Dominant pole placement with fractional order PID controllers: D-decomposition approach.

Dominant pole placement is a useful technique designed to deal with the problem of controlling a high order or time-delay systems with low order controller such as the PID controller. This paper tries to solve this problem by using D-decomposition method. Straightforward analytic procedure makes this method extremely powerful and easy to apply. This technique is applicable to a wide range of transfer functions: with or without time-delay, rational and non-rational ones, and those describing distributed parameter systems. In order to control as many different processes as possible, a fractional order PID controller is introduced, as a generalization of classical PID controller. As a consequence, it provides additional parameters for better adjusting system performances. The design method presented in this paper tunes the parameters of PID and fractional PID controller in order to obtain good load disturbance response with a constraint on the maximum sensitivity and sensitivity to noise measurement. Good set point response is also one of the design goals of this technique. Numerous examples taken from the process industry are given, and D-decomposition approach is compared with other PID optimization methods to show its effectiveness.

A new approach to the phenomena at the interfaces of finely dispersed systems.

A new idea has been applied for the elucidation of the electron and momentum transfer phenomena, at both rigid and deformable interfaces, in finely (micro-, nano-, atto-) dispersed systems. The electroviscoelastic behavior of, e.g., liquid/liquid interfaces (emulsions and double emulsions), is based on three forms of "instabilities"; these are rigid, elastic, and plastic. The events are understood as interactions between the internal (immanent) and external (incident) periodical physical fields. Since the events at the interfaces of finely dispersed systems must be considered at the molecular, atomic, and/or entities level it is inevitable to introduce the electron transfer phenomenon beside the classical heat, mass, and momentum transfer phenomena commonly used in chemical engineering. Therefore, an entity can be defined as the smallest indivisible element of matter that is related to the particular transfer phenomena. Hence, the entity can be either differential element of mass/demon, ion, phonon as quanta of acoustic energy, infon as quanta of information, photon, and electron. Three possible mathematical formalisms have been derived and discussed related to this physical formalism, i.e., to the developed theory of electroviscoelasticity. The first is the stretching tensor model, where the normal and tangential forces are considered, only in mathematical formalism, regardless of their origin (mechanical and/or electrical). The second is the classical integer-order van der Pol derivative model. Finally, the third model comprises an effort to generalize the previous van der Pol differential equations, both linear and nonlinear, where the ordinary time derivatives and integrals are replaced by corresponding fractional-order time derivatives and integrals of order p < 2 (p = n - delta, n = 1,2,delta << 1). In order to justify and corroborate a more general approach the obtained calculated results were compared to those experimentally measured using the representative liquid/liquid system.

Electroviscoelasticity of liquid/liquid interfaces: fractional-order model.

A number of theories that describe the behavior of liquid-liquid interfaces have been developed and applied to various dispersed systems, e.g., Stokes, Reiner-Rivelin, Ericksen, Einstein, Smoluchowski, and Kinch. A new theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems and is based on a new constitutive model of liquids. According to this model liquid-liquid droplet or droplet-film structure (collective of particles) is considered as a macroscopic system with internal structure determined by the way the molecules (ions) are tuned (structured) into the primary components of a cluster configuration. How the tuning/structuring occurs depends on the physical fields involved, both potential (elastic forces) and nonpotential (resistance forces). All these microelements of the primary structure can be considered as electromechanical oscillators assembled into groups, so that excitation by an external physical field may cause oscillations at the resonant/characteristic frequency of the system itself (coupling at the characteristic frequency). Up to now, three possible mathematical formalisms have been discussed related to the theory of electroviscoelasticity. The first is the tension tensor model, where the normal and tangential forces are considered, only in mathematical formalism, regardless of their origin (mechanical and/or electrical). The second is the Van der Pol derivative model, presented by linear and nonlinear differential equations. Finally, the third model presents an effort to generalize the previous Van der Pol equation: the ordinary time derivative and integral are now replaced with the corresponding fractional-order time derivative and integral of order p<1.