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.     

Estimating performance enhancement with alternate control strategies for multiloop control systems

A filter based methodology, studied earlier for SISO systems, is extended to MIMO systems. The presented approach facilitates the calculation of best achievable performance for proportional-integral (PI) controller and the optimal multiloop (ML) PI settings for stochastic disturbance rejection in ML control systems. The filter based approach is further extended to answer some of the key questions for ML control systems such as: (a) performance enhancement possible with the alternate pairing scheme, (b) benefits that will accrue through the employment of decouplers and (c) the performance achievable with the use of multivariable controller (as opposed to an ML controller). Further, the trade-off curve between output variance and control effort is generated for the various control configurations within PI controller domain.     

A SIMPLE TITO PI TUNING METHOD SUITABLE FOR INDUSTRIAL APPLICATIONS

A simple tuning method for TITO (Two-Input, Two-Output) PI controllers will be presented in this article. The method is an extension of the SISO PID tuning method based on Internal Model Control (IMC). An approximate model for tuning purpose will be developed using the information from the interaction measure of the TITO system. The procedure of the tuning method is very simple and straightforward utilizing only two bias-relay feedback tests. The tuning method can easily be applied to various industrial situations with almost no need for a priori process knowledge. Various TITO examples will be used to demonstrate the performance of this tuning method. Both setpoint and load disturbance responses will be examined     

A nonlinear pi(d) controller

The PID control algorithm remains the most widely used in the process industries. This is due to its simplicity (three tuning parameters, fixed structure) and its ability to satisfy the majority of process control needs. Here, a new nonlinear algorithm (the PI(D)) is presented, which maintains the simplicity of the PID, but is nevertheless able to outperform it in both load and set point changes. Tuning formulae and response curves for the PI(D) controller are presented.     

TUNING METHOD FOR INTERACTIVE MULTILOOP IMC, PI AND PID CONTROLLERS

An efficient method to adjust a multiloop control system based on IMC, PI or PID controllers is presented. The first step of the new method consists in designing and adjusting the individual IMC controllers assuming a noninteractive condition and using information related to model uncertainties. In a second step, a single tuning parameter is used to adjust the multiloop interactive system in order to improve both stability and performance characteristics. The extension to multiloop PI and PID controllers is made through alternative parameterizations of IMC (Rivera el al., 1986).

Several simulation results obtained using transfer function representations of distillation systems from the literature show the convenience of the proposed technique by yielding good settings with a reasonable amount of engineering and computational effort.     

化工过程总体裕量与控制性能的权衡优化

化工过程的总体裕量可以用操作优化的经济效益进行评价,根据稳态优化和动态优化的经济效益可进一步划分为服务于操作控制的控制裕量和表征过程可实现经济效益的工艺裕量,二者都与化工过程的控制性能有关。针对具有一定裕量的化工过程进行多目标动态优化,优化目标分别为操作点的经济效益与动态过程中的控制性能指标,采用0-1变量描述控制结构,将控制结构和控制器参数也作为优化变量进行混合整数动态优化,采用Constrained NSGA-Ⅱ算法求解非劣解集,根据非劣解集分析总体工艺裕量、总体控制裕量与控制性能指标的关系。通过催化裂化装置的实例分析发现,对于具有一定裕量的化工过程,控制性能越高,所需的总体控制裕量越多,表征操作优化可实现经济效益的总体工艺裕量越少,只有通过对总体控制裕量和总体工艺裕量进行权衡,才能找到兼顾工艺要求和控制性能的工艺操作点和控制设计方案。     

工业过程PI控制器性能评价

针对工业过程的PI控制器,提出了一种控制器性能评价的新算法。该算法以广义最小方差为目标,推导出最优PI控制器参数。以该最优控制器为基础,得到PI控制下系统的最优控制性能。然后,以最优控制的输出为基准,进行性能评价,并给出了性能评价的可操作步骤。最后通过仿真实验验证了该方法的有效性。     

PID最小方差控制在参数整定中的应用

流程工业的控制回路中90%以上都使用PID控制器,在线PID参数整定方法一直是一个有很大意义却比较难解决的工程问题。PID最小方差性能评价常用于评价控制性能,然而其得出的最优PID参数往往并不适用于实际系统,当出现问题时需要重新加阶跃响应整定PID参数。将PID最小方差控制和系统传统的动态性能指针评价方法结合使用,通过系统传统的动态性能指针的要求给出PID参数的取值范围,再根据过程输出方差随PID参数变化而变化的趋势整定PID参数,该方法在实验装置的参数整定中得到了验证。     

基于统计分析的多变量预测控制性能检测与诊断

A statistic-based benchmark was proposed for performance assessment and monitoring of model predictive control; the benchmark was straightforward and achievable by recording a set of output data only when the control performance was good according to the user＇s selection. Principal component model was built and an autoregressive moving average filter was identified to monitor the performance; an improved T^2 statistic was selected as the performance monitor index. When performance changes were detected, diagnosis was done by model validation using recursive analysis and generalized likelihood ratio （GLR） method. This distinguished the fact that the performance change was due to plant model mismatch or due to disturbance term. Simulation was done about a heavy oil fractionator system and good results were obtained. Thediagnosis result was helpful for the operator to improve the system performance.     

