Model FOPDT

First-Order Plus Deadtime (FOPDT) Model.1179... 

A FOPDT model is the combination of a first-order model with deadtime, which can be represented by the combination of the process gain (Kp), the process time constant (x ), and the process deadtime (0 ). The process gain represents the steady-state change in the output of the process (> ) for a change in the input (u). The time constant indicates how fast the process settles to the new steady... 

FIGURE 15.10 Graphical representation of an approach for determining the parameters of a FOPDT model. 

FIGURE 15.11 Comparison between a FOPDT model and an overdamped fifth-order process. 

PID controllers are useful for certain sluggish processes. Typical applications are temperature control and composition control. A sluggish process often has a tendency to cycle under PI control due to inertia therefore, derivative action tends to reduce the tendency to cycling and allows more proportional action to be used, both of which contribute to improved control performance. A key issue here is to determine whether a process is sluggish enough to warrant a PID controller. Assume that an FOPDT model has been fit to an open-loop step test. If the resulting deadtime, 0, and time constant, x, are such that... 

For slow-response loops (e.g., certain temperatnre and composition control loops), field tuning can be a time-consuming procednre that leads to less than satisfactory resnlts. Step test results can be used to generate FOPDT models, and tnning parameters can be calcnlated from a variety of techniques. This approach suffers from the fact that it takes approximately the open-loop response time of the process to implement a step test, and during that time, measured and unmeasured disturbances can affect the process, thus corrupting the results from the step test. In addition, it is unlikely that the selected turfing approach will result in the proper balance between reliability and... 

Changes in the FOPDT model parameters reveal changes in the raw materials, process, equipment, valves, and sensors. The size, direction. 

A FOPDT model that consists of a process gain, time delay, and time constant can be used to describe the process response and calculate the controlller tuning settings. 

The most common model of a self-regulating process response is a first-order plus dead time (FOPDT) response. 

A set of Internal Model Control (IMC) tuning rules were established by Rivera, Morari, and Skogestad for a first-order plus dead time (FOPDT) open-loop process response that simply involves the adjustment of the proportional gain in the controller, K, for tuning. The integral time constant, 7, is set equal to the first-order time constant, TFO, for PI controllers (Table 10.5). 

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