Method for Determining a Dynamical State–Space Model for Control of Thermal MEMS Devices

A method is presented for determining lumped dynamical models of thermal microelectromechanical systems (MEMS) devices for purposes of feedback control. As a case study, an electrothermal actuator is used. The physical properties and a set of assumptions are used to determine the basic structure of the dynamical model, which requires the development of the electrical, thermal, and mechanical dynamics. The importance of temperature-dependent parameters is emphasized for dynamical modeling for purposes of feedback control. To confront temperature dependence in a practical yet effective manner, an average temperature is introduced to preserve the energy balance inside the structure. This allows the development of a practical method that combines structure of the model, through the average body temperature, with finite element analysis (FEA) in novel way to perform system identification and identify the unknown parameters. The result is a lumped dynamical model of a MEMS device that can be used for the design of feedback control systems. We compare computer simulated results using the dynamical model with experimental behavior of the actual device to show that our procedure indeed generates an accurate model. This dynamical model is intended for further synthesis of driving signal and control system but also gives a qualitative insight into the relationship between device's geometry and its behavior. The method enables fast development of the model by conducting relatively few static FEA and is verifiable with dynamic experimental results even when temperature measurements are not available.
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