Parameter mismatch

Figure 9.6. (a) The temperature dependence of the flow stress for a Ni-Cr-AI superalloy containing different volume fractions of y (after Beardmore et al. 1969). (b) Influence of lattice parameter mismatch, in kX (eflectively equivalent to A) on creep rupture life (after Mirkin and Kancheev... 

Figure 4.15 Evolution of the process composition variables for a 10% increase in the production rate at t = 0, under plant-model parameter mismatch, (a) Product purity and (b) reactor impurity level.

Figure 5.20 Evolution of the process stream flow rates for a 25% unmeasured increase in the inlet impurity levels yi0 occurring at t = 0, under plant-model parameter mismatch. The reaction rate and the mass-transfer coefficient /CB in the controller model are assumed to be overestimated by 10% compared with their values in the plant, (a) Effluent and recycle flow rates, and (b) product flow rate.

Figures 7.23-7.27 show the closed-loop profiles for a 10% increase in the production rate at operating point I (attained by increasing Fo), and a decrease in the purity setpoint to Cb,Sp = 1.888 mol/1 - this reduction is necessary since the nominal purity is beyond the maximum attainable purity for the increased throughput. Although controller design was carried out to account for the inverse response exhibited by the system at operating points II and III, and in spite of the plant-model parameter mismatch, the proposed control structure clearly yields good performance at operating point I as well.

Figure 7.23 Evolution of the coolant flow rate for a 10% rise in the production rate at operating point I, under plant-model parameter mismatch. The heat transfer coefficient U in the controller model is overestimated by 10% compared with its value in the plant.

Hazards of parameter mismatch. In the present model all results are solvable. We know the exact memory kernels in (152) and we can solve for the time evolution from (156). However, in realistic applications, one must ordinarily resort to approximations. In this situation, we get equations of the type (150) but with incorrect values of the parameters in the memory function. In order to display the possible disasters that may ensue, we modify the functions /i and /2 arbitrarily and look at the time evolution of the density matrix. 

E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore. Parameter mismatches and perfect anticipating synchronization in bidirectionally coupled external cavity laser diodes. Phys. Rev. E, 66 017206, 2002. 

Figure 3.5. The convert spectra dialog box indicating parameter mismatch.

RHEED oscillations are also particularly useful in monitoring the type of growth mode of the depositing material. Four different film growth modes are generally identified mainly related to the diffusion coefficient of the adatoms on the surface, the dimensions of the substrate terraces, and the lattice parameter mismatch between the substrate and the film ... 

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