John W. Eaton

Feedback control of chemical processes using on-line optimization techniques

Abstract The objective of this research is to develop tools for feedback control and sensitivity analysis of systems modelled by nonlinear differential-algebraic equations. Features of this novel approach include: direct use of nonlinear models without linearization, the ability to handle multiple inputs and outputs without pairing, and the ability to handle input and output constraints without complicated anti-reset windup logic. In the model-predictive control framework, an optimal control policy for the nominal plant is determined using a simultaneous optimization and model solution approach. The sensitivity of the optimal solution with respect to the model parameters is also computed. The feedback from the measurements is used to update the important process model parameters and output disturbances. The optimal profile is then recomputed for the updated model. Confidence intervals can also be placed on the optimal control profiles by considering second-order variations in the Lagrangian. This approach will be illustrated with several examples including: batch and continuous chemical reactors, and a batch crystallizer, which demonstrates the method on a nonlinear, distributed parameter system.

Receding horizon control and discontinuous state feedback stabilization

This paper addresses three aspects of receding horizon control in discrete-time: (1) feedback stabilization of general nonlinear systems with receding horizon control; (2) the generation of stabili...

Model-predictive control of chemical processes

Abstract This paper discusses model-predictive control, a scheme in which an open-loop performance objective is optimized over a finite moving time horizon. Model-predictive control is shown to provide performance superior to conventional feedback control for nonminimum phase systems or systems with input constraints when future set points are known. Stabilizing unstable linear plants and controlling nonlinear plants with multiple steady states are also discussed.

Modelling and control of crystallizers

Abstract This paper provides an overview of modelling, measurement, identification and control issues arising in crystallizers. The crystal size distribution is modelled with a population balance. The remaining reactor states, such as concentrations temperature, are modelled with integro-differential equations. The models are solved numerically with global orthogonal collocation for continuous reactors and orthogonal collocation on finite elements for batch reactors. The ill-conditioned problem of estimating crystal size distribution from laser light scattering data is examined. The estimation of crystallization kinetic constants from supersaturation data and light scattering data is also discussed. Finally control problems are discussed and an optimal batch crystallization temperature profile is computed.

Model-predictive control and sensitivity analysis for constrained nonlinear processes

Abstract This paper describes methods for feedback control and sensitivity analysis of systems modeled by nonlinear differential-algebraic equations. An optimal control policy for the nominal plant is determined using a simultaneous optimization and simulation approach. The sensitivity of the optimal solution with respect to the model parameters is then computed. The feedback from the measurements is used to update the important model parameters. Confidence intervals are also placed on the optimal control profiles by considering second order variations in the Lagrangian. Computational results are shown for two process models of interest in chemical engineering.

Stability of neural net based model predictive control

This paper illustrates the stability problems associated with the use of finite horizon model predictive controllers by using a recurrent neural network to predict accurately the input-output response of a simple linear system that exhibits nonminimum-phase behavior. The stability of the resulting closed-loop system depends on the particular tuning parameters of the controller (horizon length, penalty weights, etc.) even in the absence of process-model mismatch. Although these problems are not unique to neural net models, or even finite-horizon model predictive controllers, most modern control theories have addressed the nominal stability problems encountered with controllers based on other forms of input-output models. Similarly, it is desirable to establish a framework for model predictive control using neural network models that does not suffer from nominal stability problems. In this paper, the authors propose a state-space description of a class of externally recurrent neural network model. This state-space description allows the application of theoretical results for nonlinear systems to ensure nominal stability for the resulting closed-loop system.

Model Predictive Control of Chemical Processes

This paper discusses model predictive control, a scheme in which an open-loop performance objective is optimized over a finite moving time horizon. Model predictive control is shown to provide superior control for nonminimum phase systems and systems with input constraints when future setpoints are known. Stabilizing unstable linear plants and controlling nonlinear plants with multiple steady states are also discussed.