Premium
Multiparameter adaptive process control via constrained objective functions
Author(s) -
Ryan Philip J.,
Crandall Edward D.
Publication year - 1971
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690170218
Subject(s) - control theory (sociology) , algebraic equation , exothermic reaction , controller (irrigation) , mathematics , algebraic number , adaptive control , function (biology) , process (computing) , pid controller , minification , mathematical optimization , computer science , nonlinear system , temperature control , engineering , control engineering , control (management) , mathematical analysis , chemistry , physics , artificial intelligence , evolutionary biology , agronomy , biology , operating system , organic chemistry , quantum mechanics
Abstract A method has been developed for applying classical minimization techniques to forms of algebraic performance indices for use in optimal adaptive control systems. Essentially, the derivative of a general objective function is constrained to be equal to the integrand of a desired integral performance index. This generates a set of linear algebraic equations, the solution of which results in an algebraic objective function which is explicit in the system parameters. Derivatives of this function can be taken with respect to the controllable parameters, set equal to zero, and solved for the settings which minimize the performance index over time. Alternatively, the function itself may be searched for its minimum on the controllable parameters. The method has been applied to a stirred tank chemical reactor with an exothermic first‐order reaction in which heat removal was accomplished by cooling coils. The cooling water flow rate was controlled by a proportional‐plus‐integral controller and by a three‐mode controller. The adaptive control system adjusted the controller settings periodically. The plant, which was third‐order, was controlled to a second‐order dynamic reference model. The responses to both initial offsets (start‐up problem) and disturbances in system parameters were investigated. In all cases, the adaptive control system performance was markedly superior to that for the unadapted, ordinary feedback control system.