Loop Shaping by Single-Resonant Controllers for Prescribed Tracking of Sinusoidal References

It is well-known that in ac-grid-connected or motor-driving converters, current behavior directly sets the exchange of power between the two. Moreover, in corresponding current plants, most of the disturbance (formed by grid voltage or back EMF and the dc-link voltage) may be measured/estimated and appropriately canceled, reducing the current regulation problem to tracking challenge only. The latter is still of extreme importance since the amount of active/reactive power exchanged is proportional to current magnitude and phase. Recently, a method for deriving proportional-resonant controller structure and coefficients according to desired tracking behavior of ac signal amplitude, applied to typical power converter current loop, was proposed based on the fact that if ac signal envelope is perceived as dc signal, its transient behavior may be easily shaped utilizing well-known approaches employed in dc systems loop shaping while keeping zero phase tracking error at all time. This paper extends the proposed methodology by introducing in-depth analysis of the resulting loop gain shaping, applying practical issues, such as actuator delay, damping, and finite word length to the system, yielding a closed set of hands-on design guidelines. Experimental results are also given, providing a two-fold value: successfully validating the presented material and demonstrating that some of the previously reported outcomes (based on simulations) cannot be achieved in practice due to the above mentioned real world constraints.