A case study on the universal compensation-improvement mechanism: A robust PID filter-shaped optimal PI tracker for systems with/without disturbances

Jason Sheng Hong Tsai, Hsuan Han Wang, Shu Mei Guo, Leang San Shieh, Jose I. Canelon

Research output: Contribution to journalArticle

4 Citations (Scopus)


Many dynamical systems are continuous-time non-square with unknown mismatched input and output disturbances. For such systems, a universal on-line robust optimal tracking control is often desirable. In this paper, the conventional proportional-integral-differential (PID) controller is utilized as a fictitious PID filter to shape the tracking error in the frequency-domain using a quadratic performance index as a weighting function, such that the robust PID-shaped PI tracker integrated with the equivalent input disturbance (EID) estimator is established to carry out the on-line robust optimal tracking control of the general disturbed system. The benefits and discrepancies of the proposed compensation improvement mechanism over the conventional optimal trackers for continuous-time non-square systems with/without unknown mismatched input and output disturbances are listed as follows: (i) It develops a new net EID estimator without any previously established constraints on the dimensions of the system and on the disturbances; (ii) It provides an efficient estimated-state-feedback-based EID estimator in contrast to the conventional output-feedback-based EID estimators; (iii) It is able to carry out on-line EID estimation of the tracking errors for systems with endogenous/exogenous output disturbances; (iv) It is a universal tracker which can be simply implemented as a plug-in EID estimator for most servo systems, to improve the performance of any existing observers/trackers which are not allowed to be removed from the system. The advantages of the proposed method over two existing outstanding approaches reported in the literature are pointed out using illustrative examples.

Original languageEnglish
Pages (from-to)3583-3618
Number of pages36
JournalJournal of the Franklin Institute
Issue number8
Publication statusPublished - 2018 May


All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics

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