Will Cluett

Contact Information:

Department of Chemical Engineering & Applied Chemistry

University of Toronto

200 College Street

Toronto, Ontario M5S 3E5

Canada

Tel: 416-978-5889

Fax: 416-978-8605

Email: cluett@ecf.utoronto.ca

Feeling relaxed after my administrative leave!

With my sons Owen (12) and Taylor (14) in Grand Bend, Ontario during summer 2004

Recent Progress in Research Activities of the Group

Identification and Control of Time-Varying pH Processes

Control of pH is a challenging problem when the concentration of the buffering species varies with time. This causes the process nonlinearity to become time-dependent as the system moves among several titration curves. The resulting gain change is unpredictable and this is what makes pH control difficult.

The identification and control of pH processes based on the Wiener model construct (a dynamic linear element representing the mixing dynamics of the process in series with a static nonlinearity representing the titration curve) has been studied extensively. Linearization by output transformation using an estimate of the inverse titration curve has been employed to make the pH process appear linear, enabling the application of a linear feedback controller for pH control purposes. Although other researchers have utilized an identified nonlinearity for linearizing feedback control of pH processes, much less work has been done on using the nonlinearity for linearizing feedforward control. In our research, a simple linearizing feedforward controller has also been proposed based on a current estimate of the inverse titration curve. Simulated closed-loop results have demonstrated the superiority of the linearizing feedforward-feedback strategy versus linearizing feedback only, when the inverse titration curve is accurately estimated.

Recognizing the importance of having an accurate estimate of the inverse titration curve for effective pH control, a novel approach to the identification of time-varying, nonlinear pH processes based on the Wiener model structure has been developed. The algorithm produces an on-line estimate of the titration curve, where the shape of this static nonlinearity changes because of changes in weak species concentration and/or composition of the process feed stream. The identification method is based on the recursive least squares algorithm, a frequency sampling filter model of the linear dynamics and a polynomial representation of the inverse static nonlinearity. A sinusoidal signal for the control reagent flow rate is used to generate the input-output data along with a method for automatically adjusting the input mean level to ensure that the titration curve is identified in the pH operating region of interest. Experimental results have been obtained from a pilot-scale pH process to illustrate the performance of the proposed approach.

In the third stage of this work, a new on-line titrator for pH control has been developed. The on-line identification method described above has been used to generate an estimate of the inverse titration curve as a continuous smooth function, eliminating any need for prior selection of break points on the titration curve. The time required to obtain the titration curve in the spanned pH range is approximately twice the settling time of the titrator and thus no significant identification lag is introduced. The results from the titrator are used directly to linearize the pH process enabling the application of the previously described linearizing feedforward-feedback control strategy.

Controller Performance Assessment

Model predictive control (MPC) technology is widely applied throughout the process industries. In our research, a methodology has been developed for the performance assessment of univariate model predictive controllers. The proposed benchmark used in this assessment is shown to be useful both as a model diagnostic and as a tuning guide during commissioning of the control system. In the proposed approach, an MPC performance curve is created by plotting the variance of the controlled variable against that of the differenced manipulated variable over a range of values of the move suppression parameter. In the absence of mismatch between the estimated and actual process dynamics, the operating point of an MPC controller is expected to lie on or near this curve.

The formal procedure underlying the methodology uses routine operating data to update the process model. In the end, two performance curves are constructed: one representing the operation of the installed MPC on the current process, and the other illustrates the performance on the current process of a hypothetical MPC controller re-designed for this process. If the distance between these operating curves is deemed significant, this may be used to justify the engineering time and expense associated with redesigning the MPC application.

Identification Relevant to Control System Design

Our research in this area has involved the development of a framework for designing control relevant process identification experiments to obtain process models for use in a worst-case robust optimal controller design. The problem of designing a control relevant input signal for an open-loop identification experiment has been formulated and the difficulties associated with solving this design problem have been revealed. The two issues that make the problem difficult to solve are (1) obtaining an updated estimate of the process model without actually performing the identification experiment, and (2) evaluating a measure of the controller performance without actually implementing the controller on the real process. In each case, a practical approach to circumventing the issue has been developed.

A sensitivity analysis approach to designing the input test signal, making use of the natural relationship between the energy of the input signal and the accuracy of the process frequency response estimate, is used. By taking advantage of the special properties of the frequency sampling filter model, the computation time required for a complete sensitivity analysis has been dramatically reduced. Using this approach, a method that allows the engineer to predict the amount of improvement in the achievable controller performance prior to actually performing a further identification experiment has been developed. An iterative procedure for conducting a control relevant identification experiment has also been proposed.

Dual Control

The dual control problem has challenged control engineers for decades. Instead of using a fixed model for computation of the future control actions, future controls are computed using models predicted to result from those control actions applied earlier. The resulting optimal policy balances system excitation, to improve model accuracy, against system regulation, to achieve good immediate control performance. The name, dual control, arises from the need to simultaneously satisfy these two competing objectives.

Practical solution of the dual control problem continues to be hindered by the difficulties involved in numerically solving the associated stochastic dynamic programs. In particular, their high dimension coupled with the nesting of optimizations and integrations within these programs renders their exact numerical solution computationally prohibitive. In our research, a new stochastic dynamic programming algorithm has been developed that uses a Monte Carlo approach to circumvent the need for numerical integration, thereby dramatically reducing computation requirements. Also, given that the algorithm is a generalization of iterative dynamic programming to the stochastic domain, the new algorithm exhibits reduced sensitivity to the problem dimension and therefore is well suited to the solution of dual control problems.

Analysis Tools for Achieving Low Variability Process Designs

In this area of research, a new process analysis tool has been developed consisting of a systematic algorithm for analyzing a block diagram representation of a process flowsheet and identifying the different paths that exist between a given input and output variable. Transfer function representations of different paths are calculated to determine the contribution of each path to the overall attenuation characteristics of the process. To improve these characteristics for a given process, the paths that contribute the most to the overall variability are identified and can then be addressed by the design engineer. This analysis tool has been extended for use as a design tool through the development of a set of guidelines that the engineer can use to come up with alternate process designs or control strategies to eliminate these identified paths, reduce their contribution to overall variability, or negate their effects by adding new paths. Although the ingenuity of the design engineer remains central, this tool provides the engineer with a means to identify problems in a process design, to help develop design alternatives/modifications, and a quantitative basis for comparison.

Proposed Research Directions for the Group

Ø Research and develop a better understanding of the interplay between process model identification and process controller performance based on the identified model;

Ø Research and develop novel methods of identification for control using a dual control formulation;

Ø Research and develop new methods for extending process identification, control and design into the field of systems biology.

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