Fractional order integrator for the relay feedback identification of a process Nyquist point in the third quadrant

A fractional order integrator can be used for the relay feedback identification of a process Nyquist point in the third quadrant, and to implement the fractional order integrator, it is often approximated by integer order systems. Here, instead of the usual rational transfer function approximation of the fractional order integrator in the relay feedback system, a simple analytic method which utilizes the on-off characteristics of relay output is proposed. Simulation results show that the proposed method can find process Nyquist points in the third quadrant without worrying about the approximation errors and ranges of the fraction order integrator.     

Relay feedback identification for processes under drift and noisy environments

Relay feedback identification methods are widely used to find the process ultimate information and tune proportional‐integral‐derivative controllers. The conventional relay feedback method has several disadvantages, which include poor estimates of the process ultimate information for low‐order processes, chattering of relay for noisy environments, and asymmetric relay responses for constant biases or slow drifts in the process outputs. Methods to mitigate each of the above disadvantages are available. However, a systematic method to treat all of them has not been studied yet. Here, simple relay feedback methods that resolve these problems by introducing band‐pass filters in the feedback loop are proposed. The high‐pass filter part in band‐pass filter removes a constant bias or low frequency drift, and the low‐pass filter part removes high frequency noise and high‐order harmonic terms in the relay feedback oscillation, resulting better estimates of the process ultimate information. Because filters used for the proposed methods are able to reject constant biases, the process steady state gains can be estimated without disturbing the relay feedback oscillations and first order plus time delay (FOPTD) models can be obtained by combining the process steady state gains with the relay oscillation information. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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.     

Process operation near an unstable steady state using nonlinear feedback control

Process performance is sometimes best at an unstable steady state. Following a new control philosophy, stable operation near an unstable steady state can be realized using a relay with hysteresis as a feedback controller. Properly designed, this control scheme produces a stable, small amplitude oscillation in the neighborhood of the desired state. Approximate solutions for such oscillations can be obtained by Tsypkin's method or Describing Function analysis. Comparisons of these solutions with exact simulation results for an example reveal that replacing the relay with the describing function is a major source of error in the approximate analysis.     

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。     

Magic sampling—a digital sampling strategy that discriminates against mains interference (noise)

Mains interference is a problem because its fundamental frequency (50 Hz in Australia and the U.K., 60 Hz in the U.S.A.) lies in the centre of the frequency range within which electrochemical phenomena are usually perturbed (10⁻³Hz to 10⁵Hz), and, therefore, once it has entered a measurement it is virtually impossible to remove it without distorting the true signal in some way. In the present work we first review the background to this problem, and then propose a digital sampling strategy that discriminates against mains interference even when the interference is harmonically distorted. The strategy consists of three parts: first, a digital presampling filter to attenuate high frequency harmonics in the interference; second, a ‘magic’ sampling rate to manoeuvre all the surviving harmonics to the Nyquist frequency; and third, a postsampling digital filter to block everything at the Nyquist frequency whilst allowing the true signal to pass. Since the only restrictions on this strategy are minor (the signal to be measured should be continuous and have no frequency components greater than f_mains) it should find widespread application in the digital acquisition of electrochemical data.     

Impedance spectroscopy analysis of glucose electro-oxidation on Ni-modified glassy carbon electrode

The electro-oxidation of glucose on nickel-modified glassy carbon electrode (GC/Ni) in a 1 M NaOH solution at different concentration of glucose was studied by the method of ac-impedance spectroscopy. In low concentration of glucose (<7 mM) two semicircles in the first quadrant of a Nyquist diagram were observed corresponding to charge transfer resistance and adsorption of intermediates. In higher concentration of glucose (>10 mM) negative resistance is observed in impedance plots as signified by semicircles terminating in the third quadrant. The impedance data in high concentration of glucose show different behavior at different applied anodic potential. The influence of the electrode potential on impedance pattern in high concentration of glucose is studied and a mathematical model was put forward to quantitative account for the impedance behavior of glucose oxidation. At potentials higher than 0.525 V/Ag-AgCl, a pseudoinductive behavior is observed but at higher than 0.4 V/Ag-AgCl, impedance patterns terminate in the second and third quadrants. The conditions required for this behavior are delineated with the use of the impedance model.     

AUTOMATIC TUNING OF SYSTEMS WITH ONE OR TWO UNSTABLE POLES

Stabilizability and identification of systems with one or two unstable poles is addressed. Two limit points of conditional stability are characterized using closed-loop dynamics with a relay and a novel nonlinear element. An algorithm is developed to analyze information from the resultant stable limit cycles in the process input and output. An easily tuned cascade PID control structure is then proposed to stabilize the system and achieve desirable performance. The proposed autotuning technique is tested with good results on a wide variety of unstable systems.     

