For First Order Plus Dead Time Research Articles

Event-Based Implementation of Fractional Order IMC Controllers for Simple FOPDT Processes

Fractional order calculus has been used to generalize various types of controllers, including internal model controllers (IMC). The focus of this manuscript is towards fractional order IMCs for first order plus dead-time (FOPDT) processes, including delay and lag dominant ones. The design is novel at it is based on a new approximation approach, the non-rational transfer function method. This allows for a more accurate approximation of the process dead-time and ensures an improved closed loop response. The main problem with fractional order controllers is concerned with their implementation as higher order transfer functions. In cases where central processing unit CPU, bandwidth allocation, and energy usage are limited, resources need to be efficiently managed. This can be achieved using an event-based implementation. The novelty of this paper resides in such an event-based algorithm for fractional order IMC (FO-IMC) controllers. Numerical results are provided for lag and delay dominant FOPDT processes. For comparison purposes, an integer order PI controller, tuned according to the same performance specifications as the FO-IMC, is also implemented as an event-based control strategy. The numerical results show that the proposed event-based implementation for the FO-IMC controller is suitable and provides for a smaller computational effort, thus being more suitable in various industrial applications.

Discrete-Time First-Order Plus Dead-Time Model-Reference Trade-off PID Control Design

The present study proposes a novel proportional-integral-derivative (PID) control design method in discrete time. In the proposed method, a PID controller is designed for first-order plus dead-time (FOPDT) systems so that the prescribed robust stability is accomplished. Furthermore, based on the control performance, the relationship between the servo performance and the regulator performance is a trade-off relationship, and hence, these items are not simultaneously optimized. Therefore, the proposed method provides an optimal design method of the PID parameters for optimizing the reference tracking and disturbance rejection performances, respectively. Even though such a trade-off design method is being actively researched for continuous time, few studies have examined such a method for discrete time. In conventional discrete time methods, the robust stability is not directly prescribed or available systems are restricted to systems for which the dead-time in the continuous time model is an integer multiple of the sampling interval. On the other hand, in the proposed method, even when a discrete time zero is included in the controlled plant, the optimal PID parameters are obtained. In the present study, as well as the other plant parameters, a zero in the FOPDT system is newly normalized, and then, a universal design method is obtained for the FOPDT system with the zero. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

Optimal Robust PID Control for First- and Second-Order Plus Dead-Time Processes

The present study proposes a new design method for a proportional-integral-derivative (PID) control system for first-order plus dead-time (FOPDT) and over-damped second-order plus dead-time (SOPDT) systems. What is presented is an optimal PID tuning constrained to robust stability. The optimal tuning is defined for each one of the two operation modes the control system may operate in: servo (reference tracking) and regulation (disturbance rejection). The optimization problem is stated for a normalized second-order plant that unifies FOPDT and SOPDT process models. Different robustness levels are considered and for each one of them, the set of optimal controller parameters is obtained. In a second step, suitable formulas are found that provide continuous values for the controller parameters. Finally, the effectiveness of the proposed method is confirmed through numerical examples.

An Optimal Robust Tuning Method for First Order plus Dead Time Systems with Parameter Uncertainty

This paper presents a simple PI tuning method for first order plus dead time (FOPDT) systems. Firstly, stabilizing PI parameters region is found for these kinds of systems. Then, optimal point of this region is selected using the Big Bang Big Crunch optimization algorithm and this work is extended to FOPDT systems that contain parameter uncertainty. After the optimizations done for a wide range of systems, an optimal and robust PI tuning method is proposed with a curve fitting of the obtained optimization data. Lastly, the proposed method is compared with other PI tuning methods for their performance and robustness.

Maximum Sensitivity Based Robust Tuning for Two-Degree-of-Freedom Proportional−Integral Controllers

A tuning method for two-degree-of-freedom (2-DoF) proportional−integral (PI) controllers for first-order-plus-dead-time (FOPDT) models is presented. It allows the designer to deal with the closed-loop control system performance−robustness trade-off specifying the lowest robustness level allowed by selecting a maximum sensitivity in the 1.4−2.0 range. In addition, a smooth performance is obtained by forcing the regulatory and servo-control closed-loop transfer functions to perform as close as possible to a target nonoscillatory dynamics. Controller tuning rules are provided for FOPDT models with normalized dead-times from 0.1 to 2.0. Comparative examples show the effectiveness of the proposed tuning method.