Design of robust PI controllers for interval plants with worst-case gain and phase margin specifications in presence of multiple crossover frequencies

Abstract

This article deals with the computation of robustly performing Proportional-Integral (PI) controllers for interval plants, where the performance measures are represented by the worst-case Gain Margin (GM) and Phase Margin (PM) specifications, in the event of multiple Phase Crossover Frequencies (PCFs) and/or Gain Crossover Frequencies (GCFs). The multiplicity of PCFs and GCFs poses a considerable complication in frequency-domain control design methods. The paper is a continuation of the authors' previous work that applied the robust PI controller design approach to a Continuous Stirred Tank Reactor (CSTR). This preceding application represented the system with a single PCF and a single GCF, but the current article focuses on a case of multiple PCFs and GCFs. The determination of a robust performance region in the P-I plane is based on the stability/performance boundary locus method and the sixteen plant theorem. In the illustrative example, a robust performance region is obtained for an experimental oblique wing aircraft that is mathematically modeled as the unstable interval plant. The direct application of the method results in the (pseudo-)GM and (pseudo-)PM regions that "illogically" protrude from the stability region. Consequently, a deeper analysis of the selected points in the P-I plane shows that the calculated GM and PM boundary loci are related to the numerically correct values, but that the results may be misleading, especially for the loci outside the stability region, due to the multiplicity of the PCFs and GCFs. Nevertheless, the example eventually shows that the important parts of the GM and PM regions, i.e., the parts that have an impact on the final robust performance region, are valid. Thus, the method is applicable even to unstable interval plants and to the control loops with multiple PCFs and GCFs.