Reference Management for Steady-State Transitions Under Constrained Model Predictive Control

Abstract

There are increasing economic incentives within the chemical process industry towards demand driven operation with product diversification, requiring flexible operation in responsive plants. In continuous processes, this is realized through steady-state transitions but requires consideration of process dynamics arising from operation that is inherently transient in nature. The steady-state economic optimum is typically defined at the intersection of constraints, and requires multivariable control with optimal constraint handling capabilities. Thus, constrained model predictive control is well-suited to realize the profit potential at the economic optimum. In this thesis, feasible and optimal steady-state transitions are achieved using reference management with consideration of the closed-loop dynamics of constrained model predictive control. The supervisory control scheme is used to determine the optimal setpoint trajectory which is subsequently tracked by regulatory control, incorporating feedback for the rejection of high frequency disturbances and eliminating steady-state offset in the presence of model mismatch. The separation of economic and control objectives enables the lower level to be tuned for stability and the upper level to be tuned for performance. The mathematical formulation results in a multi-level optimization problem with an economic objective function at the upper level, and a series of control performance objective functions arising from constrained model predictive control at the lower levels. The solution strategy proposed converts the multi-level optimization problem into a single-level optimization problem using the Karush-Kuhn-Tucker conditions, and solves the resulting complementarity conditions using an interior point approach. Alternative objective formulations are investigated based on maximizing profit during transient operation. The first formulation is typically based on a quadratic objective function minimizing the transition time, indirectly improving economic operation by reducing the amount of off-specification product produced. The second formulation is based on the explicit consideration of economics. The profit calculated during transient operation is based on the difference between the revenue generated by the production of acceptable product within specified univariate product quality bands, and the operational costs of raw materials and utilities. The resulting linear objective function is further extended to incorporate control performance considerations to improve conditioning for gradient based optimization. The proposed methodology is applied to a single-input single-output linear system, demonstrating the potential benefits of simultaneous rather than sequential optimization in terms of computational efficiency and solution reliability. Alternative objective function and constraint formulations are investigated, and the effect on the optimal solution assessed. In particular, the possibility of indeterminacy is shown and handled using hierarchical optimization. The methodology is also demonstrated on additional examples including non-minimum phase systems and multi-input multi-output linear systems. Application to a multi-input multi-output nonlinear system corresponding to styrene polymerization using the proposed methodology is detailed. The set of differential and algebraic equations defining the process is discretized using orthogonal collocation on finite elements. The optimal operation during grade transitions based on explicit consideration of economics is determined, and additional improvements realized by manipulating the production rate. Finally, reference management with online re-optimization is investigated for a single-input single-output linear system based on a bias update, and the improvement in closed-loop performance assessed for output disturbances and model mismatch. The methodology is also demonstrated on a multi-input multi-output system based on a linear model when applied to the nonlinear process. The proposed methodology developed for steady-state transitions may also be applied to batch operation, startups and shutdowns. Future extensions include analysis of closed-loop stability due to the incorporation of feedback within the cascade control scheme, and the explicit consideration of uncertainty.