Computation of Tight Uncertainty Bounds from Time-domain Data with Application to a Reactive Distillation Column

When deriving data-driven uncertainty descriptions that are compatible with robust controller design methods, it is still a challenge to quantify potentially nonlinear and time-varying model errors. One way to deal with such errors is to choose norm bounds on the error that are not contradicted by measured data which is here called model unfalsification. This methodology enables particularly reliable statements about the model error, if no a priori assumptions about measurement noise are made. Usually, in order to reduce the impact on the control performance, linear filters must be chosen. In this paper, in order to systematise the choice of linear filters, a methodology that minimises the conservatism in the frequency domain while maintaining the unfalsification property in the time domain is proposed, leading to a mixed frequency-and time-domain optimisation problem. The advantages of the approach are that tightness issues can be addressed in the frequency domain while time-domain unfalsification enables the consideration of nonlinearities and time-varying errors. The method is applied to experimental data from a reactive distillation process that exhibits nonlinear and time-varying behaviour.