Synthesis of robust PID controllers with complete information on pre-specifications for the FOPTD systems

Abstract

Given a first order plus time delay (FOPTD) model, all stabilizing PID controllers can be found in terms of a 3D plot of three gains. Given specifications such as gain crossover frequency and phase margin, the three PID gains are not unique. To make three gains unique, this paper adds an additional specification called “flat phase” condition, that is, the phase slope at the gain crossover frequency is zero, guaranteeing robustness to loop gain variations. This paper offers an analytical synthesis method for obtaining unique PID gains. Furthermore, a procedure is suggested to find out all feasible specifications. With a scaling idea, the FOPTD model can be reduced to having only one plant parameter (delay to time constant ratio), therefore, a lookup table can be constructed for practical design scenario: given the delay to time constant ratio, the feasible ranges of specifications can be determined; given (feasible) specifications, unique PID parameters can be retrieved from the table, with “flat phase” property embedded. This paper serves as an example to completely solve the robust PID synthesis problem for FOPTD models widely used in process industry.