Process Transfer Function Research Articles

A condition number scaling policy for stability robustness analysis

AbstractThe condition number of the process transfer function G(s) has been proposed and used as an indicator of the inherent controllability of a process even though it is a scale‐dependent quantity. A rapid suboptimal scaling policy known as G‐balancing is developed for the case of the l2 norm where the condition number is the ratio of the largest to the smallest singular value of G(s). For 2 × 2 systems, G‐balancing gives the same optimal scaling as an available analytical solution. The higher order examples given compare the results of G‐balancing with the known analytic results for l2 norm optimal scaling.

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 Inferential Control for Chemical Processes

A SISO adaptive inferential control system is proposed to deal effectively with many real process control problems characterized by unmeasured disturbances, nonlinearities and/or time-varying process parameters, the proposed control system couples the basic structure of an inferential control (internal model control) with an on-line system identification method for estimation of the process model parameters and optimal adjustment of the controller. To obtain a stable approximation to the inverse of the process model as the controller, the use of adaptive inverse modeling based on a discrete convolution model (adaptive deconvolution model) is examined with two different process models, transfer function and convolution models. Simulation results of two numerical examples are presented to illustrate and compare the performance of the proposed adaptive inferential control system with those of conventional PID control and inferential control. The proposed control system is shown to perform well with both minimum and nonminimum phase systems in the presence of unmeasured load changes and dead time variations. In addition, Vogel-Edgar's adaptive dead time compensator and its modified controller (pole-zero placement adaptive controller) for discrete convolution models are analyzed from the viewpoint of adaptive inferential control.

Identification of the transfer function of dynamic cutting processes — A comparative assessment

A knowledge of the transfer characteristics of the cutting process is one of the crucial factors needed for the assessment of the dynamic stability of the machining system. Yet, it is still not possible to obtain a reliable analytical model, neither based on theoretical considerations nor on experimental data. The objective of this paper is to introduce a method for the determination of the cutting process transfer function in the form of analytical models based on experimental data. The Dynamic Data System (DDS) approach has made it possible to adequately characterize the dynamic cutting process from observations of random force and vibration components. The theoretical concepts and modelling procedure have been demonstrated using actual experimental data. Subsequently, a comparative assessment of the obtained results is given with respect to two typical existing methods, the shear plane method and the double modulation method, representing the static and dynamic methods respectively.

TWO-WAY OR ONE-WAY DECOUPLING IN DISTILLATION?†

Abstract A systematic simulation study of dual composition control of distillation has been carried out in order to compare different decoupling strategies and contrast them with well-tuned SISO-controllers. Two column models are studied. One describes the experimental pilot plant used by Wood and Berry (1973) and the other the experimental pilot plant investigated by Luyben and Vinante (1972). A better control quality–compared to the control quality obtained by SISO-control–may be achieved if suitably chosen decoupling elements are introduced. The best control quality does not, however, necessarily correspond to the best decoupling. In the studied systems, where the controllers of the decoupled systems have been tuned according to the Ziegler-Nichols settings for the effective process transfer functions, there is no incentive to use two decouplers (two-way decoupling): the same or better control quality is obtained with the simpler scheme utilizing only one decoupler (one-way decoupling). Actually, for the Luyben and Vinante system SISO-control is superior to two-way decoupling, whereas one-way decoupling is superior to SISO-control.

An improved method for process identification in the frequency domain

An improved method which used frequency domain data for the determination of process transfer functions is presented. The method presented uses a sign transformation for regression models to ensure positive parameters. A statistical test, based on a right-hand tail F-ratio test and an uncertainty test, is discussed for selecting an adequate system transfer function. The procedure is demonstrated by two examples.

A comparison of the Smith predictor and conventional feedback control

The utility of employing the Smith predictor versus conventional proportional plus integral control for a control loop containing time delays in both the forward and feedback paths has been examined. A theoretical analysis and simulation results employing first order load and process transfer functions for load and setpoint changes are presented. For setpoint changes the Smith predictor always gave improved performance compared to proportional plus integral control. However, for load changes, the Smith predictor was less effective when the system contained small time delays and/or a large load time constant.

