Addressing uncertainty and modeling error in the design and control of process systems : methods and applications
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A process system faces the challenge of uncertainty throughout its lifetime. At the design stage, uncertainty originates from inaccurate knowledge of design parameters and unmeasured or unmeasurable ambient disturbances. Oftentimes, designers choose to increase system size to account for uncertainty and fluctuations; however, this approach has an economic limit, past which the capital expenditure outweighs the potential operational benefits. In the operational stage, uncertainty is manifest, amongst others, in fluctuations in operating conditions, market demand and raw material availability. Another type of uncertainty in (modern) process operations is related to the quality of process models that are used for making control and operational decisions. Of particular importance is the quality of the dynamic models that are used in real-time optimal control computations. The chemical industry has been the pioneer (and is currently the leader) of model predictive control (MPC) implementations, whereby the control moves are computed, over a receding time horizon, by solving an optimal control problem at each time step. While uniquely able to deal with large-scale, non-square constrained systems, MPC is vitally dependent on the predictive abilities of the built-in model. Changes in plant conditions are a a source of uncertainty in this case as-well, leading to a discrepancy (mismatch) between the model predictions and the true plant behavior. In this dissertation, I address the problems of design under uncertainty and plant-model mismatch. For the former, identification-based optimization (IBO) framework is proposed as a new, computationally efficient framework for optimizing the design of dynamic systems under uncertainty problem. The framework uses properly designed pseudo-random multilevel signals (PRMS) to represent time-varying uncertain variables. This allows us to formulate the design under uncertainty problem as a dynamic optimization problem. A solution algorithm is proposed using a sequential approach. Several application examples are discussed, demonstrating the superior computational performance of the IBO approach. Furthermore, an extension of the method that explicitly considers the tradeoff between conservativeness and dynamic performance is introduced. The latter, plant-model mismatch problem, is addressed using a novel autocovariance-based approach. Under appropriate assumptions, an explicit relation is established between the autocovariance of the process output and the plant-model mismatch terms, represented either in a step response model or a transfer function model. It is demonstrated that an asymptotically correct set of estimates of the values of plant-model mismatch for each model parameters is the global minimizer of the discrepancy between the autocovariance predicted using the relation and the autocovariance calculated from a data set collected from closed-loop operating data. Extensions of this approach handle cases where the active set of the MPC is changing over time and there are setpoint change and measurable disturbances occur in the control loop.