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Analytic Expressions of Ultimate Gains and Ultimate Periods with Phase‐Optimal Approximations of Time Delays
Author(s) -
Lee Jietae,
Park Ho Cheol,
Sung Su Whan
Publication year - 2005
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450830609
Subject(s) - simple (philosophy) , inverse trigonometric functions , stability (learning theory) , mathematics , term (time) , pid controller , control theory (sociology) , function (biology) , computer science , mathematical analysis , control (management) , physics , engineering , control engineering , temperature control , philosophy , epistemology , quantum mechanics , machine learning , artificial intelligence , evolutionary biology , biology
Ultimate gains and ultimate periods have long been used to tune PI/PID controllers since the Ziegler‐Nichols tuning. Recently, very simple analytic equations for ultimate gains and ultimate periods by approximating the arctangent function have been presented, which can be used to obtain simple tuning rules. Here, by applying the Routh stability method and phase‐optimal approximations of the time delay term, we present analytic expressions of ultimate parameters that are as simple as the existing ones, showing better accuracy.