Linearization of shape-memory heat-transfer model using Chebyshev expansion

Ali R. Shahin; Peter H, Meckl; James D. Jones

doi:10.1117/12.148402

22 July 1993 Linearization of shape-memory heat-transfer model using Chebyshev expansion

Ali R. Shahin, Peter H, Meckl, James D. Jones

Proceedings Volume 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures; (1993) https://doi.org/10.1117/12.148402
Event: 1993 North American Conference on Smart Structures and Materials, 1993, Albuquerque, NM, United States

Abstract

The primary factor governing response time in SMA actuators is heat transfer rate which is represented by a nonlinear differential equation for cooling by free convection. To use classical control theory for controlling the temperature of the SMA wire, the nonlinear model must be linearized. In this paper, the heat transfer rate model is linearized using Chebyshev polynomials. This method of linearization has the same desirable local stability properties as the more traditional Taylor series expansion. It is shown that the maximum errors between the actual and linearized responses and their derivatives using Chebyshev linearization are smaller in magnitude than the errors obtained using Taylor series expansion, making Chebyshev linearization more desirable for this application.

Citation Download Citation

Ali R. Shahin, Peter H, Meckl, and James D. Jones "Linearization of shape-memory heat-transfer model using Chebyshev expansion", Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); https://doi.org/10.1117/12.148402

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