Processing gain

Adaptive Control. An adaptive control strategy is one in which the controller characteristics, ie, the algorithm or the control parameters within it, are automatically adjusted for changes in the dynamic characteristics of the process itself (34). The incentives for an adaptive control strategy generally arise from two factors common in many process plants (/) the process and portions thereof are really nonlinear and (2) the process state, environment, and equipment s performance all vary over time. Because of these factors, the process gain and process time constants vary with process conditions, eg, flow rates and temperatures, and over time. Often such variations do not cause an unacceptable problem. In some instances, however, these variations do cause deterioration in control performance, and the controllers need to be retuned for the different conditions. 

Controller gain Load transfer function gain Measurement gain Process gain... 

Feedback Control In a feedback control loop, the controlled variable is compared to the set point R, with the difference, deviation, or error e acted upon by the controller to move m in such a way as to minimize the error. This ac tion is specifically negative feedback, in that an increase in deviation moves m so as to decrease the deviation. (Positive feedback would cause the deviation to expand rather than diminish and therefore does not regulate.) The action of the controller is selectable to allow use on process gains of both signs. 

The controller gain is inversely proportional to the process gain for constant dead time and time constant. 

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

However, the steady-state process gain described by this derivative varies inversely with liquid flow Adding a given increment of heat flow to a smaller flow of liquid produces a greater temperature rise. 

This transfer function provides us with an estimate of the process gain... 

The positive results obtained at production scale give us confidence in the validity of our approach. Derivation of a simple scaling factor enabled us to conduct a series of experiments in a small pilot plant which would have been expensive and time-consuming on a production scale. Time series analysis not only provided us with estimates of the process gain, dead time and the process time constants, but also yielded an empirical transfer function which is process-specific, not one based on... 

The process gain (sensitivity) can be determined from steady-state values, and using these values can reduce the work required by the parameter estimation routines later. For narrow ranges of temperature, the following formulas for steady-state temperatures should be adequate ... 

Kll, K12, K21, K22 = process "gains", the proportional constants between a process input (the fraction of total of power going to the heaters in this extruder) and the steady state temperature of a node,... 

Recent considerations of metal UPD on semiconductor surfaces suggest that light-assisted processes gain much significance in the relevant technology. The use of photoinduced UPD as an approach for the preparation of compounds and composite semiconductors either in thin films (layered structures) or in particulate suspensions is a challenging issue that will be outlined promptly. 

This quantity is also called the static gain or dc gain by electrical engineers. When we talk about the model of a process, we also use the term process gain quite often, in distinction to a system gain. 

Example 5.2 Derive the closed-loop transfer function of a system with proportional control and a second order overdamped process. If the second order process has time constants 2 and 4 min and process gain 1.0 [units], what proportional gain would provide us with a system with damping ratio of 0.7 ... 

Let s take a look at the logic when we control the liquid level by manipulating the outlet valve (Fig. 5.9). In this case the process gain Kp associated with the outlet flow is negative. If the liquid level drops below the set... 

Figure 5.9. Manipulate liquid level with an outlet valve. The process gain is negative in this case.

However, MATLAB allows us to get the answer with very little work—something that is very useful when we deal with more complex systems. Consider a numerical problem with values of the process gain Kp = 1, and process time constants X = 2 and x2 = 4 such that the closed-loop equation is... 

We may question other obvious scenarios of the process gain matrix. The sweetest is an identity matrix, meaning no interaction among the manipulated and controlled variables. A quick summary of several simple possibilities 10... 

You may not find observing the process gain matrix satisfactory. That takes us to the relative gain array (RGA), which can provide for a more quantitative assessment of the effect of changing a manipulated variable on different controlled variables. We start with the blending problem before coming back to the general definition. 

No doubt there are interactions from other loops, and from (10-37), some of the process gains must have opposite signs (or act in different directions). When Ay = 0.5, we can interpret that the effect of the interactions is identical to the open-loop gain—recall statement after (10-36). When Ay > 0.5, the interaction is less than the main effect of nij on Cj. However, when Ay < 0.5, the interactive effects predominate and we want to avoid pairing nij with c . 

There are interactions from other loops as well, but now with all the process gains having the same sign. Avoid pairing nij with c if Ay is... 

Assuming that the maximum target velocity is equal to 3M (lOOOm/s), the maximum value of the time-bandwidth product is limited to 150,000. The maximum processing gain is then equal to 51.7 dB. The use of a windowing function will decrease this value by a few dB. The maximum detection range for the noise radar is given by the formula... 

In Chap. 15 we reviewed a tittle matrix mathematics and notation. Now that the tools are available, we will apply them in this chapter to the analysis of multivariable processes. Our primary concern is with closedloop systems. Given a process with its matrix of openloop transfer functions, we want to be able to see the effects of using various feedback controllers. Therefore we must be able to find out if the entire closedloop multivariable system is stable. And if it is stable, we want to know how stable it is. The last question considers the robustness of the controller, i.e., the tolerance of the controller to changes in parameters. If the system becomes unstable for small changes in process gains, time constants, or deadtimes, the controller is not robust. 

The last group of dyads considered here are those that incorporate TTFs in their structure. TTFs are powerful organic donors, which, when linked to the fullerene core and engaged in charge-separation processes, gain rather than lose aromaticity [128]. The modification of the donor strength on the TTF moiety in dyads (31a-c) allows the tuning of the... 

Above 180 K, 16a decays by both intersystem crossing (/cjsc) and cyclization (A r), with the latter process gaining relative to the former as... 

The moisture content of the 15 tray-dried batches following final mix remained essentially unchanged from the drying step. The batches from the fluid bed process gained moisture. This is probably attributable to handling very dry material in a relatively humid environment. Both groups are still below the target for this step of 1.5 %, however. 

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