Empirical Detection of Time Scales in LTI Systems using Sparse Optimization Techniques

Dynamical Soft Sensors from Scarce and Irregularly Sampled Outputs Using Sparse Optimization Techniques

“…In this section, an auxiliary model which estimates the outputs at base uniform sampling interval, to be further used for parametric soft sensor model development from irregularly sampled scarce measurements, is formulated. The proposed formulation is similar to the work by Pinnamaraju et al, 17 where overparameterized Laguerre filters are combined with SPOPT for empirical detection of time scales in LTI systems. In this work, we formulate these ideas to deal with irregularly sampled systems for the purpose of developing efficient AMs for soft sensing applications.…”

“…Also, a certain choice of Laguerre pole and order limits the maximum delay that it can explain, as shown below: d max = prefix− 2 ( L − 1 ) T s log ( p ) where d max is the maximum delay, L is the order of Laguerre filters, T s is the sampling interval, and p is the chosen discrete-time pole. The choice of poles becomes extremely difficult when the dynamics are spread at multiple time scales either within a particular input–output channel , or across the channels, in the case of multi-input systems. It is therefore important to choose a model structure which is flexible to capture all the process complexities such as delays and fast-slow dynamics yet maintains model parsimony.…”

“…In this work, in order to deal with different complexities of linear dynamics, we introduce sufficient flexibility in the model structure by expanding the LTI system using finite-order Laguerre filters not just at a single pole but at multiple poles. These ideas were previously used by Pinnamaraju et al 17 for empirical detection of time scales in LTI systems. The output that is irregularly sampled is represented by a redundant basis, which comprises of filtered inputs that are generated by finiteorder Laguerre filters characterized by multiple poles.…”

A Contraction-constrained Model Predictive Control for Multi-timescale Nonlinear Processes

“…Whilst many chemical processes can be modelled with a high level of accuracy by using more than one time scale [4], [5], the use of such models can be computationally challenging [6]. In some cases, this introduced complexity is necessary since controller design using a model in only one timescale may cause instability when applied to the physical system.…”