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Relay in the feedback loop produces a stable oscillation whose cyclic steady state response contains process information of ultimate gain and ultimate period. By measuring these process data and Zi...

A hydrogen (H2)-rich gas mixture is used as the fuel of the proton exchange membrane fuel cell (PEMFC). A small amount of the carbon monoxide (CO) gas in the gas mixture can significantly deactivate the catalyst of the PEMFC, resulting in a reduction in the efficiency of power generation. Preferential oxidation is used to reduce the CO concentration less than 10 ppm in the gas mixture. It has an optimal reaction temperature at which the reaction shows the minimum exit CO concentration with minimum consumption of H2. This optimal temperature continuously changes under the varying conditions of operation and catalyst deactivation. In this study, two modified extremum seeking control (ESC) methods were proposed to continuously seek and maintain this optimal reaction temperature, guaranteeing CO concentration under 10 ppm even under time-varying conditions. The proposed methods have a smaller number of design parameters than the conventional extremum seeking approaches so that tuning the ESC method is much easier, more intuitive, and efficient. In addition, the proposed method can additionally use the secondary measurement to improve the performance of the ESC method by removing the possibility that the modeling error of the linear dynamic block can deteriorate the accuracy of calculating the gradient of the nonlinear static block. The experimental results confirmed that the proposed methods can track the optimal temperature within a short time compared to the conventional approach while successfully maintaining the CO concentration below 10 ppm.

The relay (on–off) controller can stabilize wide ranges of processes including open-loop stable, integrating, and unstable processes, producing sustained oscillations. For improved proportional-integral-derivative controller tunings, methods to find process models with mixed closed-loop tests of relay feedback and proportional-derivative (PD) controllers are proposed. For unknown processes with arbitrary initial states, relay feedback tests are first applied and, after cyclic steady states are obtained, PD controllers or other relay feedback tests with set point changes are followed. This full closed-loop operation is desirable for integrating and unstable processes and will be useful even for stable processes when processes are far from their desirable operating points. Refined methods to find exact frequency responses of processes from initial and final cyclic steady states are derived. Whole relay feedback responses need not be saved. Several integrals at the relay switching times are used without iterative tests or computations.

Step and pulse responses have long been used to identify process dynamics and design control systems such as PID (proportional-integral-derivative) and model predictive control. They are simple and...

Detailed transient behaviors of mass and heat transfer processes are required to solve partial differential equations. When those partial differential equations are coupled, they are still difficul...

Many methods are available to tune proportional integral (PI) controllers for first order plus time delay (FOPTD) models of overdamped processes. The two asymptotes for small and large ratios of time delays over time constants are easily calculated. These two asymptotes can be used to evaluate and provide guidelines for the performance and application ranges of PI controller tuning rules. By matching these two asymptotes, a simple analytic tuning rule is suggested. For some overdamped processes whose transfer functions have large zero terms, half-order plus time delay (HOPTD) models are found to yield better results than the FOPTD models. Applying the technique of matching two asymptotes, a simple analytic PI controller tuning rule has also been proposed for the HOPTD models. To apply these tuning rules to high order processes with known transfer functions, model reduction methods to obtain the FOPTD and HOPTD models are investigated. Simulation results for empirical and full models of processes show the ...

Recent extremum seeking control that uses a continuous perturbation and the integral feedback of perturbation- output product is based on a static nonlinear process. The method can be applied to dynamic nonlinear processes for tracking and maintaining the optimal operating points. It has several tuning parameters, such as the integral controller gain and the magnitude and frequency of the continuous perturbation signal. The frequency of the continuous perturbation signal should be low enough to ensure the time-scale separation between the real-time optimization and the process dynamics for the closed-loop stability. However, for some processes, fast perturbations are preferred because they can be attenuated easily in subsequent processes such as buffers and storages. For this, we propose an extremum seeking control method where the partial sum of perturbation-output product is used for a faster squarewave perturbation. Simulations for two processes of parallel competing reactions have been given, and a simple liquid level system to test extremum seeking control methods is suggested.

The first-order plus time delay (FOPTD) model-based method is a standard approach to tune proportional–integral (PI) controllers in plants. The FOPTD model can be obtained easily from step responses. However, because of their structural limitations, FOPTD models suffer from difficulties in approximating step responses for some processes including processes with overshoot, resulting in PI controllers with unacceptable performance. To remove these drawbacks, models combining two FOPTD models that can be obtained easily from step responses are proposed to tune PI controllers. Several simulations and experimental examples are given, illustrating the improved performance of the proposed method.

