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.     

A theoretical examination of closed-loop properties and tuning methods of single-loop PI controllers

The dependence of the dominant closed-loop poles on the controller parameters is quantitatively elucidated by a Taylor expansion about the critical (ultimate) gain. The leading expansion coefficients are estimated from the critical (ultimate) gain and frequency and one or two closed-loop measurements of the decay ratio and frequency of system response to set-point/load changes or natural disturbances. An explicit model for the process transfer function is not required. By relating controller performance criteria to the leading poles, optimal gain settings to achieve these criteria can then be determined. In the present work, three tuning methods of increasing accuracy (the modified Ziegler-Nichols rule and Methods A and B) are constructed to satisfy a performance criterion (D.R. = 0.25) and a stability consideration. Method A is presented in a convenient chart and is especially easy to use on line. Stability robustness as measured by the Doyle-Stein index and the estimated closed-loop frequency at the proposed setting are also presented in the same chart.     

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.     

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.     

CLOSED-LOOP IDENTIFICATION FOR PARAMETRIC MODELS USING FREQUENCY RESPONSE TECHNIQUES

A parametric identification technique via closed-loop testing using frequency response techniques is presented in this study. Under an operation of proportional control, a single dynamic test (such as an arbitrary pulse or step change) in the set point was introduced to the system. The closed-loop transients could numerically be translated into frequency response data by Fourier integral transforms, and the parameters of a given process model were then be obtained by a least-squares fit in the frequency domain based on Parseval's theorem. This identification technique could apply not only for self-regulating processes but also for integrating or open-loop unstable processes. Furthermore, the proposed technique was also extended to the controller settings for the feedforward-feedback control system. Simulation results demonstrated that the proposed technique could yield good model parameters and can be applied in many different types of processes.     

Model based robust control approach for batch crystallization product design

The paper presents a novel control approach for crystallization processes, which can be used for designing the shape of the crystal size distribution to robustly achieve desired product properties. The approach is based on a robust optimal control scheme, which takes parametric uncertainties into account to provide decreased batch-to-batch variability of the shape of the crystal size distribution. Both open-loop and closed-loop robust control schemes are evaluated. The open-loop approach is based on a robust end-point nonlinear model predictive control (NMPC) scheme which is implemented in a hierarchical structure. On the lower level a supersaturation control approach is used that drives the system in the phase diagram according to a concentration versus temperature trajectory. On the higher level a robust model-based optimization algorithm adapts the setpoint of the supersaturation controller to counteract the effects of changing operating conditions. The process is modelled using the population balance equation (PBE), which is solved using a novel efficient approach that combines the quadrature method of moment (QMOM) and method of characteristics (MOC). The proposed robust model based control approach is corroborated for the case of various desired shapes of the target distribution.     

Closed-loop tuning of process control systems

A technique for tuning PID controllers, involving a single dynamic test (such as a step or pulse change in set point) implemented during closed-loop operation, is proposed. The resulting transient data are used to predict the frequency response of the open-loop process which in turn is used to compute the optimum controller settings. Simulation results reveal that this technique provides reliable tuning constants even when such practical problems as process noise and unanticipated load upsets arise during implementation. A comparison with the recently proposed tuning alternative (Yuwana and Seborg, A.I.Ch.E. J.28, 434, 1982; Jutan and Rodriguez, Can. J. Chem. Engng62, 802, 1984) confirms that in general the suggested procedure, apart from being more flexible, yields also relatively better results.     

PID CONTROLLER TUNING FOR UNSTABLE SYSTEMS BY OPTIMIZATION METHOD

Simple Tuning formulae are provided for optimal PID controller settings for unstable first order plus time delay systems. The method is based on minimization of integral squared errors (ISE). A method of calculating the set point weighting parameter is proposed to reduce the overshoot for servo problems. The performances of the proposed PID settings are compared with the settings recently proposed by Huang and Chen (1997, 1999) for both the servo and regulatory problems. The performance of the controller is also evaluated under parameter uncertainty in time delay and separately in process gain. Tuning formulae are given for PI controller along with the set point weighting. The performance of the PI controller is compared with that of Poulin and Pomerleau (1996). Two simulation studies, one on control of an unstable nonlinear bioreactor and a second on an unstable chemical reactor using the proposed PID controller settings, show improved performances both for servo and regulatory problems.     

A new method for on-line controller tuning

A new method for tuning controllers on-line has been developed based on a single experimental test, a step change in controller set point. The set-point response data and analytical formulae are used to calculate model parameters for a first-order plus time delay transfer function. Controller settings can then be calculated using the model parameters and standard controller tuning relations. Simulation results demonstrate that the new method provides good initial values for PID controller settings despite gross modeling errors and unanticipated load disturbances that may occur during the experimental test.     

