Input-output behavior

This system clearly appears decomposed into a linear subsystem zi, which is the only responsible for the input-output behavior, and a non linear subsystem Z2, whose behavior is stable. Then, by defining the control error as e = St — S ), it is clear to observe that the solution of the linear subsystem is given by e = exp —Kc t), which implies that St S as t oo. ... 

We will speak of a reverberation algorithm, or more simply, a reverberator, as a linear discrete-time system that simulates the input-output behavior of a real or imagined room. The problem of designing a reverberator can be approached from a physical or perceptual point of view. 

The preceding pages demonstrate that the input-output behavior of many molecular systems can already be described in terms of fundamental logic operations. It has also been suggested above that what is explicitly described is the tip of an iceberg when one takes into account the rich literature on analytical reagents in various domains. The identification and taxonomy of individual cases must be a natural... 

Truncation is the exclusion of some of the last state variables of the balanced system, which are the state variables of least importance for the input-output behavior. This results in a system of lower order than the original system, with an input-output behavior similar to that of the linearized, but not exactly the same. In the coming section we will describe the mathematical procedure of balanced truncation, but for more details we refer to Chapter 7 in the book by Athanasios [107]. 

There are n HSVs, each corresponding to a state variable in the balanced system. The states that correspond to low HSVs, also have little influence on the input-output behavior of the system, and can hence be truncated away without much loss. It is not the absolute values that are of interest, but the difference between the values. The principle is illustrated in the the next section. 

Finally, let us consider the limit gq —> 0 in the slow time scale t, where the ratios lim l o C// i become indeterminate. By denoting these unknown, yet finite terms by Zi, i = 0,..., N + 1, we obtain a description of the slow dynamics of the column that captures its slow input-output behavior. This description is in the form of a DAE system of nontrivial index, since the algebraic constraints Ci = 0 are singular with respect to the algebraic variables zq a state-space... 

Once the large internal flow rates have been set via appropriate control laws, the index of the DAE system (7.21) is well defined, and a state-space realization (ODE representation) of the slow subsystem can be derived. This representation of the slow dynamics of the column can be used for the derivation of a model-based nonlinear controller to govern the input-output behavior of the column, namely to address the control of the product purity and of the overall material balance. To this end, the small distillate and bottoms flow rates as well as the setpoints of the level controllers are available as manipulated inputs. 

Cross-correlation can be used to investigate the input-output behavior of an analytical system to compare a theoretical band shape with an observed one. The greatest correspondence between the two time series is observed in the correlogram at the position where a maximum for the empirical correlation is found (Figure 3.26). 

Model order reduction (MOR) is a set of theories and techniques that reduce the order of a complex dynamic system while preserving its essential properties and input-output behavior for efficient and accurate simulation and design. 

At the time Vhdl was designed, the main objective of the language was to describe and simulate the input/output behavior of an existing hardware module. As a consequence, the semantics of Vhdl was based on the concept of the event-driven hardware simulator ... 

A particularly important requirement is to preserve the input/output behavior of the original language (for the chosen subset), with respect to some abstraction of the interface to the external world. L. Berrojo et al. [2] suggest a subset somewhat similar to that presented in the following subsection, but the interpretation of their subset violates this cardinal rule. 

In order to ensure preservation of the input/output behavior between the Vhdl and the ProcVhdl interpretation, the following abstraction is imposed on the interface ... 

In the previous chapters deterministic models were derived. They were designed based on the chemical and physical balances and mechanisms of the process and consequently the model described the internal functional behavior. Black-box models, on the other hand, are designed based on the input-output behavior of the process and consequently the model describes the overall behavior. A black-box model consists of a certain stmcture of which the parameters are determined by means of experimental results. Therefore, they often are called experimental models. The main properties of black-box models are the stmcture characteristics, which are level of detail, degree of non-linearity and the stmctural way in which dynamics are composed. 

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