闭环辨识与PID整定：混合Box-Jenkins结构的应用

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"混合Box-Jenkins结构的系统闭环辨识及其在PID整定中的应用" 本文是一篇研究论文，主要探讨了混合Box-Jenkins模型在闭环系统识别以及PID控制器整定中的应用。Box-Jenkins模型是一种广泛用于时间序列分析的统计模型，它包括自回归（AR）、滑动平均（MA）和移动自回归（ARIMA）等成分。在本文中，研究者提出了一种新的方法，即在混合Box-Jenkins结构下进行闭环系统识别。首先，文章介绍了使用混合Box-Jenkins模型对闭环系统的识别过程。这种模型结合了连续时间和离散时间的特性，可以更好地模拟实际工程系统中的动态行为。特别是，该方法利用了仪器变量算法来从预滤波的离散时间数据中识别出Box-Jenkins形式的连续时间传递函数模型。在这个过程中，过程模型被视为一个连续时间的传递函数，而噪声则被表示为离散时间的ARMA过程。接着，文章引入了一种新颖的惩罚最大似然估计方法来估计离散时间ARMA模型的参数。这种方法有助于在存在噪声和不确定性的情况下，提高模型的识别精度。通过这种方式，可以更准确地理解系统的动态特性，这对于后续的控制策略设计至关重要。然后，文章重点讨论了如何将识别结果应用于基于内模控制（IMC）的PID控制器的整定。PID控制器是工业中最常用的反馈控制策略，其性能往往取决于控制器参数的设定。通过闭环系统识别得到的模型，可以更好地理解系统的动态响应，从而为PID控制器提供更精确的参数整定依据。这有助于改善系统的稳定性和控制性能，减少调节时间，并降低超调。总结来说，这篇论文贡献了以下几点： 1. 提出了一种混合Box-Jenkins结构的闭环系统识别方法，结合了连续时间与离散时间模型的优点。 2. 引入了仪器变量算法和惩罚最大似然估计，提高了在噪声环境下的模型识别准确性。 3. 展示了识别结果如何应用于PID控制器的参数整定，为实际工程问题提供了理论支持。关键词：混合Box-Jenkins模型、ARMA模型、仪器变量、闭环识别、PID调优这篇研究对于理解和优化具有复杂动态特性的闭环控制系统具有重要的理论和实践价值，对于工业界和学术界的控制系统设计人员都具有参考意义。

Closed-loop identiﬁcation of systems using hybrid Box–Jenkins structure

and its application to PID tuning

☆

Quanshan Li

1,2

,DaziLi

⁎

,LiulinCao

Institute of Automation, Beijing University of Chemical Technology, Beijing 100029, China

Beijing Century Robust Technology Co. Ltd., Beijing 100020, China

abstractarticle info

Article history:

Received 25 May 2015

Received in revised form 5 June 2015

Accepted 25 June 2015

Available online 29 August 2015

Keywords:

Hybrid Box–Jenkins models

ARMA models

Instrumental variable

Closed-loop identiﬁcation

PID tuning

The paper describes a closed- loop system identiﬁcation procedure for hybrid continuou s-time Box–Jenkins

models and demonstrates how it can be used for IMC based PID controller tuning. An instrumental variable algo-

rithm is used to identify hybrid continuous-time transfer function models of the Box–Jenkins form from discrete-

time preﬁltered data, where the process model is a continuous-time transfer function, while the noise is repre-

sented as a discrete-time ARMA process. A novel penalized maximum-likelihood approach is used for estimating

the discrete-time ARMA process and a circulatory noise elimination identiﬁcation method is employed to esti-

mate process model. The input–output data of a process are affected by additive circulatory noise in a closed-

loop. 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 estima-

tion 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 IMC based ﬂow controller

and a practical application demonstrates the applicability of the algorithm.

1. Introduction

Process models play an important role in design and implementations

of several modern or traditional control theories. The model of a process

to be controlled is essential in controller parameters tuning, model pre-

dictive control (MPC) and other model based control approaches [1–3].

The modeling and identiﬁcati on of a system have been a subject of atten-

tion to many researchers. It is well known that most physical systems are

continuous-time (CT) in nature, and can conveniently be described by CT

models. These models are attractive because some physical interpretation

may be attached to their components, more appealing to engineers and

system operators to understand their behaviors.

Some identiﬁcation algorithms are only optimal in the case of addi-

tive white noise. However, in practical situations the additive noise may

not be nice white. It is likely that the noise will be a colored noise

process. In this situation, it is possible to use a hybrid modeling approach,

where an auto-regressive and moving average model (ARMA) for the

noise part is estimated and used in the preﬁltering operation, while the

plant model would be in continuous time, as suggested in [4].

There are several approaches for ARMA process identiﬁcation. In the

Gaussian case, the prediction error method (PEM) is an efﬁcient estima-

tor for ARMA process and it has been proven that optimal instrument

variable (IV) method has the same asymptotic accuracy as the PEM [5,

6]. Gaussian maximum likelihood estimation (MLE) for causal and in-

vertible ARMA time series models has been demonstrated theoretically

to be consistent and asymptotically normal [7].

Process model identiﬁcation is the procedure of developing models

from experimental data. A good choice for model identiﬁcation is apply-

ing input–output data from open-loop tests. In this situation, the noise

sequence is not correlated to the input sequence. Model estimates can

be directly developed without problems of inconsistency and bias [8].

For many industrial processes, production restrictions and safety are

often strong reasons for not allowing identiﬁ cation experiments in

open-loop. In such cases, exper imental data can only be obtained

under closed-loop conditions [9,10]. The main difﬁculty in closed-loop

identiﬁcation is due to the correlation between the disturbances and

the control signal induced by the loop [11]. Thus, most of the structures

that are effective for open-loop identiﬁcation result in models that are

biased and not consistent in parameters. Several alternatives are avail-

able to cope with this problem [12,13]. Although these methods have

given effective identiﬁcation results, seldom methods make fully use

of sampling data of a loop for closed-loop identiﬁcation.

CT model identiﬁcation has some difﬁculties because of the presence

of the derivative operators associated with the input and output signals.

Chinese Journal of Chemical Engineering 23 (2015) 1997–2004

☆

Supported by the National Natural Science Foundation of China (61573052, 61174128).

⁎ Corresponding author.

E-mail address: lidz@mail.buct.edu.cn (D. Li).

http://dx.doi.org/10.1016/j.cjche.2015.08.026

Contents lists available at ScienceDirect

Chinese Journal of Chemical Engineering

journal homepage: www.elsevier.com/locate/CJChE

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