On the dynamics of unstable film boiling

A recently developed feedback system for the control of boiling heat transfer made possible the experiental investigation of process dynamics as well as static characteristics in all boiling regions. The region in which the process is normally unstable has now been studied experimentally for water boiling on a wire. A process transfer function previously developed analytically for this region gives quite good agreement between analytical and experimental transfer functions when heater end effects are taken into account.

Experimental evaluation of feedback, feedforward and combined feedforward‐feedback binary distillation column control

AbstractThe control behavior of a nine inch diameter eight tray bubble cap column separating a methanol‐water mixture has been studied using feedback, feedforward and combined feedforward‐feedback control. Top product composition was controlled by manipulation of the reflux rate to compensate for feed flow disturbances. Pulse testing was used to determine the process transfer functions. Gain, gain plus time delay and gain plus time lag feedforward control were implemented by means of an IBM 1800 digital computer. Combined feedforward‐feedback control, using gain and gain plus time lag feedforward control action, was also studied. The improved column control behavior is compared with results obtained using only feedback control.

Control of distillation columns with sharp temperature profiles

AbstractTemperature control problems are frequently encountered in distillation columns that, as a result of high purity products and an easy separation, have large temperature changes over a few trays. The describing function technique is used in this paper to analyze the stability of this type of column in which a nonlinear feedback control loop for column temperature control manipulates vapor boilup.The cycling usually experienced in these systems is shown to be unavoidable in many cases because the process transfer function has such a high gain that it acts like an on‐off switch. The process also displays nonlinear dynamics: system time constants vary with the magnitude of change in vapor boilup.To overcome these difficulties an adaptive, nonlinear feedback controller is proposed that keeps the loop in a small‐amplitude limit cycle by adaptively changing controller gain. The system is evaluated by digital simulation of a nonlinear model of the column.

The Comparative Analysis of the Estimation of a Process Transfer Function

The Comparative Analysis of the Estimation of a Process Transfer Function

The determination of the parameters of a dynamic process

The paper shows how the mathematical methods of steepest descent may be used to minimize certain functions of the ‘satisfaction error’ of a dynamic process.This minimization procedure forms the basis of certain automatic techniques for determining the coefficients or parameters of the process transfer function. The techniques, which are easily mechanized from normal analogue computer components, appear to be limited to the investigation of low order processes. In addition to their value as a new approach to the experimental analysis of dynamic systems (termed the ‘analysis of dynamic experiments’), it is shown that equipment of this type could be utilized in the design of a simple ‘self adaptive’ control system. Finally, possible future developments are discussed, with particular emphasis on the employment of digital mechanization.

Minimum sensitivity adaptive systems

Publisher Summary This chapter presents the minimum sensitivity adaptive systems. It discusses the problem of reducing system sensitivity caused by small variations of process parameters. In the case of small parameter variations, it is possible to design adaptive systems in which the appropriate adjustment of controller parameters is achieved by online solution of linear algebraic equations. The number of equations to be solved in the online parameter computer is equal to the number of adjustable controller parameters. One of the major advantages of such a system is that coefficients of the equations may be calculated off-line. This type of adaptation avoids the widely applied principle of cancellation of the process and controller transfer functions and, thus, ceases to be restricted to linear systems only. Besides the requirement imposed on system linearity, adaptive systems based on transfer functions cancellation suffer from the additional deficiency that the number of adjustable controller parameters must equal the number of variable process parameters.

Determination of dynamic characteristics of processes in the presence of random disturbances

The problem of determining process dynamic characteristics from process operating records is treated for the case when the input and output quantities have random perturbations. The correlation and spectral analysis techniques necessary are briefly reviewed and then applied to some data obtained from a computer simulation of a stirred tank reactor. A digital computer was used for analysis; and the effect of length of record, the spacing between points, and type of weighting function used to estimate the process transfer function and impulse response are considered. The effect of process non-linearity is also considered.