Time delay model

Two-parameter time-delay model (Buffham,14 Buflham and Gibilaro,15 and Buflham el al.18) This model is based on the concept of fluid elements being randomly delayed in time on their passage through the bed. The model has been mainly applied to the liquid-phase backmixing in a trickle-bed reactor. The model assumes that the liquid would flow in plug flow except for the fact that molecules... 

There are several approaches that can be used to tune PID controllers, including model-based correlations, response specifications, and frequency response (Smith and Corripio 1985 Stephanopoulos 1984). An approach that has received much attention recently is model-based controller design. Model-based control requires a dynamic model of the process the dynamic model can be empirical, such as the popular first-order plus time delay model, or it can be a physical model. The selection of the controller parameters Kc, ti, to) is based on optimizing the dynamic performance of the system while maintaining closed-loop stability. 

Models Considering a Membrane Diffusion Model. Sobotka et al. (1982) claimed that the empirical time delay models previously described do not properly consider the physical nature of the electrode response. Instead, they insisted that models based on Pick s second law are superior and encouraged their use to more accurately model system dynamics. Sobotka et al. (1982), in their review, presented many of the different diffusional models that have been developed and discussed their usefulness. 

An RCM optimization module enabling calculation of effective failure rates for common RCM activity types, i.e., age replacement, functional proof testing, inspection in time-delay models and a gradual failure progression model, see e.g. Vatn (2007) for a description of these models. The RCM module enables maintenance interval optimization taking the entire regularity model into accoimt. 

One should be careful to take data when other plant fluctuations are minimized. For many processes, the response of the system Ay (change in the measured value of the controlled variable using a sensor) follows the curve shown in Fig. 18.57 (see case 6 in Fig. 18.50). Also shown is the graphical fit by a first-order plus time delay model, which is described by three parameters ... 

A variety of different tuning rules exists which are based on the assumption that the model can be accurately approximated by a first-order plus time delay model. One popular approach, which is not... 

TABLE 18.5 IMC Tuning Relations for First-Order Plus Time Delay Model... 

The normalized step responses of the original and approximate transfer functions are shown in Fig. 6.11. The second-order model provides an excellent approximation, because the neglected time constants are much smaller than the retained time constants. The first-order-plus-time-delay model is not as accurate, but it does provide a suitable approximation of the actual Mnse. 

By inspection determine which of the following process models can be approximated reasonably accurately by a first-order-plus-time-delay model. For each acceptable case, give your best estimate of 0 and t. 

In order to account for higher-order dynamics that are neglected in a first-order model, a time-delay term can be included. This modification can improve the agreement between model and experimental responses. The fitting of a first-order plus time-delay model (FOPTD),... 

Figure 7.10 Comparison of step responses for a FOPTD model (solid line) and the approximate integrator plus time delay model (dashed line).

Fit an integrator plus time-delay model to the unit step response in Figure E7.5 for t < 15. The step response has been normalized by the steady-state gain. Compare the experimental response with the response predicted... 

To further illustrate the influence of controller settings, we consider a simple closed-loop system that consists of a first-order-plus-time-delay model and a PI controller. The simulation results in Fig. 12.1 show the disturbance responses for nine combinations of the controller gain Kc and integral time t/. As Kc increases or t/ decreases, the... 

Consider the standard first-order-plus-time-delay model. 

Second-Order-Plus-Time-Delay (SOPTD) Model Consider a second-order-plus-time delay model,... 

A comparison of (12-30) and (12-31) indicates that the type of controller that is designed depends on the time-delay approximation. Furthermore, the IMC controller in (12-31) is identical to the DS controller for a first-order-plus-time-delay model. This equivalence can be confirmed by noting that the DS controller settings in (12-14) reduce to the IMC settings in (12-31) for Ti = T and T2 = 0. 

Approximate the lag-dominant model by an integrator-plus-time-delay model (Chien and Fruehauf, 1990). As indicated in Section 7.2.3, the integrator-plus-time-delay model in Eq. 12-33 provides an accurate approximation to the FOPTD model in Eq. 12-10 for the initial portion of the step response ... 

Table 12.3 Controller Design Relations Based on the ITAE Ferformance Index and a First-Order-plus-Time-Delay Model (Smith and Corripio, 1997) ...

OT the first-order-plus-time-delay model of Example 12.4, [le PI controller for case (b) provided the best distur-ace response. However, its set-point response had a sig-ficant overshoot. Can set-point weighting significantly educe the overshoot without adversely affecting the set-... 

A block diagram for the closed-loop system is shown Fig. 12.17. This block diagram is similar to Fig. 11.7, bul the feedback loop has been opened between the cor and the current-to-pressure (I/P) transducer. A first-< plus-time-delay model can be developed from the ] reaction curve in Fig. 12.16 using the graphical met Sectio 7.2. The tangent line through the inflection i intersects the horizontal lines for the initial and flnal composition values at 1.07 min and 7.00 min, respectively. The slope of the line is... 

Suppose that a process can be adequately modeled by the first-order-plus-time-delay model in Eq. 12-10. 

For processes that can be described by a second-order-plus-time-delay model (Eq. 17-67), Vogel and Edgar (1988) have developed a controller that eliminates the ringing pole caused by inverting G. The de-... 

Pottmann et al. (2000) identified a first-order-plus time-delay model for each combination of inputs and outputs (3X3 problem) with the following parameters (time units are dimensionless) ... 

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