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

Simple linear models including the linear driving force (LDF) model for approximating unsteady-state diffusion, adsorption in an adsorbent under cyclic operating environments have been proposed to reduce the computational load of the exact partial differential equations. The models are in the form of a first-order ordinary differential equation and consist of a term with the external concentration surrounding the adsorbent particle and another term with the average adsorbate concentration in the adsorbent. Although very simple to use, the approximation models are first-order approximations of the pore diffusion model, and hence their accuracy is not high enough to compute fine details of fast responses. By incorporating the time derivative of the external concentration into the approximation, an improved linear formula for cyclic adsorption is developed in this study. As the time derivative is usually computed simultaneously with the external concentration, the improved formula has little additional complexity over the previous approximations in its applications, and yet it is considerably more accurate than the previous first-order approximations for cyclic adsorption.

A nonlinear process with input multiplicity has two or more input values for a given output at the steady state, and the process steady state gain changes its sign as the operating point changes. A control system with integral action will be unstable when both signs of the process gain and the controller integral gain are different, and its stability region will be limited to the boundary where the process steady state gain is zero. Unlike processes with output multiplicities, feedback controllers cannot be used to correct the sign changes of process gain. To remove such stability limitation, a simple control system with parallel compensator is proposed. The parallel compensator can be easily designed based on the process steady state gain information and tuned in the field. Using the two time scale method, the stability of proposed control systems for processes with input multiplicities can be checked.

Well-designed nonlinear proportional-integral (PI) controllers are successful for nonlinear dynamical processes like linear PI controllers are for linear processes. Two nonlinear blocks representing proportional and integral terms can be designed so that the linearized controllers perform the same as linear PI controllers for linearized processes at the given operating points. For some nonlinear processes, nonlinear blocks for nonlinear PI controllers can be singular at some operating points, and control performances can be poor for set points near those points. To mitigate such disadvantages, new nonlinear PI controllers that introduce output transformations are proposed. Several examples are given, showing the performance of the proposed nonlinear PI controllers. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4264–4269, 2015

Hydrogen rich gas produced by hydrocarbon reforming contains CO up to several thousand ppm which acts as a poison for the proton exchange membrane fuel cells. Preferential oxidation (PROX) is one of the promising methods that reduce its concentration below 10ppm. The PROX reactor with the CuO-CeO2 catalyst shows optimal reactor temperature and a control system that maintains the PROX reactor temperature at its optimal one under changing environments and catalyst deactivations. Experimental studies to obtain a dynamic model for the CO PROX reactor have been done and the Wiener-type nonlinear model is obtained. Then the extremum seeking control that can track the optimal temperature for the Wiener-type nonlinear system is applied and its performance is verified experimentally. The extremum seeking control is a non-parametric real-time optimization method and can be applied effectively to other CO PROX reactors with different operating conditions.

Model reduction and tuning rules given in the SIMC (Simple Internal Model Control) method are very effective in tuning PI controllers. For some processes with large lead elements, control performances by the SIMC method are somewhat oscillatory or sluggish. To mitigate such drawbacks, additional tuning rules based on the second order plus time delay model with lead term are proposed. Improvements for certain types of models are critical. For such processes, besides the SIMC tuning rule, no PI controller tuning rules that are analytic and given in terms of process parameters are not available. Since the proposed tuning rules are very simple, they can be used in the field, effectively complementing the SIMC method.

고급 홍삼의 생산 수율을 증가시키는 제어 방법에 관한 실험을 수행하였다. 수삼에서 홍삼을 만드는 과정 중 수증기로 수삼을 찌는 증삼 공정에서 동체균열, 내공, 내백 등이 발생하는데 이는 홍삼의 품질을 저하시키는 원인이 된다.고급 홍삼의 수율을 증가시키기 위해서는 이런 불량 요인을 최소화하는 방법이 필요하다. 최근까지 대부분의 증삼 공정의 제어는 증삼 과정의 필수 인자인 온도만을 조절하거나 온도와 압력을 동시에 조절하여 제어하는 방법이 연구되었다. 그러나 이는 불량 요인을 최소화하는 목적에 적합하지 못한 것으로 보인다. 이와 달리, 본 연구에서는 기존의 홍삼 o제조 방식을 토대로 96~99C의 온도를 유지하면서 수삼의 무게 제어를 통하여 불량 요인을 최소화하는 제어 방법을 제시한다. 무게 제어를 적용한 실험 결과 증삼 과정 후 수삼의 동체균열의 불량요인이 줄어드는 것을 확인할 수 있었다.Abstract − Experiments for a control method that enhances the yield to produce high quality red ginsengs have beenperformed. In the first steaming process of a series of processes to produce red ginsengs from raw ginsengs, there occurseveral undesirable defects on ginsengs such as cracks of ginseng body, inside cavity and inside white. These defectslead to deterioration in product qualities. Therefore an improved control method that minimizes these undesirabledefects is needed in order to increase the yield of high quality red ginsengs. Until these days, the steaming process con-trol methods such as controlling the steaming temperature and/or pressure have been studied. However, such controlmethods are not adequate enough to minimize the undesirable defects in steamed ginsengs. On the other hand, in thisexperiment, we suggest a control method that minimizes the undesirable defects through a weight control of steamedginsengs, keeping the steaming temperature at 96~99

Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. Rational approximations of the Laplace solutions such as the Pade approximation can be used for this purpose. For some heat conduction problems appearing in a semi-infinite slab, however, such rational approximations are not easy to obtain because the Laplace solutions are not analytic at the origin. In this article, a continued fraction method has been proposed to obtain rational approximations of such heat conduction dynamics in a semi-infinite slab.

In this paper, a new model reduction method and an explicit PID tuning rule for the purpose of PID auto-tuning on the basis of a fractional order plus time delay model are proposed. The model reduction method directly fits the fractional order plus time delay model to frequency response data by solving a simple single-variable optimization problem. In addition, the optimal tuning parameters of the PID controller are obtained by solving the Integral of the Time weighted Absolute Error (ITAE) minimization problem and then, the proposed PID tuning rule in the form of an explicit formula is developed by fitting the parameters of the formula to the obtained optimal tuning parameters. The proposed tuning method provides almost the same performance as the optimal tuning parameters. Simulation study confirms that the auto-tuning strategy based on the proposed model reduction method and the PID tuning rule can successfully incorporate various types of process dynamics.

Very simple proportional-integral-derivative (PID) controller tuning rules for a wide range of stable processes are available. However, for unstable processes, the design trend is for controllers to be more complex for better performances. Here, the design concept of “simplicity” is extended to unstable processes. Simple desired closed-loop transfer functions for the direct synthesis method and simple approximations of the process time delay are utilized for unstable processes. Very simple tuning rules for PID controllers and set-point filters are obtained, yielding similar or even improved performances over previous more complicated PID controller tuning methods.

The SIMC method by Skogestad (J. Process Control 2003, 13, 291–309) to tune the PID controller is revisited, and a new method (K-SIMC) is proposed. The proposed K-SIMC method includes modifications of model reduction techniques and suggestions of new tuning rules and set point filters. Effects of such modifications are illustrated through simulations for a wide variety of process models. The proposed modifications permit the SIMC method to be applied with more confidence.

An in-line mixer pH system is proposed to identify the titration curve before changes in the input stream affect the main pH neutralization reactor. It is operated under integral control and shows oscillatory responses for a wide range of controller integral gain. The bifurcation diagram for the change of the controller integral gain is very similar to that of the quadratic map which is often used in illustrating the chaos phenomena of nonlinear processes. Various bifurcation diagrams are obtained as operating conditions of the in-line mixer system such as the set point of pH and components of the input stream change. The integral control keeps oscillations be around the set point, providing plentiful information about the pH process. The oscillations can be used to identify the titration curve of the input acid stream. Simulation and experimental results show that the chaotic operations of a small in-line mixer can be positively used for the identification of the titration curve.

In the preferential oxidation of CO in hydrogen mixtures (PROX), CO and H 2 oxidation occur in parallel on the surface in a porous catalyst. The diffusion of the reactants into the pore structure of the catalyst can affect the catalyst performance significantly, and its effect can be accounted for in terms of the effectiveness factor. Conventional methods for estimating the effectiveness factor are not directly applicable because they have been developed for a single reaction in a catalyst particle. A novel method for a simultaneous estimation of the effectiveness factors of the two reactions was developed in this study. This method is based on the PROX kinetics over a CuO–CeO 2 catalyst and is applicable to the cases where the CO oxidation can be approximated by a first-order reaction and both oxidations are zero-order reactions with respect to the O 2 partial pressure. With the method, the performance of an isothermal PROX reactor was simulated to determine the effects of the feed flow rate, feed composition, reactor temperature and catalyst size on the CO clean-up.

Methanol partial oxidation (POX) is a well-known reforming reaction for the production of hydrogen from methanol. Since POX is relatively fast and highly exothermic, this reforming method will be efficient for the fast startup and load-following operation. However, POX generates hot spots around catalyst and even oscillations in the reactor temperature. These should be relieved for longer operations of the reactor without catalyst degradations. For this, temperature oscillations in a POX reactor are investigated experimentally. Various patterns of temperature oscillations according to feed flow rates of reactants and reactor temperatures are obtained. The bifurcation phenomena from regular oscillations to chaotic oscillations are found as the methanol flow rate increases. These experimental results can be used for theoretical analyses of oscillations and for designing safe reforming reactors.

