Model Based Tuning of Proportional Resonant Controllers for Voltage Source Inverters

The paper considers the optimal choice of gains of proportional-resonant controllers applied to control voltage source inverters. An inverter, controlled in closed loop, but without proportional resonant controllers, is modeled as a second order transfer function from reference to output. The system is augmented with proportional-resonant controllers by feeding the error between reference and output back through a set of N proportional resonant controllers to subsequently alter the reference. The root locus of the closed loop system is considered as a function of the proportional-resonant gains. To find the optimal choice of gains, we maximize the damping of the mode with smallest damping. This corresponds to solving a nonlinear min-max problem. After linearization, the problem is stated as a linear program.