A one-step tuning method for PID controllers with robustness specification using plant step-response data

This paper presents a novel method for proportional-integral-derivative (PID) controller tuning directly using the step response data of the process without resorting to a process model. The required process data are collected from a one-shot step test that can be conducted under either closed-loop or open-loop conditions. The proposed method derives the PID parameters so that the resulting control system behaves as closely as possible to the prescribed reference model. Two structures of the reference model are considered for general design and improved disturbance rejection, respectively. A simple one-dimensional optimization problem is formulated to determine an appropriate reference model for the controlled process. Moreover, the proposed PID tuning method includes a robustness specification based on the maximum peak of sensitivity function that enables the user to explicitly address the trade-off between performance and robustness. Simulation examples are provided to illustrate the superiority of the proposed method over existing (model-based) tuning methods.     

OPTIMALITY CHARACTERISTICS OF PI/PID CONTROLLERS: A COMBINED MIN-MAX/ISE INTERPRETATION

This communication addresses the tuning of PI and PID controllers on the basis of the IMC approach. The tuning is based upon a first order plus time delay (FOPTD) model and aims to achieve a step response specification. Through analysis it has been found that by using the IMC approach we get a PI or a PID depending on the rational approximation used for the time delay term. This article raises the question that the use of a PID instead of a PI controller should be based on another reason more related to the control objectives rather than the use of a better approximation for the time delay. An alternative tuning is presented here, from within the IMC formulation, based on a min-max optimization. From the tuning rule provided by this approach the optimum settings from an integral squared error criterion point of view are derived. The optimal controller results in being a PI controller. From this optimal controller as the starting point, the introduction of the derivative action can be seen as a detuning procedure that can increase the robustness of the controller. This approach provides further insight into the tuning of PI and PID controllers giving the (alternative) parameters a precise engineering meaning.     

General rules for optimal tuning the PIλDµ controllers with application to first‐order plus time delay processes

For two main reasons optimal tuning the PI^λD^µ controllers is a challenging task: First, the search space is very large in dealing with such controllers, and second, there is not any generally applicable method for stability testing of the linear feedback systems containing both time delay and fractional‐order controllers. Hence, easy‐to‐use and effective rules for optimal tuning such controllers are highly demanded. In this paper, explicit formulas for optimal tuning the parameters of the PI^λD^µ controller, when it is applied in series with a first‐order plus time‐delay process in a standard output‐feedback system, are proposed. © 2012 Canadian Society for Chemical Engineering     

基于遗传退火策略的PID整定研究

有机结合具有概率突跳特性的模拟退火和群体并行搜索的遗传算法的遗传退火策略是一类有效的组合优化算法，通过对算法操作和参数的合适设置，本文将其推广到PID控制器的整定。基于典型问题的仿真结果验证了混合算法的有效性，其性能大大优于单一遗传算法和传统方法。     

An automatic pid controller tuning method by frequency response techniques

An alternative Ziegler-Nichols (1942) controller tuning technique was proposed in this study. Under the proportional control of a single-loop control system, an arbitrary pulse testing in the set point was introduced to the system. The ultimate frequency and gain could both be directly calculated from the transients by frequency response techniques without any trial and error procedures. PID controller settings were thus obtained according to the Ziegler and Nichols' rules. Furthermore, this technique was extended to the tuning of a cascade control system. A procedure for simultaneously tuning the primary and secondary controllers with both loops in proportional control from a single pulse testing also is presented.     

On‐line Tuning of Model Predictive Controllers Using Fuzzy Logic

This paper addresses the problem of tuning model predictive controllers for good performance. An automatic online tuning strategy is developed to adjust the prediction horizon, P, the diagonal elements of the input weight matrix, Λ, and the diagonal elements of the output weight matrix, Γ. The control horizon is left constant because its relative value with respect to P is more important. The tuning algorithm is based on the fuzzy logic concepts. Predefined fuzzy rules that formulate the general tuning guidelines available in the literature and the performance violation measure in the form of fuzzy sets determine the new tuning parameter values. Therefore, the tuning algorithm is cast as a simple and straightforward mechanism with modest computational requirements. This feature makes it more appealing for online implementation. The effectiveness of the proposed tuning method is tested through simulated implementation on a binary distillation column example and on a non linear CSTR example. The result of the simulations revealed the success of such a method.     

TUNING PID CONTROLLER FOR OPEN-LOOP UNSTABLE PROCESSES WITH TIME DELAY

A calculation method of PID controller tuning for the first- and the second-order open-loop unstable process models with time delay is presented in this study. Optimum PID controller tuning data based on the models and minimum IAE criterion were obtained via Powell searching technique, and these data were then empirically correlated into several multiple-regression equations by a least-squares method. Thus PID controller tuning based on the models can easily be obtained by the calculation of these correlated equations. Simulation with a reset-feedback PID control algorithm has demonstrated that the proposed tuning method based on the first-order model can provide better results than the latest studies. In addition, simulation has also unveiled that tuning results based on the second-order models are superior to the first-order model for a higher-order process.     

