Parametric and Nonparametric PID Controller Tuning Method for Integrating Processes Based on Magnitude Optimum

Abstract

Integrating systems are frequently encountered in power plants, paper-production plants, storage tanks, distillation columns, chemical reactors, and the oil industry. Due to the open-loop instability that leads to an unbounded output from a bounded input, the efficient control of integrating systems remains a challenging task. Many researchers have addressed the control of integrating processes: Some solutions are based on a single closed-loop controller, while others employ more complex control structures. However, it is difficult to find one solution requiring only a simple tuning procedure for the process. This is the advantage of the magnitude optimum multiple integration (MOMI) tuning method. In this paper, we propose an extension of the MOMI tuning method for integrating processes, controlled with a two-degrees-of-freedom (2-DOF) proportional–integral–derivative (PID) controller. This extension allows for calculations of the controller parameters from either time domain measurements or from a process transfer function of an arbitrary order with a time-delay, when both approaches are exactly equivalent. The user has the option to emphasise disturbance-rejection or tracking with the reference weighting factor b or apply two different reference filters for the best overall response. The proposed extension was also compared to other tuning methods for the control of integrating processes and tested on a charge-amplifier drift-compensation system. All closed-loop responses were relatively fast and stable, all in accordance with the magnitude optimum criteria.

A Simple Analytical Method for Estimation of the Five-Parameter Model: Second-Order with Zero Plus Time Delay

“…On the other hand, the characteristic areas can also be obtained from the arbitrary process transfer function with a time delay (frequency-domain approach). Both approaches are equivalent [42,43].…”

“…As can be seen above, the characteristic areas can be calculated directly and analytically from the process transfer function [42,43].…”

“…In practice, the computation of Expressions ( 4) can be terminated when the process has settled down. Note that the Expressions (4) can also be computed recursively, and that the characteristic areas can be obtained from any change of the process steady-state [42,43]. A more detailed procedure, including some practical guidelines for computing characteristic areas from the process input and output time signals, even in noisy environments, is given in [45].…”

“…The characteristic areas can be computed from any change of the process steadystate in the closed-loop or open-loop configuration (time-domain approach). Moreover, it has been shown in [41,42] that the characteristic areas can also be obtained from integrating processes, and that the characteristic areas can be easily used for model reduction.…”

“…On the other hand, the same characteristic areas can also be obtained from any process transfer function with a time delay (frequency-domain approach) [43], and conversely, SOPDT (four-parameter model) can be calculated analytically from the moments or characteristic areas, as shown in [28,44]. However, since the SOPDT model does not contain a zero, it is not suitable for certain applications; see, for example, a calculation of higher-order reference filter parameters in [42].…”