| Summary: | Commonly used variants of the proportional-integral, PI, and the integral-proportional, IP, compensator gains selections, merged with the <inline-formula> <tex-math notation="LaTeX">$\mathfrak {D}$ </tex-math></inline-formula>-decomposition technique are presented in this paper. The motivation to this work is the willingness to check whether such a combination can lead to unified and perhaps simplified approach in this matter. Therefore, the <inline-formula> <tex-math notation="LaTeX">$\mathfrak {D}$ </tex-math></inline-formula>-decomposition technique has been effectively combined with the frequency- and the time-domain driven requirements regarding the control dynamics. Criteria such as the gain- and phase-margins, <inline-formula> <tex-math notation="LaTeX">$(GM, PM)$ </tex-math></inline-formula>, the sensitivity, <inline-formula> <tex-math notation="LaTeX">$M_{\text {S}}$ </tex-math></inline-formula>, the pole placements by means of the <inline-formula> <tex-math notation="LaTeX">$(\sigma, \omega _{\text {d}})$ </tex-math></inline-formula> and the <inline-formula> <tex-math notation="LaTeX">$(\xi, \omega _{\text {n}})$ </tex-math></inline-formula>, and the overshoot with the rise time <inline-formula> <tex-math notation="LaTeX">$(\delta, t_{\text {r}})$ </tex-math></inline-formula> are considered. It has been shown that the control design effort can be reduced by the means of the <inline-formula> <tex-math notation="LaTeX">$\mathfrak {D}$ </tex-math></inline-formula>-decomposition to intuitive judgments in the proportional and integral gains coordinates <inline-formula> <tex-math notation="LaTeX">$(K_{\text {P}}, K_{\text {I}})$ </tex-math></inline-formula> with parametric curves. As such it can be thought of as a promising scenario in a case considered. The analyses are presented and discussed in details. They are conducted basing on example of output voltage closed loop control of the Dual Active Bridge, DAB, converter. The circuit operates under the phase shift control scheme. The control-to-output transfer function identification and the control circuit delays are included in the analyses. The case analysis have shown that the time domain requirements are less effectively met with the PI regulator when compared to its IP configuration. This is due to the commonly used simplifications during conversion between the <inline-formula> <tex-math notation="LaTeX">$(\xi, \omega _{\text {n}})$ </tex-math></inline-formula> and the <inline-formula> <tex-math notation="LaTeX">$(\delta, t_{\text {r}})$ </tex-math></inline-formula> in presence of uncompensated zero of the closed loop transfer function. The paper contains complete and intelligible approach to dedicated mathematical investigations verified experimentally.
|
|---|