基于常数对角优势补偿阵的多变量控制系统逆Nyquist阵列设计

化工过程中的多变量系统变量之间往往存在耦合作用,在控制系统设计时一般将传递函数阵对角优势化,对角优势化后按多个单变量系统进行设计。由于传递函数逆阵的对角优势化更容易实现,本文采用伪对角化方法设计常数对角优势补偿阵实现传递函数逆阵的对角优势化,在一个或多个频率点上通过使开环传递函数逆阵每行的非对角项元素模平方之和最小,实现对角优势。然后,利用逆Nyquist阵列设计法对补偿后的系统设计控制器,基于逆Nyquist稳定判据,通过绘制优势度曲线和Gershgorin带判断系统的优势程度,根据Gershgorin带选定反馈矩阵的参数范围,按照单变量控制系统的方法设计动态补偿器,使系统满足动态控制品质的要求。最后通过3个示例说明本文的设计方法简便,且具有良好的控制性能。     

Improved Relay Auto-Tuning of PID Controllers for Unstable SOPTD Systems

In the present work an improved analysis of the relay auto-tuning method is proposed to calculate the maximum value of the controller gain by considering the higher-order harmonics. The reported Fourier series analysis for a first-order plus time delay (FOPTD) unstable system (Vivek and Chidambaram, 2005 Vivek, S., and Chidambaram, M. (2005). An improved relay autotuning of PID controllers for unstable FOPTD systems, Comput. Chem. Eng., 29, 2060–2068[Crossref], [Web of Science ®] , [Google Scholar]) is modified to an unstable second-order plus time delay system (SOPTD). Improved results in the ultimate gain values of the controller are obtained. The effectiveness of the method is demonstrated by simulation on three SOPTD transfer function models. The different models considered are: (i) a system with two unstable poles and a negative zero; (ii) a system with one stable and one unstable pole; and (iii) a system with two unstable poles and a positive zero. A simple method is also proposed to calculate the minimum value of the controller gain. The proposed method gives enhanced closed-loop performances in all the cases. The method is also applied by simulation on the nonlinear model equations of an unstable bioreactor.     

基于PID对角优势补偿阵的过程多变量控制系统设计

化工过程一般为多变量系统,输入输出变量之间往往存在耦合作用,常规分散PID控制系统难以保证控制质量。为了削弱多变量系统的耦合作用,基于对角优势的设计准则,通过在若干频率点加权优化,设计PID动态预补偿阵。然后利用正Nyquist阵列设计法对补偿后的系统设计控制器,基于对角优势系统的Nyquist稳定判据,通过绘制优势度曲线和Gershgorin带判断系统的优势程度,初步确定反馈矩阵的稳定参数范围,再按照单输入单输出系统设计动态补偿器,使得系统满足动态控制品质要求。最后通过示例说明,该方法设计的集中控制系统与分散控制相比,控制性能具有一定的优势,且方法简便,容易实现。     

Assessment of controller performance: a relay feedback approach

Assessment of control loop performance is one of the important tasks to be carried out in a plant, regardless of the control strategy. The present work utilizes the shape information from single relay feedback test to assess the performance of a feedback system. The process considered is a typical first-order plus dead time process and the controller used is PI type of controller. An ideal relay is introduced in the feedback loop before the controller. The shape of the relay output characterizes the performance of the controller. The mismatch in the integral time can also be observed from the shape. Based on the shape information, analytical expressions for relay feedback responses are derived and straightforward procedures are evolved to assess the performance of the controller. The proposed scheme assesses the controller performance and computes the new tuning parameters, in case retuning of the controller is necessary. The robustness of the method is also tested for second-order plus dead time as well as for higher order systems. More importantly the present approach employs only one relay test for (1) assessment and (2) retuning of the controller. It provides a reliable way that is compatible even to a non-expert operator to assess the controller performance.     

Tuning PI and fractional order PI controllers with an additional fractional order Pole

The PI controller with an additional pole (PI?+?P) already has been proposed to decrease the noise effect on the control signal. In this paper, a fractional order pole is employed to increase the PI?+?P controller performance. The fractional order is obtained by adjusting the Nyquist plot slope in gain crossover frequency. This condition as well as gain crossover frequency and phase margin specifications are utilized to design the PI controller augmented with an additional fractional order pole (PI?+?FO[P]). To design these two controllers, a first-order plus delay time (FOPDT) model is utilized. For plants that could not be described by this model, its fractional order version (FFOPDT) could be utilized. In this case, a FOPI?+?FO[P] controller is obtained that could improve the transient response of the closed-loop system. The numerical simulations accomplished on various plant models (including chemical plants) demonstrate the effectiveness of the proposed controller comparing with the PI?+?P, PID, FOPI, and fractional order proportional-integral-derivative controllers.     

