Model reduction state truncation

In this paper we present a Model Reduction technique incorporated with multi-parametric programming and control, namely Balanced Truncation (T3T). The use of Balanced Truncation eliminates a number of states of dynamic linear systems, while a bound on the maximum error obtained for the output vector can be established. This then allows for the derivation of (approximate) linear parametric controllers, which can be tested and validated (against the original high-fidelity model) off-line. These theoretical developments are presented next. 

Linearize the open-loop dynamic model of the process at the two fixed points in Table 4. Then perform model reduction [38,39] to derive two reduced linear 4-state models. From the Jacobian of the full state model, balanced truncation was used to reduce the model order. The... 

In this chapter several model reduction techniques will be discussed. The first method is based on firequency response matching, other methods make use oficonversion ofi the model structure to a state space model and subsequently truncating the states that have a minimum impact on the input-output relationship. The main indicator used fior this purpose is the so-called Hankel singular value. In addition, the model structure is converted to a balanced realization, afiter which the reduction techniques can be applied. Several examples are given on how to apply the dififierent methods. 

These results have been explained in terms of two models in which account is taken of a non-equilibrium distribution over vibrational states the truncated harmonic oscillator and the Morse oscillator with all transitions allowed [83]. The dissociation may take place from any vibrational level. It is shown that as the temperature is increased, the contribution to the decomposition process from the high vibrational levels is severely diminished and it is the lower states that make the major contribution. It is the reduction in the number of reactive states that is... 

From the historical point of view and also from the number of applications in the literature, the common method is to use activity coefficients for the liquid phase, i.e., the polymer solution, and a separate equation-of-state for the solvent vapor phase, in many cases the truncated virial equation of state as for the data reduction of experimental measurements explained above. To this group of theories and models also free-volume models and lattice-fluid models will be added in this paper because they are usually applied within this approach. The approach where fugacity coefficients are calculated from one equation of state for both phases was applied to polymer solutions more recently, but it is the more promising method if one has to extrapolate over larger temperature and pressure ranges. 

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