Closed-loop multiplicity

Closed-loop Multiplicity. One of the interesting features of nonlinear systems is the possible appearance of multiple steady states. Most researchers have explored open-loop multiplicity. We found that closed-loop multiplicity occurs in the methyl acetate/methanol/ water system. 

Fignre 6.13 MeAc/Me0H/H20 closed-loop multiplicity. 

A control system may have several feedback control loops. For example, with a ship autopilot, the rudder-angle control loop is termed the minor loop, whereas the heading control loop is referred to as the major loop. When analysing multiple loop systems, the minor loops are considered first, until the system is reduced to a single overall closed-loop transfer function. 

Figure 11. Output coil for either open-loop or closed-loop operation. Multiple output coils may be used in a variety of configurations.

Thus we have described a system and process having a multiplicity of iterative feedbacks and feedforwards from each component and subprocess, to every other component and subprocess, all increasing the energy collected in the system and furnished to the load. In open-loop operation, this results in COP >1.0 permissibly, since the excess energy is freely received from an external source. In closed-loop operation, the COP concept does not apply except with respect to operational efficiency. In that case, the operational... 

A closed loop optimization experiment was presented in order to investigate the ability to control the ionization of NaK clusters in a molecular beam. The analysis of the optimized pulse shows that the maximum intensity of the ion signal was obtained with a pulse structure containing intensity maxima separated by a multiple of half vibrational periods. The proposed simple model in order to explain the pulse structure is based on previously performed pump-probe experiments [6]. 

The GA procedure has an interactive feedback (closed) loop structure without any intervention by the experimentalist. An initial guess of multiple sets of control fields is evaluated for its success in achieving the target. The most successful members of this population are transformed by the three GA operators, and their offspring are evaluated. 

For two-time-scale systems, it is well established that inversion-based controllers designed without explicitly accounting for the time-scale multiplicity are ill-conditioned and can lead to closed-loop instability. In order to avoid such issues, controller design must be addressed on the basis of the reduced-order representations of the slow and fast dynamics, an approach referred to as composite control (see, e.g., Chow and Kokotovic 1976, 1978, Saberi and Khalil 1985, Kokotovic et al. 1986, Christofides and Daoutidis 1996a, 1996b). 

In the example illustrated in Figure 8 the isotope of interest is concentrated in the liquid phase. A feed solution is introduced at the top of a cold tower where it equilibrates in a multiplate column against a gas stream with which it undergoes an isotopic exchange reaction. The isotope concentration builds up to a maximum at the bottom of the cold tower. The hot tower serves as a refluxer for the cold tower. Its performance and function can be seen by focusing attention on the gas stream which is in a closed loop. At the top of the cold tower the gas stream composition is determined by equilibration against the cold feed liquid... 

The results obtained in the closed-loop control are summarised in Fig. 1 where five time varying curves are presented. The first one is the controlled variable (< B), the second is the input or control variable (A / F) he third is the feed concentration change ( ao), the fourth is the performance index (or objective function) and the last one is the computational time required to get the solution. It should be noted that it happens to the system under consideration to exhibit a steady-state input multiplicity and thus several solutions. This point is well discussed in [12],... 

Another fundamental state variable that can be regulated during the cycle is cavity pressure. Closed loop control of cavity pressure could automatically compensate for variations in melt viscosity and injection pressure to achieve a consistent process and consistency of molded products. Adaptive control methods have been developed to track the cavity pressure profile at one location in the mold. In these earlier works, cavity pressure control was handicapped by the absence of actuators for distributed pressure control, as conventional molding machines are equipped with only one actuator (the screw), which prevents the simultaneous cavity pressure control at multiple points in the mold. This problem has been solved with the development of dynamic melt flow regulators that allow control of the flow and pressure of the polymer melt at multiple points in the mold.[ °l... 

As alternatives to the closed-loop balling circuit (see Section 4.2.1.3.5) there have been several proposals to achieve classification in the drum by various internal designs. For example, a multiple-cone drum pelletizer was described. 

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