PARAMETER IDENTIFICATION AND THE SELF-TUNING ADAPTIVE CONTROL BY A SENSITIVITY APPROACH

Parameter deviation identification and optimal controller tuning are derived by the sensitivities of the parameters. There are non-iterative and iterative algorithms which can be used for parameter identification, no matter the data come from an open-loop test or from a closed-loop operation. The controller tuning is based on the parameter sensitivities of an optimal regulator. The same tuning algorithm has been proved satisfactory for the PID control of the first order process with delay. By sequential implementations of both the identification and tuning, a self-tuning adaptive control system can be obtained. Numerical examples show the feasibility of such algorithms.     

PARAMETER IDENTIFICATION AND THE SELF-TUNING ADAPTIVE CONTROL BY A SENSITIVITY APPROACH

Parameter deviation identification and optimal controller tuning are derived by the sensitivities of the parameters. There are non-iterative and iterative algorithms which can be used for parameter identification, no matter the data come from an open-loop test or from a closed-loop operation. The controller tuning is based on the parameter sensitivities of an optimal regulator. The same tuning algorithm has been proved satisfactory for the PID control of the first order process with delay. By sequential implementations of both the identification and tuning, a self-tuning adaptive control system can be obtained. Numerical examples show the feasibility of such algorithms.     

Simultaneous optimization and control for polypropylene grade transition with two-layer hierarchical structure

In this paper, a two-layer hierarchical structure of optimization and control for polypropylene grade transition was raised to overcome process uncertain disturbances that led to the large deviation between the open-loop reference trajectory and the actual process. In the upper layer, the variant time scale based control vector parametric methods (VTS-CVP) was used for dynamic optimization of transition reference trajectory, while nonlinear model predictive controller (NMPC) based on closed-loop subspace and piece-wise linear (SSARX-PWL) model in the lower layer was tracking to the reference trajectory from the upper layer for overcoming high-frequency disturbances. Besides, mechanism about trajectory deviation detection and optimal trajectory updating onlinewere introduced to ensure a smooth transition for the entire process. The proposed method was validated with the real data from an industrial double-loop propylene polymerization reaction process with developed dynamic mechanismmathematicalmodel.     

A robust pole-placement self-tuning controller for chemical process control: Theoretical studies and simulation

A single variable pole-placement self-tuning controller (PPSTC) is used to simulate examples typical of chemical processes; i.e., open-loop stable, unstable, and unstable non-minimum phase systems with unknown varying process dead time. The PPSTC is shown to be effective in each case. Set-point tracking and rejection of randomly occurring deterministic disturbances for all three types of processes are achieved. Simultaneous estimation of process parameters and process time delay is realized by using a recursive extended least squares method.     

DETECTING STATIONARY GAIN CHANGES IN LARGE PROCESS SYSTEMS

Stationary process gains are critical model parameters for determining targets in commercial MPC technologies. Consequently, important savings can be reached by accessing an early prevention method capable of detecting whether the actual process moves away from the modeled dynamics, particularly by indicating when the process gains are no longer represented by those included in the model identified during commissioning stages. In this first approach, a subspace identification method is used under open-loop process condition to estimate the process gain matrix. The main reason for using the subspace identification (SID) method is that it works directly with raw data; it directly yields a multivariable state space model and has proved to be successful in dealing with multivariable processes and periodic batch-wise data collection. To detect significant changes in the estimator population, a monitoring sequence of hypothesis tests can be done through simple confidence limits directly on each gain estimator, or increasing the sensitivity by using the exponentially weighted moving average (EWMA) or the cumulative sum (CUSUM) algorithms. The objective of this aticle is to present a rational combination of inferential tools capable of detecting which gain of a multivariable model starts moving away from its original value. The anticipated knowledge of these events could provide a warning to process engineers and prevent targeting process conditions with wrong gain estimations. The regular follow-up of the gain matrix should also help to localize those dynamics needing an updating identification and reduce the frequency of time-consuming re-identification of the complete model.     

Handling sensor malfunctions in control of particulate processes

This work focuses on feedback control of particulate processes in the presence of sensor data losses. Two typical particulate process examples, a continuous crystallizer and a batch protein crystallizer, modeled by population balance models (PBMs), are considered. In the case of the continuous crystallizer, a Lyapunov-based nonlinear output feedback controller is first designed on the basis of an approximate moment model and is shown to stabilize an open-loop unstable steady-state of the PBM in the presence of input constraints. Then, the problem of modeling sensor data losses is investigated and the robustness of the nonlinear controller with respect to data losses is extensively investigated through simulations. In the case of the batch crystallizer, a predictive controller is first designed to obtain a desired crystal size distribution at the end of the batch while satisfying state and input constraints. Subsequently, we point out how the constraints in the predictive controller can be modified as a means of achieving constraint satisfaction in the closed-loop system in the presence of sensor data losses.     

