Page 289 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

Identification and Control of Hammerstein Systems With Hysteresis Non-linearity 291

hysteresis non-linearities is compensated, whereas the steady-state track-
ing error is larger than DASMC; this may be caused by the modeling
uncertainties. The DASMC, on the other hand, can achieve better steady-
state tracking control response (e.g., smaller tracking error), but may lead
to worse transient performance due to the hysteresis dynamics. In order
to improve both the transient and steady-state performance, the proposed
composite control is tested. Fig. 18.7C depicts the tracking performance
of the proposed composite control. From Fig. 18.7A–C, one may find that
better transient and steady-state control performance can be obtained, e.g.,
the reaching time of composite control is 0.5 s, which is significantly smaller
than that of DASMC. Moreover, the tracking error can be retained at the
same level as that of DASMC in the steady-state, which is smaller than that
of DIMBC. The mean absolute errors (MAE) of DIMBC, DASMC, and
composite control are 0.112, 0.0813, and 0.0215, respectively. From all the
above results, one can conclude that the proposed composite control can
obtain the best control performance as long as the effect of hysteresis can
be identified and compensated.

18.6 CONCLUSION

This chapter addresses the identification and control of Hammerstein sys-
tems with hysteresis non-linearity described by a Preisach model. Hankel
matrix is firstly used to determine the order of linear dynamics, and then
blind identification is used to estimate the coefficients of linear dynamics
by using the over-sampling output measurements only. Furthermore, an
identification approach was suggested for identifying the Preisach model of
hysteresis non-linearity. Finally, a composite control consisting of a feedfor-
ward control and a feedback control is designed. This control strategy can
take the advantages of inverse model based feedforward control and sliding
mode based feedback control. Simulation results based on a servo motor
system verify the effectiveness of the introduced identification and control
methods.

REFERENCES

[1] Xuemei Ren, Xiaohua Lv, Identification of extended Hammerstein systems using dy-
namic self-optimizing neural networks, IEEE Transactions on Neural Networks 22 (8)
(2011) 1169–1179.