A method of optimal control for switched-mode power converters

An optimal control method allowing to achieve the high dynamic performances of switched-mode power converters described by the second-order difference equation is offered. To this purpose, control vector is formed as a linear combination of differences of system variables, and matrix transformation of the linear equation to the nilpotent form is implemented. This control approach gives an ability to achieve a convergence of transient in a fixed point within two steps and to remain this property under regulation and perturbation of system parameters. Matrix transformation of the equation to the nilpotent form is realized by the system solution of the linear algebraic equations regarding the multipliers at the differences of system state variables. A proposed control method can be used as a basis for development of systems with as much as possible high dynamic behavior. To confirm the efficiency of this method, the system for load current control of a PWM buck converter is resulted as an example of the switched-mode power supply.