-zone input non-linearity and coloured noise. Based on the parameterized H model, we derive a dead-zone compensating control law and a recursive estimator. Theoretical analysis shows that global convergence and closed-loop stability can be guaranteed using the proposed algorithms. What is more, theoretical results show that the output tracking error is convergent with a specific residue, which is related to the variance of the noise and the parameter estimate. Simulation results confirm that the proposed method leads to satisfactory output tracking performance.
AstromKJBorissonULjungL. (1977) Theory and applications of self-tuning regulators. Automatica13(5): 457–476.
2.
BaiE (1998) An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems. Automatica34(3): 333–338.
3.
BaiE (2002) Identification of linear systems with hard input nonlinearities of known structure. Automatica38(5): 853–860.
4.
BloemenHVan de BoomTVerbruggenH (2001) Model-based predictive control for Hammerstein-Wiener systems. International Journal of Control74(5): 482–495.
5.
ChaouiFZGiriFRochdiY. (2005) System identification based on Hammerstein model. International Journal of Control78(6): 430–442.
6.
ChenHF (2005) Strong consistency of recursive identification for Hammerstein systems with discontinuous piecewise-linear memoryless block. IEEE Transactions on Automatic Control50(10): 1612–1617.
7.
ChenHFGuoL (1991) Identification and Stochastic Adaptive Control. Boston, MA: Birkhauser.
8.
ChoHBaiEW (1998) Convergence results for an adaptive deadzone inverse. International Journal of Adaptive Control and Signal Processing12(5): 451–466.
9.
DolancGStrmcnikS (2005) Identification of nonlinear systems using a piecewise-linear Hammerstein model. Systems and Control Letters54(2): 145–158.
10.
DolancGStrmcnikS (2008) Design of a nonlinear controller based on a piecewise-linear Hammerstein model. Systems and Control Letters57(4): 332–339.
11.
DongRTanYH (2009) Internal model control for dynamic systems with preceded backlash. Journal of Dynamic Systems, Measurement, and Control131(2): 1–5.
12.
FruzzettiKPalazogluAMcDonaldK (1997) Nonlinear model predictive control using Hammerstein models. Journal of Process Control7(1): 31–41.
13.
GiriFBaiE (2010) Block-oriented Nonlinear System Identification. London: Springer.
14.
GiriFRochdiYChaouiFZ (2009) Hammerstein system identification in presence of hard nonlinearities of preload and dead-zone type. IEEE Transactions on Automatic Control54(9): 2174–2178.
HongXIplikciSChenS. (2014) A model-based PID controller for Hammerstein systems using B-spline neural networks. International Journal of Adaptive Control and Signal Processing28(3–5): 412–428.
17.
IbrirSXieWFSuCY (2007) Adaptive tracking of nonlinear systems with non-symmetric dead-zone input. Automatica43(3): 522–530.
18.
JoJ (2001) A dead-zone compensator for a DC motor system using fuzzy logic control. IEEE Transactions on Systems, Man and Cybernetics31(1): 42–47.
19.
KungMCWomackBF (1984) Discrete time adaptive control of linear systems with preload nonlinearity. Automatica20(4): 477–479.
20.
LiYMaoZWangY. (2011) Model predictive control synthesis approach of electrode regulator system for electric arc furnace. International Journal of Iron and Steel Research18(11): 20–25.
21.
LjungL (1999) System Identification: Theory for the User, 2nd ed.Englewood Cliffs, NJ: Prentice-Hall.
22.
LvXRenV (2012) Non-iterative identification and model following control of Hammerstein systems with asymmetric dead-zone nonlinearities. IET Control Theory and Applications6(1): 84–89.
23.
PatikirikoralaTWangLColmanA. (2012) Hammerstein–Wiener nonlinear model based predictive control for relative QoS performance and resource management of software systems. Control Engineering Practice20(1): 49–61.
24.
SelmicRLewisF (2000) Dead-zone compensation in motion control systems using neural networks. IEEE Transactions on Automatic Control45(4): 602–613.
25.
SinKSGoodwinGC (1982) Stochastic adaptive control using a modified least squares algorithm. Automatica18(3): 315–321.
26.
TakaoKYamamotoTHinamotoT (2008) Design of a memory-based prefilter supplementing a robust PID control system. Asian Journal of Control10(3): 301–313.
27.
TanYDongRLiR (2009) Recursive identification of sandwich systems with dead zone and application. IEEE Transactions on Control Systems Technology17(4): 945–951.
28.
TaoGKokotovicPV (1994) Adaptive control of plants with unknown dead-zones. IEEE Transactions on Automatic Control39(1): 59–68.
29.
TaoGTianM (1998) Discrete-time adaptive control of systems with multi-segment piecewise-linear nonlinearities. IEEE Transactions on Automatic Control43(5): 719–723.
30.
VorosJ (1999) Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities. IEEE Transactions on Automatic Control44(11): 2145–2149.
31.
VorosJ (2003) Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones. IEEE Transactions on Automatic Control48(12): 2203–2206.
32.
VorosJ (2005) Identification of Hammerstein systems with time-varying piecewise-linear characteristics. IEEE Transactions on Circuits and Systems II, Express Briefs52(12): 865–869.
33.
WangXSSuCYHongH (2004) Robust adaptive control of a class of nonlinear systems with unknown dead-zone. Automatica40(3): 407–413.
34.
XieYTanYDongR (2011) Identification of sandwich systems with a dead zone using combinational input signals. Transactions of the Institute of Measurement and Control33(8): 957–970.
35.
YuFMaoZJiaM (2013) Recursive identification for Hammerstein–Wiener systems with dead-zone input nonlinearity. Journal of Process Control23(8): 1108–1115.
36.
ZhouJShenXZ (2007) Robust adaptive control of nonlinear uncertain plants with unknown dead-zone. IET Control Theory and Applications1(1): 25–32.
37.
ZhouJWenCYZhangY (2006) Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity. IEEE Transactions on Automatic Control51(3): 504–511.
