Off-line model predictive control of dc-dc converter

Control systems with switching modes in which different dynamics are assigned are called hybrid dynamical systems and are being actively researched (1–6). The continuous behavior in the hybrid dynamical system is expressed generally by differential or difference equations, while the discrete behavior is described by logics or state machines such as automata. If a system can be regarded as a hybrid dynamical system, both continuous and discrete properties can be dealt with concurrently. Therefore, a hybrid dynamical system has the ability to represent many systems as a single model without dividing into separate continuous and discrete systems. Power electronic circuits can also be regarded as hybrid dynamical systems as they share both continuous and discontinuous behaviors(7–14). The continuous behavior of current or voltage in such a system is subject to passive elements such as resistance, capacitance and inductance, whereas the discontinuous element of switching devices such as MOSFETs and IGBTs yields an on-off signal that is essentially discrete. A conventional method currently being used for the control of dc-dc converters is PWM (Pulse Width Modulation) with triangular wave. The average output voltage is controlled by PWM, which determines on-off switching timing by employing relatively high carrier frequency. However, the reference may vary in the half period of triangular wave carrier if the carrier frequency is lowered to decrease switching loss for saving energy. Then, the average voltage can no longer approximate the voltage reference. One possible reason is that the control frequency is determined by the carrier frequency only. Another reason may be that the PWM method focuses only on the average output characteristic and excludes switching property. Therefore, a novel method is desired for dc-dc converters by considering switching property explicitly as hybrid dynamical systems. For synthesis of the hybrid dynamical system, various approaches have been proposed. Specifically, modeling and synthesis based on mixed logical dynamical (MLD) systems has much potential since the formulation is similar to the linear discrete time state space representation(19). The solution of the design is obtained by solving an optimization problem with the help of model predictive control (MPC)(16; 17). It derives the optimal input to minimize an estimation of a given cost function by predicting controlled variables for anMLD system. Specifically, the problem is reduced to a mixed-integer linear or quadratic programming (MILP orMIQP) problem. Themethod is expected to achieve better control performance than that achieved by conventional methods when applied to the output control of a power 12