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This class of processes is very important for chemical engineering.
In this paper, we present and illustrate a strategy for identifying appropriate control-relevant models for this class of processes.
For this class of processes, it is essential to have good estimation of the very small difference between certain transfer functions, or, low gain direction.
For this class of processes we derive a SMB analog the R-SMB process and demonstrate, under the framework of the equilibrium theory, that this process has the same separation region as the classical SMB for linear adsorption systems.
In this class of processes the flow through a zone (or column) is always in one of the three states: (i) frozen, (ii) completely directed to the next zone (or column), or (iii) entirely diverted to a product line.
The control system claims to be of practical implementation in the sense that: (i) it manages both measurement types existing in this class of processes: continuous-instantaneous, and discrete-delayed with a periodic sampling-time; and (ii) its designing exploits the linear systems theory on the basis of the reactor model.
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For this class of stable processes it is proposed to apply a higher-order filtering to the open-loop process step response and to approximate the filtered step response with stable SOPDT models.
Although there is much to say about the theoretical aspects of this class of stochastic processes, we basically refer to the power law in Eq. (8) in the following.
For this class of stochastic processes we prove that it is difficult if not impossible to design an exact parallel algorithm if the function f(k) is monotonous with an injective derivative.
Actually, this class of proteolytic processes (macrocategory "folding, sorting and degradation" in Fig. 2) has the highest values of phase i.e., it has the slowest response to the transcription bursts.
An adaptive controller is designed for this general class of processes so that the external substrate can be regulated by the dilution rate into a prespecified arbitrarily small neighbourhood of a constant setpoint reference.
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