Identification of Hammerstein Systems with Rate-Dependent Hysteresis Nonlinearities in a Class of Smart Material-Based Actuators

In [1], we introduced an algorithm to identify rate-independent hysteresis nonlinearities of a class of smart material-based actuators, which is modeled as a Hammerstein system, that is, a cascade of a Prandtl-Ishlinskii (PI) hysteresis nonlinearity with a linear dynamic system. In this paper, we extend the results in [1] to Hammerstein systems with rate-dependent hysteresis nonlinearities. We consider a rate-dependent PI model, which has been used to model rate-dependent hysteresis nonlinearities in smart micro-positioning actuators such as piezoceramic actuators and magnetostrictive actuators. The rate-dependent hysteresis nonlinearity, the linear dynamic system, and the intermediate signal between them are assumed to be unknown. Least squares is used with a finite impulse response (FIR) model structure to identify the linear part of the Hammerstein system. Then, the output of the Hammerstein system is used along with the identified model of the linear plant to reconstruct the unknown intermediate signal. A nonparametric model of the rate-dependent hysteresis loop is obtained by plotting the reconstructed intermediate signal versus the input signal.

[1]  D. Davino,et al.  Phenomenological dynamic model of a magnetostrictive actuator , 2004 .

[2]  J. Juang.  Applied system identification , 1994 .

[3]  Mohammad Al Janaideh,et al.  Further results on open-loop compensation of rate-dependent hysteresis in a magnetostrictive actuator with the Prandtl-Ishlinskii model , 2018 .

[4]  Β. L. HO,et al.  Editorial: Effective construction of linear state-variable models from input/output functions , 1966 .

[5]  Santosh Devasia,et al.  Feedback-Linearized Inverse Feedforward for Creep, Hysteresis, and Vibration Compensation in AFM Piezoactuators , 2007, IEEE Transactions on Control Systems Technology.

[6]  Hassan K. Khalil,et al.  Design and Analysis of Sliding Mode Controller Under Approximate Hysteresis Compensation , 2015, IEEE Transactions on Control Systems Technology.

[7]  Alberto Cavallo,et al.  Hysteresis compensation of smart actuators under variable stress conditions , 2008 .

[8]  Er-Wei Bai,et al.  Identification of linear systems with hard input nonlinearities of known structure , 2002, Autom..

[9]  Dennis S. Bernstein,et al.  Laurent Series and ℓp Sequences , 2016, Am. Math. Mon..

[10]  Marcel François Heertjes,et al.  A Model-Based Inferential Feedforward Approach to deal with Hysteresis in a Motion System , 2018, 2018 Annual American Control Conference (ACC).

[11]  Dennis S. Bernstein,et al.  Nonparametric Identification of Hammerstein Systems Using Orthogonal Basis Functions as Ersatz Nonlinearities , 2013 .

[12]  Xiaobo Tan,et al.  An incremental harmonic balance-based approach for harmonic analysis of closed-loop systems with Prandtl-Ishlinskii operator , 2018, Autom..

[13]  Stéphane Régnier,et al.  Velocity characterization and control strategies for nano-robotic systems based on piezoelectric stick-slip actuators , 2017, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[14]  Fouad Giri,et al.  Identification of Hammerstein systems in presence of hysteresis-backlash and hysteresis-relay nonlinearities , 2008, Autom..

[15]  Alessandro Masi,et al.  On the identification of Hammerstein systems in the presence of an input hysteretic nonlinearity with nonlocal memory: Piezoelectric actuators – an experimental case study , 2016 .

[16]  M. Al Janaideh,et al.  Inverse Rate-Dependent Prandtl–Ishlinskii Model for Feedforward Compensation of Hysteresis in a Piezomicropositioning Actuator , 2013, IEEE/ASME Transactions on Mechatronics.

[17]  John S. Baras,et al.  Modeling and control of hysteresis in magnetostrictive actuators , 2004, Autom..

[18]  Dennis S. Bernstein,et al.  Closed-loop identification of unstable systems using noncausal FIR models , 2013, 2013 American Control Conference.

[19]  Feng Ding,et al.  Identification methods for Hammerstein nonlinear systems , 2011, Digit. Signal Process..

[20]  Dennis S. Bernstein,et al.  Identification of Hammerstein systems using input amplitude multiplexing , 2013, 2013 American Control Conference.

[21]  Micky Rakotondrabe,et al.  Enhancement of micro-positioning accuracy of a Piezoelectric positioner by suppressing the rate-dependant hysteresis nonlinearities , 2014, 2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[22]  Deepa Kundur,et al.  Identification of Precision Motion Systems with Prandtl-Ishlinskii Hysteresis Nonlinearities , 2018, 2018 Annual American Control Conference (ACC).

[23]  Yves Rolain,et al.  Fast approximate identification of nonlinear systems , 2003, Autom..

[24]  Stéphane Régnier,et al.  A multi-model design for robust hybrid control of non-linear piezoelectric actuators at the micro/nano scales , 2018, 2018 Annual American Control Conference (ACC).

[25]  Micky Rakotondrabe,et al.  Internal model-based feedback control design for inversion-free feedforward rate-dependent hysteresis compensation of piezoelectric cantilever actuator , 2018 .

[26]  B. Ninness,et al.  Quantifying the accuracy of Hammerstein model estimation , 2000, Autom..

[27]  D. Bernstein,et al.  Non-linear system identification using Hammerstein and non-linear feedback models with piecewise linear static maps , 2001 .