Simulation of thin-film battery response to periodic loading by a transition matrix approximation using boundary and nonlinearity error analysis

- Improved modeling thin-film battery for disparate timescales from periodic loading.
- Numerical cost reduction from our prior work by implementing a key state definition.
- Error analysis allowing understanding of error sources in state projection.
- Apply error analysis for targeted updating of transition matrix during projection.
- Case study implementation of modeling approach in a mock microrobot application.

Simulating repeating loading events on dynamic systems can be challenging when large timescale disparities exist coupled with aperiodic effects. Batteries driving switched/pulsed loads represent one such situation. Large timescale disparity can be experienced by solid-state batteries driving switching microactuators or microelectronics, due to extremely short transient response times of microscale systems relative to some of the battery's own dynamics. Projecting state changes over a long series of fast-timescale loading events using a transition matrix approach was shown previously to significantly reduce numerical expense of simulation compared to full modeling. Here we develop an approach for further accelerated simulation of a battery driving a microelectromechanical system (MEMS) actuator that quantifies errors and addresses overhead expenses in projecting battery states across multiple fast events. This is done with a definition of system states that allows efficient transition matrix generation, and an analysis of key errors associated with projection. This error analysis enables targeted modification to the transition matrix during projection. A case study explores these modeling approaches in a capacitively loaded, battery usage scenario of a piezoelectrically-driven microrobot where the proposed improvements reduce the numerical cost (function calls) by over 44x from the prior approach. Conditions for further simplified modeling are discussed.