ADAPTIVE DOMINANT POLE DESIGN OF PID CONTROLLERS BASED ON A SINGLE CLOSED-LOOP TEST

A novel method, based on a single experimental test under proportional feedback, has been developed to tune PID controllers on-line. The tuning method involving an identification scheme and a dominant pole design technique is ideal for automatic tuning. It also provides an adaptive algorithm to adjust the controller settings to achieve the desirable control performance satisfying the prescribed decay ratio and stability margin. A simulation study demonstrates that the method is valid for processes with large dead-times as well as open-loop underdamped processes.     

基于相角裕度优化的PID参数整定方法研究

针对复杂工业过程的大滞后、参数不确定等特性,提出一种新的鲁棒PID控制器参数整定方法.该方法通过使系统开环传递函数的相角裕度最大化,来求取各个PID参数.由于该方法的稳定裕量是通过取明确依赖于频率的模型来获得,从而避免了陷入保守性.仿真结果表明,使用本文提出的控制器整定方法,在命令输入发生阶跃变化时,控制系统都有很好的动态响应,同时在系统参数发生变化或存在未建模动态时,也能保证系统的稳定鲁棒性.     

PID controller design for integrating processes with time delay

A simple IMC-PID controller design technique is proposed on the basis of the IMC principle for two representative integrating processes with time delay. Further, it is extended to integrating processes with negative and positive zero as well. The proposed PID controller design method is mainly focused on the disturbance rejection, which causes the overshoot in the setpoint response, and a two-degree-of-freedom (2DOF) control structure is used to eliminate this overshoot. The simulation results show the superiority of the proposed tuning rule over other existing methods, when the controller is tuned to have the same robustness level by evaluating the peak of the maximum sensitivity (Ms). The closed loop time constant (λ) has only one user-defined tuning parameter in the proposed method. A guideline is suggested for the selection of λ for different robustness levels by evaluating the value of Ms over a wide range of θ/τ ratios.     

A SIMPLE METHOD FOR TUNING CASCADE CONTROL SYSTEMS

A simple method for tuning controllers in a cascade system is presented, In this method, all the relations that facilitate the tuning procedures are well prepared in terms of figures or simple equations. Using these figures and equations, the controller tuning for different configurations of cascade systems becomes easy and straightforward when process models are available. On the other hand, when process models are not available, a simple method that uses one single run of step input experiment to develop such models is proposed. Based on these developments in the controller tuning and process models, an autotuning system that uses relay feedback is presented. Unlike the existing autotuning systems, this proposed system conducts identification and controller tuning in a decoupled manner. As a result, no excessive trial- and-error efforts for modeling and tuning are required. Simulation results show the potential usage of such a method, It is interested to see that the resulting systems have almost compatible responses to those systems which have been designed optimally in one way or another as reported in the literature. It is not, however, the purpose of this article to emphasize on obtaining superior performance to all other existing methods, but to emphasize on its effectiveness and simplicity for application.     

New results on VRFT design of PID controller

Virtual reference feedback tuning (VRFT) design method can be applied to determine the parameters of a PID controller from the available process input and output data without resorting to the identification of a process model. Although it is an attractive alternative to the popular model-based controller design methods, the existing results are restricted to the linear systems. In this paper, an adaptive VRFT design method with application to the adaptive PID controller design is proposed. In addition, the relationship between the VRFT and IMC designs is analyzed as well. Simulation results are presented to illustrate the advantage of the adaptive VRFT design over the conventional VRFT design.     

A simple adaptive control strategy for temperature trajectory tracking in batch processes

In this paper, a simple adaptive control strategy is suggested for temperature tracking control of batch processes. A nonlinear controller, which is in structure very simple and consists of a single parameter, is proposed. To enable this controller to control a batch process adaptively, a simple parameter tuning algorithm is derived based on the Lyapunov stability theorem. The proposed adaptive control scheme is directly operational, which does not depend on process model and the only a priori process information required is the system response direction. To demonstrate the effectiveness and applicability of the proposed scheme, illustrative examples are provided. Extensive simulation results reveal that the proposed adaptive control strategy appears to be a simple and effective approach to batch process control, which provides robust control despite the wide range of operating conditions and nonlinear dynamics of the system.     

