Stability margins and \(H_{\infty}\) co-design with fractional-order \(\mathrm{PI}^{\lambda}\) controllers. (English) Zbl 1327.93157
Summary: This article considers the co-design of gain and phase margins and \(H_{\infty}\) performance for fractional-delay systems using fractional-order \(\mathrm{PI}^{\lambda}\) controllers. The stability region in the proportional – integral plane of the \(\mathrm{PI}^{\lambda}\) controller for a fixed fractional-order \(\lambda\) is first determined graphically in terms of a stability equation method applicable to fractional-delay systems. Then, in the stability region, the system performance design is carried out, including the classical gain-margin and phase-margin and the modern \(H_{\infty}\)-norm constraint of the sensitivity function of the closed-loop. A numerical example is given to show the superiorities of the fractional-order \(\mathrm{PI}^{\lambda}\) controller over the integer-order \(\mathrm{PI}\) controller.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
| 34A08 | Fractional ordinary differential equations |
Keywords:
fractional-order systems; fractional-order \(\mathrm{PI}^{\lambda}\) controllers; time-delay systems; stabilizing regions; gain and phase margins; \(H_{\infty}\)-normReferences:
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