Glass electrodes for measuring pH in solutions show relatively fast responses with slow drifts. To design compensators to remove the drifts that hinder fast measurements of pH, a dynamic model that consists of ordinary and partial differential equations is proposed. It can explain such two-time scale responses of glass electrodes. The fitting accuracies of the proposed model are experimentally evaluated in frequency-domain and time-domain. The frequency responses obtained from the square wave responses show the fitting abilities of the proposed model, and the step responses also support this. The step responses filtered based on the proposed model show that pH measurements can be made considerably faster. The proposed model can be used to improve the dynamics of glass pH electrodes by compensating dynamic elements causing slow drifts.

The partial differential equation for unsteady-state diffusion, adsorption and a first-order reaction in a catalyst is often approximated to ordinary differential equations for reduced computational loads. Very high-order models obtained by the continued fraction expansion method are accurate for a wide range of the Thiele modulus and the changing frequency of surface concentration. In addition, they are numerically well-conditioned. However, due to their high dimensionalities, they will not have merits over other low-order models. Here, high-order models based on the continued fraction expansion method are shown to be used to obtain various practical models. With the Taylor series obtained from high-order models, Pade approximations are easily obtained regardless of the Thiele modulus and the shape of catalyst. Low-order models by applying the balanced truncation method to a high-order model can also be obtained, providing better approximations than the well-known Pade models.

The pore diffusion model that describes unsteady-state adsorption, diffusion, and reaction in a porous catalyst is in the form of a parabolic partial differential equation. To relieve computational loads, approximate ordinary differential equations are often used and they can be derived from the transfer function between the surface and average concentrations in the particle. The transfer function shows half-order behaviors at the high-frequency range. The rational transfer functions cannot describe well this half-order behavior. Here, introducing the half-order term to rational transfer function candidates for approximation, models valid throughout low- and high-frequency ranges are derived. Since the proposed approximate models are valid globally, they can be applied to reactive porous catalysts easily. They can also be used for noninteger shape factors that will show better performances for adsorbents different from ideal geometries of infinite slab, infinite cylinder and sphere, and for biporous adsorbents. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 2540-2548, 2013

A new frequency response identification method is presented to estimate frequency responses of discrete-time processes. It provides exact frequency response data sets for any desired frequency. This method incorporates various process signal types such as both initial and final steady state, initial steady state and final cyclic steady state and both initial and final cyclic steady state. Also, the proposed algorithm completely removes the effect of static disturbances and it shows acceptable robustness to measurement noises.

We propose a new process identification method that combines the two methods of the relay feedback to activate the process and the backward integrals to estimate the model parameters. Novel deviation variables are introduced to incorporate the case that the initial part of the process is unsteady-state without sacrificing the dynamic information included in the initial part, while the previous approaches assign zero-weighting to the initial parts, resulting in loss of the dynamic information included in the initial part. The final cyclic-steady-state part of the process input and output data is chosen as the reference of the deviation variables. The proposed method can estimate the model parameters analytically by using the backward integrals and the least squares method.

For unsteady-state diffusion, adsorption and a first-order reaction in a slab, cylinder and sphere catalyst, high-order approximations in the form of coupled ordinary differential equations are developed to substitute the exact partial differential equations. An infinite continued fraction is developed, which unifies the exact transfer functions of the three geometries as a function of the shape factor and the Thiele modulus in the Laplace domain. The time-domain approximations are obtained from the truncated continued fractions. The coefficients in the time-domain approximations are very easy to determine, and increasing the order of approximation is simple and straightforward.

Sustained oscillations are obtained by putting relays in the feedback loop, which provide ultimate periods and gains of processes that can be used to tune PID controllers. The ultimate periods obtained by conventional relay autotuning have relative errors up to 5% for first order plus time delay processes. To improve the estimation of ultimate periods, modified relays such as a saturation relay and a relay with preload have been available. However, these modifications lose the binary (on-off) property of the conventional relay. Here relays with multiple switching which produce pulse-widthmodulation (PWM) signals are proposed. They retain the binary property and show improved identification accuracies of ultimate parameters.

A new nonparametric process identification method is proposed to obtain the frequency response model from given process input and output data. The proposed algorithm can estimate exact models for all desired frequencies. It is applicable to various process conditions (initial/final steady-state, initial steady-state/final cyclic-steady-state, and initial/final cyclic-steady-state) and requires a smaller amount of memory than previous methods. Also, it provides the exact models even in the presence of a static disturbance and shows an acceptable robustness to measurement noises. © 2011 American Institute of Chemical Engineers AIChE J, 2011