Multiloop PI/PID control system improvement via adjusting the dominant pole or the peak amplitude ratio

Multiloop control systems designed by simple methods such as the biggest log-modulus tuning may be too sluggish or too oscillatory. Sluggish responses are due to dominant poles near the origin, and oscillatory responses are due to dominant poles with large imaginary parts or large peak amplitude ratios in the closed-loop systems. A method that adjusts such dominant poles and amplitude ratios through the continuation method is proposed. Several examples show that the improved multiloop control system can be obtained without resorting to complicated design methods.     

Half order plus time delay (HOPTD) models to tune PI controllers

Methods based on the first‐order plus time delay (FOPTD) model are very popular for tuning proportional‐integral (PI) controllers. The FOPTD model‐based methods are simple and their utility has been proved with many successful applications to a wide range of processes in practice. However, even for some overdamped processes where the FOPTD model seems to be applied successfully, these empirical FOPTD model‐based methods can fail to provide stable tuning results. To remove these drawbacks, a PI controller tuning method based on half‐order plus time delay (HOPTD) model is proposed. Because FOPTD model‐based methods can be applied to higher order processes, the proposed HOPTD model‐based method can be applied to higher order processes as well. It does not require any additional process information compared to the FOPTD model‐based method and hence can be used for overdamped processes in practice, complementing the traditional FOPTD model‐based methods. © 2016 American Institute of Chemical Engineers AIChE J, 63: 601–609, 2017     

Frequency domain tuning approach for adaptive feedforward control using lead–lag compensators

The tuning of lead–lag compensators to be used as feedforward controllers for measured disturbances is performed in the frequency domain. The identification of process G_u and disturbance dynamics G_d uses extended recursive least squares, and the frequency responses are calculated from the least squares coefficients. A lead–lag compensator G_ll is designed which minimises the function $G_{{\rm ll}} (j\omega ) + (G_{{\rm d}} (j\omega ))/(G_{{\rm u}} (j\omega ))$ over a finite number of frequencies, using the Nelder–Mead simplex method. The effectiveness of the frequency domain tuning strategy is compared by simulation to established tuning rules for first‐order plus delay processes. The tuning method is experimentally verified on a pilot scale methanol–water distillation column. © 2011 Canadian Society for Chemical Engineering     

Closed-loop identification of systems using hybrid Box-Jenkins structure and its application to PID tuning

The paper describes a closed-loop system identification procedure for hybrid continuous-time Box-Jenkins models and demonstrates howit can be used for IMC based PID controller tuning. An instrumental variable algorithmis used to identify hybrid continuous-time transfer function models of the Box-Jenkins formfromdiscretetime prefiltered data, where the process model is a continuous-time transfer function, while the noise is represented as a discrete-time ARMA process. A novel penalizedmaximum-likelihood approach is used for estimating the discrete-time ARMA process and a circulatory noise elimination identification method is employed to estimate process model. The input-output data of a process are affected by additive circulatory noise in a closedloop. The noise-free input-output data of the process are obtained using the proposed method by removing these circulatory noise components. The process model can be achieved by using instrumental variable estimation method with prefiltered noise-free input-output data. The performance of the proposed hybrid parameter estimation scheme is evaluated by the Monte Carlo simulation analysis. Simulation results illustrate the efficacy of the proposed procedure. The methodology has been successfully applied in tuning of IMCbased flowcontroller and a practical application demonstrates the applicability of the algorithm.     

A Comparison of PID Controller Tuning Methods

The derivative mode is often omitted in PID control strategies because it proves difficult to arrive by trial‐and‐error at a set of constants which meet plant requirements. The primary objective of this paper was to evaluate several model‐based PID tuning methods. For lag‐dominant processes, it was recommended that the SIMC algorithm first be employed to determine whether satisfactory performance can be obtained with PI control. If it cannot, then derivative action should be introduced using the DS‐d technique. For delay‐dominant systems, IMC tuning is preferred. It was observed that when configured with the same derivative filter factor, the series form of the PID controller produces smoother valve adjustments than the parallel version, at the expense of a slight decrease in best achievable performance. Increasing this parameter improves the control effort but limits achievable performance.     

PID控制器设计与参数整定方法综述

简要介绍了PID控制器的发展历程,综述PID控制器的设计与参数整定方法及其近期研究成果,并讨论了继电反馈方法的改进与扩展方法。通过分析PID控制器面临的问题与挑战,对PID控制器的发展进行了展望。     

基于幅值最优化的二自由度PID控制器参数自整定研究

通过两次继电反馈，测得被控对象两个关键信息点的频率特性，从而辨识得到二阶纯滞后模型；然后引入一种二自由度PID控制器结构，根据幅值最优化原理整定PID控制器的参数。仿真实验表明该整定方法使闭环系统具有很好的稳定性和鲁棒性。