Controlled output variance based diagnosis tree for feedforward/feedback control systems

A diagnosis tree based on the controlled output variance is proposed to assess a feedforward/feedback control performance. It is used for diagnosing and removing its fault causes. Based on the controlled output, the current output variance of the feedback/feedforward system is contributed by the feedback-only effect and the combination of feedback with feedforward effects, respectively. The feedback loop variance can be further expressed as the sum of the feedback invariant (FBI) term and the feedback-dependent (FBD) term. The feedforward loop variance can also be decomposed into the feedback/feedforward invariant (FBI/FFI) term, the feedback-invariant/feedforward-dependent (FBI/FFD) term and the feedback/feedforward-dependent (FBD/FFD) term. These effect variations are systematically conducted by a sequence of the statistic hypothesis testing procedures and the isolation strategy to compare the current control performance and the achievable benchmark operating one. Without the traditional complex physical model and/or any external input to change the current operating process, the diagnosis tree with hierarchical structure is constructed. The capability of the proposal is illustrated through two simulation cases with multiple faults.     

Synthesis of model-based controllers for an autothermal reactor

Model-based controllers for a bench scale autothermal tubular packed-bed reactor have been formulated using the Internal Model Control (IMC) approach. The Structural Dominance Analysis technique has been used in developing the reduced-order models. Controller performance at robust and sensitive steady states have been assessed through simulations and experiments. Both PI and model-based controllers can regulate reactor operation at robust steady states, but only third order IMC controllers are able to regulate reactor operation at the sensitive steady state.     

Enhanced Performance Assessment of Subspace Model‐Based Predictive Controller with Parameters Tuning

This study focuses on performance assessment of model predictive control. An MPC‐achievable benchmark for the unconstrained case is proposed based on closed‐loop subspace identification. Two performance measures can be constructed to evaluate the potential benefit to update the new identified model. Potential benefit by tuning the parameter can be found from trade‐off curves. Effect of constraints imposed on process variables can be evaluated by the installed controller benchmark. The MPC‐achievable benchmark for the constrained case can be estimated via closed‐loop simulation provided that constraints are known. Simulation of an industrial example was done using the proposed method.     

High cis‐1,4 polyisoprene or cis‐1,4/3,4 binary polyisoprene synthesized using 2‐(benzimidazolyl)‐6‐(1‐(arylimino)ethyl)pyridine cobalt(II) dichlorides

Polyisoprene (PI) with a high content of cis‐1,4 (up to 95%) or cis‐1,4/3,4 binary structures was synthesized using a cobalt system in toluene. The cobalt system, which exhibited high activities (up to 3.50 × 10⁶ g PI (mol Co)^?1 h^?1), contained a series of 2‐(benzimidazolyl)‐6‐(1‐(arylimino)ethyl)pyridine cobalt(II) dichlorides activated with ethylaluminium sesquichloride. The nature of the ligands and the reaction conditions significantly affected both the catalytic performance of the cobalt complexes as well as the structures of the resultant PI. The stereospecific polymerization of isoprene could be tuned via changing either the co‐catalyst or solvent: for example, increased content of 3,4 PI (up to 36.6%) was achievable in heptane in the presence of diethylaluminium chloride. Sequence distribution analysis by ¹³C NMR spectroscopy indicated that most 3,4 units occurred randomly in the PI chains. © 2013 Society of Chemical Industry     

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.     

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.     

高强高模聚酰亚胺纤维与对位芳纶的综合性能研究

对高强高模聚酰亚胺(PI)纤维与对位芳纶(PPTA)的形貌特征、吸湿性能、热性能(热尺寸稳定性能与耐高温性能)和耐候性能(耐水解性能与抗紫外光老化性能)进行了研究。结果表明:与PPTA纤维相比,高强高模PI纤维表面呈现明显的沟槽结构,断面没有出现明显的劈裂和原纤化现象;PI纤维吸湿率仅为PPTA纤维的1/6,且具有更高的热尺寸稳定性,在350℃下具有稳定的力学性能,在耐酸性、耐高温水解性以及抗紫外老化性能方面表现优异,但PI纤维耐碱性能弱于PPTA纤维。     

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.     

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.     

An analytic expression for closed-loop output behavior under multiloop PID control

An analytic expression is derived for closed-loop output behavior under a multiloop PID control. Based on the analytic expression obtained, optimization problems are formulated to assess 1) best achievable quadratic performance using multiloop PID control, 2) best achievable quadratic performance on key process variables while maintaining reasonable performance on other less critical process variables, 3) achievable performance improvement with decouplers, and 4) effects of loop pairing on achievable performance. It is shown through a simulated example that individual loop performance as well as the overall multiloop PID control performance can be assessed by using the proposed method. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University.     

Improving dryer energy efficiency and controllability simultaneously by process modification

This work establishes a relationship between dryer energy performance and controllability using energy balances and process resiliency analysis. It is shown that using the process gain matrix, the dryer energy efficiency can be reliably calculated with conditions for simultaneous controllability improvement established. By incorporating a drying rate modifying system such as a desiccant dehumidifier as an add-on, these conditions are shown to be achievable due to the extra dehumidification which can be manipulated using the additional degrees of freedom introduced by the sorption system. Due to the adsorbent regulation properties which are enhanced by high-temperature regeneration, the resilience of energy performance to disturbances is significantly improved compared to conventional dryers. Also, a desiccant system performance indicator, the “adsorber–regenerator net energy efficiency ARNEE” is introduced and it is shown that energy efficiency improvement is possible only if the ARNEE is greater than the energy efficiency of the stand-alone dryer.