A study of integrated experiment design for NMPC applied to the Droop model

- Two techniques for integration experiment design in NMPC.
- First technique results in nonlinear matrix inequality (NLMI).
- NMLI is tackled by Sylvester's criterion allowing implementation in existing tools.
- Second technique uses the notion of economic experiment design.
- Single scalar constraint is obtained representing the predicted economic loss.

Nonlinear model predictive control (NMPC) has become an important tool for optimization based control of many (bio)chemical systems. A requirement for a well-performing NMPC implementation is obtaining and maintaining an appropriate mathematical process model. To cope with model degradation in view of plant changes and/or system evolution, developments have been made for linear systems to incorporate the information content of future measurements in the closed loop objective. However, formulations for integrated experiment design in nonlinear systems (iED-NMPC) remain scarce. Two different formulations are studied in this paper and applied to a bioprocess, namely, algae growth as described by the Droop model. First, a formulation for the integration of experiment design in linear dynamic systems is extended to nonlinear dynamic systems resulting in an NMPC formulation with integrated experiment design. In a second approach, the notion of economic optimal experiment design is incorporated within the NMPC formulation. Here, an economic loss function related to inaccurate parameter estimates is minimized instead of a measure of the parameter variances, resulting in improved control performance. The advantage of the proposed techniques over a naive experiment design integration approach is illustrated with Monte Carlo simulations.