Robust estimation of spring stiffness in a Shape Memory Alloy actuator using Extended Kalman Filter

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Abstract

In this paper, at first a Shape Memory Alloy (SMA) actuator is modeled by Brinson model. Due to high efficiency of Brinson model in modeling SMA behavior, this model is studied in detail in all regions of temperature-stress plane. Then, an SMA actuator, that is composed of a SMA wire connected to a linear spring, is modeled. Since in many SMA actuators, some parameters, like spring stiffness in this case, cannot precisely determined or it is changed by the environment situations, an Extended Kalman Filter (EKF) is used to estimate these parameters. In this filter, an initial guess and its error covariance must be determined. But since this error covariance can’t be determined precisely, the effect of initial error covariance inaccuracy on the parameter estimation is analyzed. Also, since in actual cases the spring may have nonlinear behavior, a simulation is performed by using a nonlinear spring while the estimation is carried out by using linear spring model. These analyses show that EKF can estimate parameters of an SMA-actuated actuator quickly as well as accurately. Also these estimations are robust against the model and initial guess uncertainty.

Keywords

References

[1] Duerig T, Melton K, Stockel D, Wayman C (1990) Engineering aspects of shape memory alloys. Butterworth- Heinemann Publishers, London.
[2] Tanaka K (1986) A thermomechanical sketch of shape memory effect: one dimensional tensile behavior. Res Mech18: 251-263.
[3] Liang C, Rogers CA (1990) One-dimensional thermomechanical constitutive relations for shape memory material. J Intel Mat Syst Str 1: 207-234.
[4] Sayyaadi H, Zakerzadeh MR, Salehi H (2012) A comparative analysis of some one-dimensional shape memory alloy constitutive models based on experimental tests. Sci Iran 19(2): 249-257.
[5] Brinson LC (1993) One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions. J Intel Mat Syst Str 4(2): 229-242.
[6] Honma D, Miwa Y, Lguchi N (1984) Micro robots and micro mechanisms using shape memory alloy. Paper presented at the 3rd Toyota Conf. on Integrated Micro Motion Systems, Micro-machining. Control and Applications.
[7] Gharaybeh MA, Burdea GC (1995) Investigation of a shape memory alloy actuator force-feedback masters. Adv Robotics 9: 317-329.
[8] Hashimoto M, Takeda M, Sagawa H, Chiba I (1985) Application of shape memory alloy to robotic actuators. J Robotic Syst 2: 3-25.
[9] Simon D (2006) Optimal state estimation (Vol. 5). John Wiley & Sons, New Jersey.
[10] Elahinia MH, Ashrafiuon H, Ahmadian M, Hanghao T (2005) A temperature-based controller for a shape memory alloy actuator. J Vib Acoust 127(3): 285-291.
[11] Elahinia MH, Ahmadian M (2006) Application of the extended Kalman filter to control of a shape memory alloy arm. Smart Mater Struct 15(5): 1370-1384.
[12] Elahinia MH, Ahmadian M (2004) Design of a Kalman filter for rotary shape memory alloy actuators. Smart Mater Struct 13(4): 691-697.
[13] Hassanzadeh I, Nikdel N, Motlagh NT, Badamchizadeh MA (2010) Design of augmented EKF for shape memory alloy actuated manipulator. Int J Eng Sci Technol 2(7): 3188-3198.
[14] Parhald H, Chapora I (2001) Comparative evaluation of shape memory alloy constitutive models with experimental data. J Intel Mat Syst Str 12: 383-395.
[15] Sayyaadi H, Zakerzadeh MR (2012) Nonlinear analysis of a flexible beam actuated by a couple of active SMA wire actuators. Int J Eng 25(3): 249-264.
[16] Chung J, Heo J, LeeJ (2007) Implementation strategy for the dual transformation region in the Brinson SMA constitutive model. Smart Mater Struct 16(1): N1-N5.
[17] Brinson LC (1996) Simplifications and comparisons of shape memory alloy constitutive models. J Intel Mat Syst Str 7(1): 108-114.
[18] Ansari M, Golzar M, Behravesh AH (2013) Experimental studies of training stress effect on NiTi SMA performance in higher and lower stress than training stress. Scientific Research Monthly Journal of Modares Mechanical Engineering 13(10): 14-24.
[19] Zakerzadeh MR (2012) Modeling and position control of a beam by large deflection behavior activated by active shape memory alloy wires. PhD. Thesis, Sharif University of Technology, Tehran.
[20] Hugo YV (2012) Essays in applied macroeconomic theory: volatility, spreads, and unconventional monetary policy tools. London School of Economics, London.
 [21] Hassanzadeh I, Fallah MA (2008) Design of Augmented Extended and Unsented Kalman Filter for Differential-Drive Mobile Robots. J Appl Sci 8(16): 2901-2906.
Journal of Solid and Fluid Mechanics
Volume 5, Issue 4 - Serial Number 4
January and February 2016
Pages 69-81

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