PID-MMAC using an approximate H loop-shaping metric

Rakesh Joshi, Victoria Serrano, Konstantinos Tsakalis

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This paper proposes a PID-multi-model adaptive control (PID-MMAC) algorithm using an approximate H metric that represents the frequency loop-shaping (FLS) cost objective. Existing MMAC algorithms use L2 or least squares-based cost functionals on a suitable error signal to perform controller switching, but their strong dependency on the properties of the excitation makes them sensitive to noise, disturbances and modeling errors. Alternatively, a system-norm-based cost function is advantageous for MMAC as it is less sensitive to the specific signals used for adaptation. In this paper, the H norm in the FLS cost objective is approximated by frequency decomposition of the real-time signals using filter-banks. An MMAC algorithm using this metric is presented and its application to controller switching is discussed. The buck converter serves as the motivating application where the adaptation seeks to compensate for degradation in its components (inductors and capacitors). A comparative study is conducted of the proposed algorithm and an L2-based MMAC algorithm under various excitation conditions. The results show that the proposed algorithm is less susceptible to the properties of the excitation signals as compared to the least squares-based MMAC.

Original languageEnglish (US)
Pages (from-to)479-484
Number of pages6
Issue number4
StatePublished - Jan 1 2018


  • FLS- frequency loop shaping
  • MMAC-Multi model adaptive control
  • RSC-robust stability condition

ASJC Scopus subject areas

  • Control and Systems Engineering


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