| In this research, a new method to control switching in dc-dc converters is presented using recent advances in hybrid optimal control theory. Herein, the switched state model of the converter is embedded into a continuously parameterized family of problems, and an embedded optimal control problem (EOCP) is formulated as the minimization of a user-defined performance index (PI). Solution of the EOCP produces a single ("optimal") duty cycle control for each switch period which is implemented using a center aligned pulse width modulation scheme. Since the original hybrid model is used, the proposed control method is not equilibrium point specific and does not require formulation of an average value model (AVM). Further, since the control is optimized over individual switch periods, the controller response is faster than that of controllers relying on AVMs.;The method is implemented in real time within a control framework termed Hybrid Model Predictive Control (HMPC), which combines hybrid optimal control principles with a receding time horizon. This work constitutes the first application of recently developed hybrid optimal control theory to dc-dc converter hardware as well as the first real-time MPC control of dc-dc converters. Specifically, an evaluation of best numerical techniques is considered, resulting in a scheme that can precisely solve the discrete-time EOCP online in less than 50 microsec which is a 103 reduction in computation time compared to a more sophisticated offline solver. To handle source and/or load variation, parameter estimators are utilized to adapt the embedded model/PI online.;The combined HMPC-estimator is validated in hardware, demonstrating robust transient and steady-state performance for three dc-dc converter systems including (1) a boost converter with resistive load, (2) a boost converter with constant power load, and (3) a Cuk converter with resistive load. |