Practical improvements to autocovariance least‐squares

Identifying disturbance covariances from data is a critical step in estimator design and controller performance monitoring. Here, the autocovariance least‐squares (ALS) method for this identification is examined. For large industrial models with poorly observable states, the process noise covariance is high dimensional and the optimization problem is poorly conditioned. Also, weighting the least‐squares problem with the identity matrix does not provide minimum variance estimates. Here, ALS method to resolve these two challenges is modified. Poorly observable states using the singular value decomposition (SVD) of the observability matrix is identified and removed, thus decreasing the computational time. Using a new feasible‐generalized least‐squares estimator that approximates the optimal weighting from data, the variance of the estimates is significantly reduced. The new approach on industrial data sets provided by Praxair is successfully demonstrated. The disturbance model identified by the ALS method produces an estimator that performs optimally over a year‐long period. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1840–1855, 2015     

Synthesis of PID controller for unstable and integrating processes

Properly designed controllers provide stable closed-loop response for open-loop unstable processes. Internal model controller equivalent PID tuning rules for low order unstable plus dead time systems are synthesized in this work. The controller is approximated near the vicinity of zero (origin). Controller parameters are derived by equating the closed-loop response to a control-signature (desired closed-loop response) involving a user defined tuning parameter, λ. Simulations are carried out to show the performance of the proposed tuning scheme for both set point and disturbance rejection cases.     

Sub-optimal control of a multivariable non-linear chemical reactor using quasilinearization

The performance of a multivariable non-linear stirred tank chemical reactor has been used to compare the practicability of an optimal controller and two types of suboptimal controller. The optimal controller, which by its nature required lengthy calculations, was suitable for open-loop control only and therefore sensitive to modelling errors. By contrast a suboptimal controller, which used the method of quasilinearization to solve the two point boundary value problem, needed only a small amount of computation time and was capable of online implementation. This controller was much less sensitive to modelling errors, and also had the advantage of decoupling the control variables. An extension of this controller incorporated a feedback feature which compensated further for modelling errors and, in addition, unmeasured disturbances. This controller, which is expected to be of interest to the process industries facing inaccurate-model problems, produced responses close to the true optimal response even when the actual model used was in gross error.     

A novel framework for integrating data mining with control loop performance assessment

Data driven control loop performance assessment techniques assume that the data being analyzed correspond to single plant‐controller configuration. However, in an industrial setting where processes are affected due to the presence of feedstock variability and drifts, the plant‐controller configuration changes with time. Also, user‐defined benchmarking of control loops (common in industrial plants) requires that the data corresponding to optimal operation of the controller be known. However, such information might not be available beforehand in which case it is necessary to extract the same from routine plant operating data. A technique that addresses these fundamental requirements for ensuring reliable performance assessment is proposed. The proposed technique performs a recursive binary segmentation of the data and makes use of the fact that changes in controller settings translate to variations in plant output for identifying regions corresponding to single plant‐controller configurations. The statistical properties of the data in each such window are then compared with the theoretically expected behavior to extract the data corresponding to optimal configuration. This approach has been applied on: (1) raw plant output, (2) Hurst exponent, and (3) minimum variance index of the process data. Simulation examples demonstrate the applicability of proposed approach in industrial settings. A comparison of the three routes is provided with regard to the amount of data needed and the efficacy achieved. Key results are emphasized and a framework for applying this technique is described. This tool is of significance to industries interested in an automated analysis of large scale control loop data for multiple process variables that is otherwise left unutilized. © 2015 American Institute of Chemical Engineers AIChE J, 62: 146–165, 2016     

Controllability analysis for the liquid-phase catalytic oxidation of toluene to benzoic acid

The liquid-phase catalytic oxidation of toluene is the main industrial commercial process for producing benzoic acid. It is a strongly exothermic and highly nonlinear process that exhibits poor controllability characteristics with input/output multiplicity and non-minimum phase behavior. Focusing on inherent safety, this study explores the open and closed-loop controllability of this process. The framework contains two parts. First, an approach for analyzing the stability of zero dynamics of the system is used to investigate the phase behavior of the process and is selected as an open-loop indicator for controllability. Second, based on the model predictive controller, closed-loop dynamic simulation, including set-point tracking and disturbances rejection, is performed to illustrate the dynamic performance in various sub-regions with different controllability characteristics. The results of the dynamic simulation confirm everything predicted by the open-loop controllability analysis. The outcomes are expected to guide realistic industrial operation and process control system design. An attempt is made with the help of this liquid-phase oxidation process to show how to clarify and deal with the causes of the complex phenomena that arise in the operation and control of the chemical processes.