Parameter estimation of nonlinear thermoelectric structures using particle swarm optimization

The purpose of this investigation is motivated mainly for thermal energy harvesting devices and temperature feedback controllers interacting with electronic circuits. Mostly intended to design Linear Quadratic Gaussian (LQG) type controllers, suitable for uncertain dynamical systems, in which not all state variables are measured and available for proper feedback. We present a methodology for modeling and estimation of several internal parameters for a proposed thermal characterization apparatus that employs thermoelectric modules (TEMs). Repeated random vector sampling, similar to Monte Carlo method, is combined with particle swarm optimization (PSO) algorithm for parameter estimation. For the intended applications, is mandatory to drive apparatus that have embedded TEMs, not only using direct current powering, as usually done in literature, but also with alternate current signals over a large range of relevant frequencies. For exciting the many nonlinear and linear states during the identification procedure, a single embedded TEM is injected with a proper random electrical current signal having power spectral density of a band-limited white noise. Sensitivity to both initial conditions and different sets of random excitation, brings uncertainty in the estimated 21 parameters of our mechanical apparatus with two embedded TEMs and their corresponding dynamics. Simulation are presented showing the effectiveness of the proposed estimation technique, with convergence performance and parameter statistical distribution over a set of uncorrelated random current vector excitation.