| Summary: | In this paper, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">D</mi></semantics></math></inline-formula>-decomposition technique is investigated as an intuitive method for finding the non-linear trajectories of PI-compensator gains. The trajectories reflect the desired dynamic properties at a system level specified by the gain and the phase margin (GMPM) in the frequency domain. They are presented as parametric curves in the proportional and the integral gains coordinates in form of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>K</mi><mi mathvariant="normal">I</mi></msub><mo>=</mo><mi>f</mi><mrow><mo>(</mo><msub><mi>K</mi><mi mathvariant="normal">P</mi></msub><mo>)</mo></mrow></mrow></semantics></math></inline-formula> functions. The curves are inscribed into global stability boundaries (GSB). The corresponding Nyquist plots are included for comparison. The analysis is based on a system consisting of two serial-connected boost converters. Each converter has its input filter. The major parasitic components of the system are taken into account during the mathematical and simulation modelling. The control circuit time delays and non-linear semiconductors characteristics are also included. A complete set of practically useful system-level transfer functions in form of mathematical formulas is included. Selected aspects, such as the control-to-output voltage and the control-to-input current of one sub-system of the simulation model, have been verified experimentally. The presented results clearly indicate the need for interactions between the sub-systems of a system to be taken into account during controller gains selection.
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