Date of Award

Spring 1-1-2014

Document Type


Degree Name

Doctor of Philosophy (PhD)


Electrical, Computer & Energy Engineering

First Advisor

Frank Barnes

Second Advisor

Lijun Chen

Third Advisor

Damon Miller

Fourth Advisor

William Emslie

Fifth Advisor

Kimberly Newman


In this thesis a robust current control strategy is proposed for a grid connected three phase inverter. Current controllers based on proportional-integral (PI) control may not always offer the superior tracking performance and harmonic rejection ability of robust controllers. Robust control design offers the ability to design a controller that is robust to modeled uncertainties in the plant. A typical inverter may experience fluctuations in its input DC voltage due to uncertainties in the DC power source. In the case of a solar-inverter, large fluctuations in the input DC voltage typically occur due to (i) varying irradiance levels and (ii) phase and ground faults. An inverter is usually designed to disconnect from service in case its DC voltage strays outside a pre-defined operating range. With a current controller that's robust with respect to fluctuations in the input DC voltage, the inverter's operating range could be widened, giving the user more flexibility when designing their system.

A common step in the PI based current controller operation is the transformation of three phase signals to their direct-quadrature equivalent. With the use of the repetitive control strategy, the transformation step is no longer required. The repetitive control strategy is chosen because it can reject a large number of harmonics simultaneously, while providing a clean sinusoidal current waveform to the grid, even in the presence of grid load and/or voltage distortions. The repetitive control strategy is implemented via the internal model principle. Mu-synthesis based control is chosen to attain robust reference tracking in the presence of plant uncertainties. Uncertainty in the inverter input DC voltage is considered and expressed as a static uncertainty. By applying mu-synthesis principles, a feedback controller that simultaneously achieves robust stability and robust tracking performance is obtained.