Control‐oriented LPV Modeling for the Air Supply System of Proton Exchange Membrane Fuel Cells

Abstract

Air supply system, as a crucial subsystem of proton exchange membrane fuel cells (PEMFC), plays a very significant role in the efficiency and the reliability of the system. In order to better control the air supply subsystem, an appropriate model needs to be established to describe the subsystem covering whole working conditions from PEMFC startup to shutdown. This paper propose a linearized parameter varying (LPV) model based on system identification. To describe the subsystem in different working conditions, the subsystem is identified near 7 equilibrium points. Identification results show that the subsystem can be described as several linear models near equilibrium points. Based on these linear models, a LPV model is proposed solving 2‐D interpolation problem. It is proved theoretically that LPV system has the same steady‐state character and linear model at equilibrium points with identification models. The simulation and experiments results also verify that the LPV model can cover the working conditions from PEMFC startup to shutdown with accuracy both in dynamic condition and steady state.

Optimal gain‐scheduling control of proton exchange membrane fuel cell: An LMI approach

“…As can be seen in Figure 2, the non-linear PEMFC system with timevarying parameters is initially linearized around its equilibrium profiles, which are dependent on the time-varying parameters I and T , to derive a polytopic-LPV representation. After that, the cost function and its weights are selected, which include the two auxiliary outputs (23) and (24), as well as the control input. Finally, by utilizing the LMIs ( 28) and ( 29) in Theorem 1, the controller gain matrix is computed and the optimizing stabilizer controller is constructed.…”

“…where K is the controller gain and should be chosen to (I) assure the closed-loop stability and (II) minimize the outputs (23) and (24). The closed-loop PEMFC system is obtained as follows:…”

“…One other interesting approach to control and monitor the non-linear system is the linear parameter varying (LPV) or Takagi-Sugeno (TS) fuzzy method and has attracted many researchers [20][21][22]. In [23], an LPV model for a class of nonlinear PEMFC control systems is presented. That approach uses the linearization method to derive linear representations near seven equilibrium points.…”

“…That approach assumes that the varying parameters only appear in the system input matrix. However, the issue of controller design is not studied in [23][24][25]. In [26], a TS fuzzy predictive controller (MPC) is designed for PEMFCs.…”

“…This representation is inspired by the linearization approach of [27,28]. Though it reduces the number of polytopic-LPV vertices number to four, which is remarkably smaller than [23,28]. Considering the PEMFC output power in the optimization problem enhances the performance of the PEMFC; meanwhile, the membrane pressure is kept low to enhance the lifetime.…”