Dynamic gain variable

A variety of devices have been designed by using transparent electro-optical ceramic materials, including variable optical attenuators (VOA), polarization controllers (PC), sinusoidal filters, dynamic gain flattening filters, tunable optical filters, and (2-switches, which have been described in detail in Ref. [129]. A brief description is given for some devices as follows. 

The time constant ti, of such a process is not a constant, but varies with h. But this is of little consequence, because the dynamic gain is constant. The ratio V/F must be recognized as the determining factor. It will appear again and again in different processes, with different forms of variables, but it is the fundamental time constant of any flowing system. Its units are those of time. For example, gal/(gal/min) = minutes. 

The problem has been identified as variable dynamic gain. It is a common problem, not often recognized, still less often anticipated. It occurs in processes where the values of the secondary dynamic elements, principally dead time, vary with flow. These variations cause proportionate changes in the period of the loop, which affects the dynamic gain of the principal capacity. 

Where the dynamic adaptive system controlled the dynamic gain of a loop, its counterpart seeks a constant steady-state process gain. This implies, of course, that the steady-state process gain is variable and that one particular value is most desirable. 

The terms K , g , Kq and g, represent the steady-state and dynamic gain terms for the manipulated variable and load. The feedforward control system is to be designed to solve for m, substituting r fix c ... 

Because this dead time varies inversely with flow, hence with thermal power, the process exhibits variable dynamic gain. But the feedforward signal Q is a multiplier in both power and temperature loops, providing gain adaptation. 

The flow of heat across the heat-transfer surface is linear with both temperatures, leaving the primaiy loop with a constant gain. Using the coolant exit rather than inlet temperature as the secondaiy controlled variable moves the jacket dynamics from the primaiy to the secondaiy... 

Basic process control system (BPCS) loops are needed to control operating parameters like reactor temperature and pressure. This involves monitoring and manipulation of process variables. The batch process, however, is discontinuous. This adds a new dimension to batch control because of frequent start-ups and shutdowns. During these transient states, control-tuning parameters such as controller gain may have to be adjusted for optimum dynamic response. 

MD calculations may be used not only to gain important insight into the microscopic behavior of the system but also to provide quantitative information at the macroscopic level. Different statistical ensembles may be generated by fixing different combinations of state variables, and, from these, a variety of structural, energetic, and dynamic properties may be calculated. For simulations of diffusion in zeolites by MD methods, it is usual to obtain estimates of the diffusion coefficients, D, from the mean square displacement (MSD) of the sorbate, (rfy)), using the Einstein relationship (/) ... 

An important advantage of the RGA method is that it requires minimal process information, namely, steady-state gains. Another advantage is that the results are independent of both the physical units used and the scaling of the process variables. The chief disadvantage of the RGA method is that it neglects process dynamics, which can be an important factor in the pairing decision. Thus, the RGA analysis... 

The variability of the process parameters with flow causes variability in load response, as shown in Fig. 8-50. The PID controller was tuned for optimum (minimum-IAE) load response at 50 percent flow. Each curve represents the response of exit temperature to a 10 percent step in liquid flow, culminating at the stated flow. The 60 percent curve is overdamped and the 40 percent curve is underdamped. The differences in gain are reflected in the amplitude of the deviation, and the differences in dynamics are reflected in the period of oscillation. 

From a dynamic response standpoint, the electronic adjustable-speed pump has a dynamic characteristic that is more suitable in process control applications than those characteristics of control valves. The small amplitude response of an adjustable-speed pump does not contain the dead band or the dead time commonly found in the small amplitude response of the control valve. Nonlinearities associated with friction in the valve and discontinuities in the pneumatic portion of the control valve instrumentation are not present with electronic variable-speed drive technology. As a result, process control with the adjustable-speed pump does not exhibit limit cycles, problems related to low controller gain, and generally degraded process loop performance caused by control valve nonlinearities. 

It is important to remember that a deadtime or several lags must be inserted in most control loops in order to mn a relay-feedback test. To have an ultimate gain, the process must have a phase angle that drops below —180°. Many of the models in Aspen Dynamics have only a first-order transfer function between the controller variable and the manipulated variable. In the CSTR temperature controller example, the controlled variable is reactor temperature and the manipulated variable is medium temperature. The phase angle of a first-order process goes to only —90°, so there is no ultimate gain. The relay-feedback test will fail without the deadtime element inserted in the loop. 

Shinsky (1979) uses a relative gain matrix to select which variables to manipulate and measure. Again dynamics are ignored. The method allows one to find which variables influence which others the most if they were put into a feedback control loop. 

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