Parameter estimation of an SMA actuator model using an extended Kalman filter

Abstract Brinson model is one of the most-widely used models for shape memory alloy (SMA) wires. The parameters of this model must be determined experimentally. This paper has focused on identifying these parameters for a one-dimensional model of SMA wire. This model is identified in order to predict the outputs of a one-DOF SMA actuator. The parameters of Brinson model are estimated experimentally using an extended Kalman filter (EKF). The main contribution of this paper is designing a procedure to identify the model parameters based on experimental tests performed on the SMA actuator, without needing separate laboratory tests. In the designed procedure, the effects of unmodeled factors and sensor biases are taken into account. The estimation is performed in a pre-designed sequence to avoid the divergence of EKF and validated by comparing the outputs of the identified model with the actual output of the actuator. The results of the identified model match precisely with the experimental data in both phase transformation and linear regions. However, some mismatches are observed in transition regions that may be related to the Brinson model structure, where the governing equation suddenly changes in the transition region. The results show the capability of the EKF to estimate Brinson model parameters. This estimation can be performed directly on SMA actuators.

[1]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[2]  Kyu-Yeul Lee,et al.  Estimation of hydrodynamic coefficients for an AUV using nonlinear observers , 2002 .

[3]  Mehdi Ahmadian,et al.  Design of a Kalman filter for rotary shape memory alloy actuators , 2004 .

[4]  Inderjit Chopra,et al.  Comparative Evaluation of Shape Memory Alloy Constitutive Models with Experimental Data , 2001 .

[5]  Craig A. Rogers,et al.  One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials , 1990 .

[6]  Toru Namerikawa,et al.  Extended Kalman filter-based mobile robot localization with intermittent measurements , 2013 .

[7]  L. Brinson.  One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable , 1993 .

[8]  Afzal Khan.  Characterization and application of Shape Memory Alloy wires for micro and meso positioning systems , 2008 .

[9]  Ying Lei,et al.  The Twelfth East Asia-Pacific Conference on Structural Engineering and Construction A Two-Stage Kalman Estimation Approach for the Identification of Nonlinear Structural Parameters , 2013 .

[10]  Mohammad Reza Zakerzadeh,et al.  A comparative analysis of some one-dimensional shape memory alloy constitutive models based on experimental tests , 2012 .

[11]  Zhang Yigong,et al.  Nonlinear structural identification using extended kalman filter , 1994 .

[12]  Eric Williams,et al.  An Automotive SMA Mirror Actuator: Modeling, Design, and Experimental Evaluation , 2008 .

[13]  Jong-Ha Chung,et al.  Implementation strategy for the dual transformation region in the Brinson SMA constitutive model , 2007 .

[14]  Etienne Patoor,et al.  Parameter identification of a thermodynamic model for superelastic shape memory alloys using analytical calculation of the sensitivity matrix , 2014 .

[15]  Etienne Patoor,et al.  Analysis of the deformation paths and thermomechanical parameter identification of a shape memory alloy using digital image correlation over heterogeneous tests , 2015 .

[16]  Dimitris C. Lagoudas,et al.  Thermomechanical Characterization of Shape Memory Alloy Materials , 2008 .

[17]  K. Tanaka.  A THERMOMECHANICAL SKETCH OF SHAPE MEMORY EFFECT: ONE-DIMENSIONAL TENSILE BEHAVIOR , 1986 .

[18]  Zare Ernani Mehdi,et al.  IDENTIFICATION OF AN AUTONOMOUS UNDERWATER VEHICLE DYNAMIC USING EXTENDED KALMAN FILTER WITH ARMA NOISE MODEL , 2015 .

[19]  M. Moallem,et al.  Tracking Control of an Antagonistic Shape Memory Alloy Actuator Pair , 2009, IEEE Transactions on Control Systems Technology.

[20]  Mohammad Reza Zakerzadeh,et al.  Position control of shape memory alloy actuator based on the generalized Prandtl-Ishlinskii inverse model , 2012 .

[21]  L. C. Brinson,et al.  Simplifications and Comparisons of Shape Memory Alloy Constitutive Models , 1996 .

[22]  Eric Abel,et al.  Issues concerning the measurement of transformation temperatures of NiTi alloys , 2004 .

[23]  Mehdi Ahmadian,et al.  Application of the extended Kalman filter to control of a shape memory alloy arm , 2006 .

[24]  H Gurung,et al.  Development of an extended Kalman filter for the self-sensing application of a spring-biased shape memory alloy wire actuator , 2016 .

[25]  Nguyen Trong Tai,et al.  Output Feedback Direct Adaptive Controller for a SMA Actuator With a Kalman Filter , 2012, IEEE Transactions on Control Systems Technology.

[26]  Stefano Mariani,et al.  Stochastic system identification via particle and sigma-point Kalman filtering , 2012 .

[27]  M. Ahmadian,et al.  A Temperature-based Controller for a Shape Memory Alloy Actuator , 2005 .