PID Characteristics

Compound class selective (for organic compounds with more easily ionizable Jt-electrons, especially aromatic compounds) nondestructive mass-flow detector slightly more seusitive than FID for many compounds it detects, but with less dynamic range than the FID. 

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Foxboro developed a self-tuning PID controller that is based on a so-called expert system approach for adjustment of the controller parameters. The on-line tuning of K, Xi, and Xo is based on the closed-loop transient response to a step change in set point. By evaluating the salient characteristics of the response (e.g., the decay ratio, overshoot, and closed-loop period), the controller parameters can be updated without actually finding a new process model. The details of the algorithm, however, are proprietary... 

Ionisation detectors. An important characteristic of the common carrier gases is that they behave as perfect insulators at normal temperatures and pressures. The increased conductivity due to the presence of a few charged molecules in the effluent from the column thus provides the high sensitivity which is a feature of the ionisation based detectors. Ionisation detectors in current use include the flame ionisation detector (FID), thermionic ionisation detector (TID), photoionisation detector (PID) and electron capture detector (ECD) each, of course, employing a different method to generate an ion current. The two most widely used ionisation detectors are, however, the FID and ECD and these are described below. 

We now finally launch into the material on controllers. State space representation is more abstract and it helps to understand controllers in the classical sense first. We will come back to state space controller design later. Our introduction stays with the basics. Our primary focus is to learn how to design and tune a classical PID controller. Before that, we first need to know how to set up a problem and derive the closed-loop characteristic equation. 

With the given choices of Gc (P, PI, PD, or PID), Gp, Ga and Gm, plug their transfer functions into the closed-loop equation. The characteristic polynomial should fall out nicely. 

We could also modify the M-file by changing the PI controller to a PD or PID controller to observe the effects of changing the derivative time constant. (Help is in MATLAB Session 5.) We ll understand the features of these dynamic simulations better when we cover later chapters. For now, the simulations should give us a qualitative feel on the characteristics of a PID controller and (hopefully) also the feeling that we need a better way to select controller settings. 

It is a long and frustrating process to adjust a controller to an evaporation source, requiring several minutes for stabilization and hours to obtain satisfactory results. Often the parameters selected for a certain rate are not suitable for an altered rate. Thus, a controller should ideally adjust itself, as the new controllers in INFICON coating measuring units do. At the beginning of installation and connection the user has the unit measure the characteristics of the evaporation source. Either a PID controller is used as the basis for slow sources or another type of controller for fast sources without significant dead time. 

INFICON s Auto Control Tune is based on measurements of the system response w/ith an open loop. The characteristic of the system response is calculated on the basis of a step change in the control signal. It is determined experimentally through two kinds of curve accordance at two points. This can be done either quickly w/ith a random rate or more precisely with a rate close to the desired setpoint. Since the process response depends on the position of the system (in our case the coating growth rate), it is best measured near the desired virork point. The process information measured in this vray (process amplification Kp, time constant T., and dead time L) are used to generate the most appropriate PID control parameters. 

However, the ideal control algorithm would have no overshoot, no offset, and a quick response characteristic. For this purpose, a proportional action (P), an integral action (I), and a differential action (D) were combined as a PID controller as follows. 

When processes are subject only to slow and small perturbations, conventional feedback PID controllers usually are adequate with set points and instrument characteristics fine-tuned in the field. As an example, two modes of control of a heat exchange process are shown in Figure 3.8 where the objective is to maintain constant outlet temperature by exchanging process heat with a heat transfer medium. Part (a) has a feedback controller which goes into action when a deviation from the preset temperature occurs and attempts to restore the set point. Inevitably some oscillation of the outlet temperature will be generated that will persist for some time and may never die down if perturbations of the inlet condition occur often enough. In the operation of the feedforward control of part (b), the flow rate and temperature of the process input are continually signalled to a computer which then finds the flow rate of heat transfer medium required to maintain constant process outlet temperature and adjusts the flow control valve appropriately. Temperature oscillation amplitude and duration will be much less in this mode. 

Chang, H. Chen, L. 1984. Bifurcation characteristics of nonlinear systems under conventional PID control. Chem. Engng Sci. 39,1127-1142. 

Differences in the PID algorithm, controller parameters, units, and other fundamental control functions highlight the importance of understanding the structure of the controller and the requirement of sufficiently detailed documentation. This is especially important for the controller but is also important for the field instruments, final control elements, and device tnat have the potential to affect the signal characteristics. 

When the differential control is added to the effect of GK translocation, the beta cell acts as a PID controller [36], but with nonlinear characteristics and with saturable signals. This is shown in Fig. 6.5c. The mutual effect of the three parts depends on the actual parameters of the model. Notice that for fast changes (kj =0.005 min-1), the integrator tends to saturate [32]. 

Figure 3.2. Response characteristics of a direct acting PID controller.

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