基于谱熵的自适应广义S变换时频滤波器设计

将信息熵引入到广义S变换时频滤波中,提出一种基于谱熵的自适应广义s变换时频滤波器设计方法。计算信号广义s变换的时频谱,将时频谱各时间点的频率区间划分成若干个小区间,计算各区间时频谱熵,以时频谱熵最大区间的时频谱的平均值作为阅值,以此来衡量信号的杂乱程度。若该时间点上的时频谱值大于闻值,则将该点时频谱值清零。采用广义s逆变换进行重构。该方法可自适应地调节时频滤波因子,有效滤除干扰信息。     

On-line process identification and PID controller autotuning

We propose a new and simple on-line process identification method for the automatic tuning of the PID controller. It does not require a special type of test signal generators such as relay or P controller only if the signals are persistently exciting. That is, a user can choose arbitrary signal generators such as relay, a P controller, the controller itself, pulse signal and step signal generator because it needs only the measured process output and the controller output. It can incorporate nonlinearities due to actuator saturation or manual mode operation during identification work and shows a good robustness to measurement noises, nonlinearity of the process and disturbances. The proposed autotuner combined with the identification method and tuning rule using a model reduction shows good control properties compared with previous autotuning methods.     

工业自整定PID调节器关键设计技术综述

对十年来国内外在工业过程控制中使用的自整定PID调节的设计方法与关键技术进行了全面综述和评价,这对我国进行同类高科技自动化仪表的开发研制及商品化有重要的指导意义.     

基于FFT的被控对象频率特性估计

基于阶跃响应和FFT,提出一种获取被控对象频率特性的新方法。在阶跃响应中,通常由于初始稳态值不为零而不满足传递函数定义的条件;终止稳态值不为零而使傅立叶积分在无穷区间内不可积。直接对阶跃响应数据进行FFT,无法得到满足控制器设计要求的频率特性。采用高通滤波器,首先对阶跃响应数据进行预处理,然后进行FFT,获得了具有较高精度的频率特性,特别是用于控制器设计和自整定的中低频段,其幅频特性和相频特性的精度完全能满足应用要求。本算法的有效性在对一阶惯性环节加纯滞后系统的半实物实时闭环仿真中已经得到了全面的验证。     

The effects of mechanical and thermal perturbations on states within the hysteresis of sorption isotherms of mesoporous materials

We investigate thermodynamic states inside the hysteresis in the adsorption–desorption isotherms of mesoporous materials by perturbing the adsorbate at a point inside the loop. Scanning curves were run to points inside the hysteresis loop and then the system was perturbed by both mechanical and thermal means. Mechanical perturbations were performed by placing a speaker inside the cryogenic bath to expose the system to vibrations. Thermal disturbances were performed by changing the temperature bath ±10 K and back or by removing the bath for 30–60 s. We find that vibrations up to 500 kHz have no substantial effect on the quantity adsorbed for states that lie within the loop. On the other hand, thermal shocks do affect the system and the states inside the hysteresis loop are found to be unstable with respect to this sort of perturbation. The final state after the sample is returned to its original temperature bath depends on whether the temperature had been raised or lowered during the shock. For increases in temperature, the adsorbed state shifts onto the adsorption branch of the hysteresis; for decreases in temperature, the state shifts onto the desorption branch.     

A MODEL-BASED DIRECT ADAPTIVE PI CONTROLLER FOR NONLINEAR PROCESS CONTROL

This article proposes a model-based direct adaptive proportional-integral (PI) controller for a class of nonlinear processes whose nominal model is input-output linearizable but may not be accurate enough to represent the actual process. The proposed direct adaptive PI controller is composed of two parts: the first is a linearizing feedback control law that is synthesized directly based on the process's nominal model and the second is an adaptive PI controller used to compensate for the model errors. An effective parameter-tuning algorithm is devised such that the proposed direct adaptive PI controller is able to achieve stable and robust control performance under uncertainties. To show the robust stability and performance of the direct adaptive PI control system, a rigorous analysis involving the use of a Lyapunov-based approach is presented. The effectiveness and applicability of the proposed PI control strategy are demonstrated by considering the time-dependent temperature trajectory tracking control of a batch reactor in the presence of plant/model mismatch, unanticipated periodic disturbances, and measurement noises. Furthermore, for use in an environment that lacks full-state measurements, the integration of a sliding observer with the proposed control scheme is suggested and investigated. Extensive simulation results reveal that the proposed model-based direct adaptive PI control strategy enables a highly nonlinear process to achieve robust control performance despite the existence of plant/model mismatch and diversified process uncertainties.     

A SIMPLE AUTOTUNING METHOD USING PROPORTIONAL CONTROLLER

In this study, we propose a simple autotuning method using proportional controller. A second order plus time delay model is used in the on-line closed-loop identification and tuning of P1D controllers. This model can approximate processes over a wider frequency region than a first order plus time delay model, which is often employed in model-based autotuning methods. Moreover, since the identification method requires only a simple least squares method to estimate the model parameters, no complex numerical techniques such as root-finding or optimization methods are employed, thus making it practical, unlike many other previous identification methods. Simulation studies demonstrate that the proposed method shows satisfactory identification and better control performances than other previous methods for various processes. In the identification step, it shows insensitivity to measurement noise and input disturbances. The results of the experimental study confirm its validity and capability and show its promise in industrial situations.