N. Lawrence Ricker

Decentralized control of the Tennessee Eastman Challenge Process

A decentralized control system is developed for the Tennessee Eastman Challenge Process (TE problem). The design procedure begins with the selection of the method for production-rate control, to which inventory controls and other functions are then coordinated. Results show that production rate can be maximized at any of the three standard product compositions, even when the feed of reactant A is lost. All specifications of the challenge problem are satisfied despite large disturbances in feed composition and reaction kinetics. Variability in product rate and quality is less than that seen in previous studies. The process can operate on-spec for long periods without feedback from composition measurements. Setpoints for certain variables (such as reactor temperature and concentrations of A and C in the reactor feed) must be chosen a priori, and the effect on operating cost is estimated. The performance of the proposed decentralized control is compared to that of a nonlinear model predictive control (NMPC) developed previously. There appears to be little, if any, advantage to the use of NMPC in this application. In particular, the decentralized strategy does a better job of handling constraints - an area in which NMPC is reputed to excel. Reasons for this are discussed.

Canonical partial least squares and continuum power regression

A method, canonical PLS, is proposed for performing the basic PLS calculations in the canonical co‐ordinate system of the predictor matrix X. This reduces the size of the problem to its smallest possible dimension as determined by the rank of X. The computation is further simplified since the cross‐product matrices X TX and XX T are symmetric. PLS weights, scores and loadings referring to the canonical co‐ordinate system can be easily back‐transformed to the original co‐ordinate system. The method offers an ideal setting to carry out the continuum regression approach to PLS introduced by Wise and Ricker. By raising the singular values to some power γ, one may artificially decrease (γ < 1) or increase (γ > 1) the degree of multicollinearity in the X data. One may investigate a series of models by considering various values of the power γ. This offers a means to push the model into the direction of ordinary least squares (γ = 0) or principal components regression (γ→∞), with PLS regression as an intermediate case (γ = 1). Since all these computations are mainly performed in canonical space, obtained after one singular value decomposition, a considerable gain in speed is achieved. This is demonstrated over a wide range of data set sizes (number of X and Y variables, number of samples) and model parameters (number of latent variables and number of powers considered). The gains in computational efficiency (as measured by the ratio of the number of floating point operations required relative to the original algorithm) range from a factor of 3·9 to over 100. Copyright

Model predictive control of a continuous, nonlinear, two-phase reactor

Abstract The Tennessee Eastman challenge problem is simplified to a plant with eight states, four manipulated variables, and 10 outputs. Six regulation/optimization scenarios are proposed. The modified problem retains nonlinearities that cause difficulties in the original, e.g. certain gains can change sign. Steady-state relative-gain analysis suggests variable pairings for multi-loop feedback control that turn out to be inappropriate. A more robust, near-optimal multi-loop design is proposed and tested in simulations. Two model predictive control (MPC) designs are also tested. The first is based on a linear time-invariant (LTI) model of all the plant interactions. Gain variations make it impossible to achieve acceptable performance. The second uses a LTI model in which 10 of the 16 transfer functions are zero, i.e. it includes only the most important plant responses. The resulting MPC performance is comparable or better than the multi-loop design. Alternative MPC strategies are also discussed.

Panel Discussion: Emerging Industrial Applications

This panel was organized to allow representatives of several firms to describe some current, practical applications of biological methods, including genetic technologies, in control of hazardous wastes and other pollutants. Our moderator, Dr. Ricker, is engaged in chemical engineering approaches to wastewater problems. There is a growing relationship between our School of Engineering and the Health Sciences Schools in high-tech applications. I trust that in the years ahead, both here and elsewhere, there will be more substantial collaboration across academic fields between scientists and engineers both in universities and with their counterparts in industry.

Automatic Control of Chemical Processes

Modern strategies for the automation of chemical processes are surveyed with an emphasis on control algorithms that incorporate a mathematical model of the system to be controlled. This approach can be advantageous when simpler classical feedback methods fail to provide adequate control.