Switch with delay model

The accuracy of fhe previous model decreases as the frequency of the signal source is increased due to the delay of the transistor. The delay at the turn off is generally greater than that at the turn on. The turn-off delay is easily included into the model using a pulse-delay device (Device 53) and 

99VBE1DF53+VBE1 C [NAME]63+[ INI] 99VBE1IN63+VBE1 C [NAME]60+[ INI] 99VBEIF 60+ZERO 98SW1CTL60+ZERO 

The nonlinear characteristic between the collector and emitter cannot be expressed by any conventional nonlinear resistor model, such as TYPE-92 resistor, because its characteristic depends not only on its terminal volt-age Vqe but also on the base current /g. The resistor is expressed by the TYPE-91 TACS-controlled resistor. Its resistance is calculated in the TAGS according to the collector-emitter voltage Vce base current /g, and transient characteristic of a transistor. This modeling technique is explained in the next section. 

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Responses of the switching circuit (a) measured result and (b) calculated result by the switch model. Responses of the switching circuit (c) calculated result by the switch model (with delay) and (d) calculated result by the proposed model. 

Presentation of a Reaction Mechanism. In the Na0 -CO reactions, after the reaction had achieved a steady state, the reaction gas mixture was switched into either a pure helium stream or a 02-He stream. The responses of C02 and CO were then followed. The CO(dec. , 0)-CO response obtained instantaneously responded zero with no delay, indicating that there was no reversibly adsorbed CO. Furthermore, the C0(dec.,0)-C02 response obtained was not affected by the presence of 02 in the stream, suggesting the nonexistence of irreversible adsorption of CO which could react with oxygen. Thus, a model of the direct reaction of gaseous CO with adsorbed oxygen, an Eley-Rideal type mechanism, may be proposed. 

The model thus shows how thresholds in the phosphorylation-dephosphorylation cascade controlling cdc2 kinase play a primary role in the mechanism of mitotic oscillations. The model further shows how these thresholds are necessarily associated with time delays whose role in the onset of periodic behaviour is no less important. The first delay indeed originates from the slow accumulation of cyclin up to the threshold value C beyond which the fraction of active cdc2 kinase abruptly increases up to a value close to unity. The second delay comes from the time required for M to reach the threshold M beyond which the cyclin protease is switched on. Moreover, the transitions in M and X do not occur instantaneously once C and M reach the threshold values predicted by the steady-state curves the time lag in each of the two modification processes contributes to the delay that separates the rise in C from the increase in Af, and the latter increase from the rise in X. The fact that the cyclin protease is not directly inactivated when the level of cyclin drops below C prolongs the phase of cyclin degradation, with the consequence that M and X will both become inactivated to a further degree as C drops well below C. ... 

Automatic control of purities is difficult due to the long time delays and the complex dynamics that are described by nonlinear distributed parameter models and switching of the inputs, leading to mixed discrete and continuous dynamics, small operating windows, and a pronouncedly nonlinear response of the purities to input variations. Because of the complex nonlinear dynamics of SMB processes, their automatic control has attracted the interest of many academic research groups and many different control schemes have been proposed however, few of them have been tested in experimental work for real plants with limited sensor information. 

The numerical results shown in Fig. 6.2 confirm that the rotation direction of n electrons temporally changes between clockwise and counterclockwise in the case of a single-pulse control. Switching of the rotation direction can be prevented efficiently, and unidirectional rotation of Jt electrons can be realized consecutively in a simple manner. In the three-level model analysis in a short-pulse limit, as already stated, the pulse with e+ (e ) creates a coherent superposition L) - - H) ( L) — H)), and L) - - H) created by a pump pulse with e+ evolves as L) - - H) L) — i H). Then the population in —) can be dumped to G) by applying a dump pulse with e just after the created state has completely shifted as L) — i H) L) — H). Thus, only clockwise rotation can be generated. Figure 6.3 shows the results of a pump-dump control simulation of an R enantiomer of DCPH. The values of the parameters of the pump pulse were/ = 2.24 GVm i, = 19.4 fs, co = 7.72 eVM, and e = e+, and those of the dump pulse were / = 2.37 GVm , tj = 19.4 fs, co = 7.72 eV/h, and e = e. The delay time between the pulses was 19.4 fs. 

A lock-in amplifier (Princeton Applied Research Model 5204) is used to measure in-phase and quadrature amplitudes of both the load and displacement signals and phase relation of each signal with respect to a reference from the Rheovibron . The calculator program sends a command to the multiprogrammer to switch on the load signal to the lock-in amplifier which, after a program delay for settling, reads the in-phase and quadrature components with respect to the reference, and stores them in the calculator memory. 

For systems described by a hybrid model at least some ARRs are mode-dependent. As a result, incipient faults may start when the system is in a mode that does not enable an ARR based approach to detect the fault because its contribution to an ARR or to a set of ARRs is cancelled out by switch states being equal to zero in that mode. An approach adopted from [6] and illustrated by a simple passive network with one switch is to allow for a delay time in fault isolation at least until the next mode change has happened so that faults that cannot be detected in the current mode can be detected and isolated after a mode change. 

Figure 4.21c illustrates the results obtained using the switch model with the turn-off delay. Even if the switching delay is included into the simulation, the accuracy is not improved. 

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