This paper provides comprehensive design method of compensator for grid-connected PWM inverters with LCL-filter to supply high quality electric power from distributed generations. The proposed compensator ensures: i) high speed tracking with low distortion and zero steady-state errors for sinusoidal current reference; ii) robust responses against frequency and voltage changes of grid power supply. The proposed design methodology is based on the utmost compensator that covers all realizable linear control systems. Various multi-objective control requirements can be considered in the design framework directly, and then, trial-and-error process is reduced. The software-in-the-loop simulations are presented to support the advantages of the design and to demonstrate the system performance compared to traditional Linear Quadratic Regulator with Internal Model controller.