Lag compensator

The multiloop controller contains a variety of func tion blocks (for example, PID, totalizer, lead/lag compensator, ratio control, alarm, sequencer, and Boolean) that can be soft-wired together to form complex control strategies. The multiloop controller, as part of a DCS, communicates with other controllers and man/machine interface (MMI) devices also on the DCS network. 

Using passive components, a phase lag compensator may be constructed, whose transfer function is of the form... 

Fig. 6.41 Lag compensated and uncompensated open-loop bode diagram for Example 6.7.

X Example 8.13. Derive the magnitude and phase lag of the transfer functions of phase-lead and phase-lag compensators. In many electromechanical control systems, the controller Gc is built with relatively simple R-C circuits and takes the form of a lead-lag element ... 

Here, z0 and p0 are just two positive numbers. There are obviously two possibilities case (a) z0 > po, and case (b) z0 < p0. Sketch the magnitude and phase lag plots of Gc for both cases. Identify which case is the phase-lead and which case is the phase-lag compensation. What types of classical controllers may phase-lead and phase-lag compensations resemble ... 

The shape of the magnitude plot resembles that of a PI controller, but with an upper limit on the low frequency asymptote. We can infer that the phase-lag compensator could be more stabilizing than a PI controller with very slow systems.1 The notch-shaped phase angle plot of the phase-lag compensator is quite different from that of a PI controller. The phase lag starts at 0° versus -90°... 

From the perspective of a root locus plot, a phase-lag compensator adds a large open-loop zero... 

Example 8.14. Designing phase-lead and phase-lag compensators. Consider a simple unity feedback loop with characteristic equation 1 + GCGP = 0 and with a first order process... 

In this illustration, we do not have to detune the SISO controller settings. The interaction does not appear to be severely detrimental mainly because we have used the conservative ITAE settings. It would not be the case if we had tried Cohen-Coon relations. The decouplers also do not appear to be particularly effective. They reduce the oscillation, but also slow down the system response. The main reason is that the lead-lag compensators do not factor in the dead times in all the transfer functions. 

Can sense as the basis of phase-lead and phase-lag compensator design... 

There are several other methods of achieving stability in potentiostatic circuits. A capacitor may be added between the counter and reference electrodes to reduce phase shift in the critical frequency region. Some caution must be exercised since a low-resistance reference electrode then becomes the counterelectrode at high frequencies. A particularly interesting method is known as input lead-lag compensation a series RC is connected between the input terminals of the control amplifier, and a second resistor is connected between the noninverting input and common. This form of compensation has minimum effect on the slew rate of the control amplifier. Further details can be found in the book by Stout and Kaufman listed in the bibliography. 

The output of the element represented by equation 7.155 lags the input. However, the destabilising effect of this additional lag is more than offset by an associated decrease in amplitude ratio. This decrease is more pronounced as the difference between r, and tj is increased. Lag compensators can be designed to produce different total open-loop stability specifications (e.g. in terms of allowable gain margin, phase margin, etc.) in a manner similar to that for lead compensators. 

On the other hand, conventional control approaches also rely on models, but they are usually not built into the controller itself. Instead the models form the basis of simulations and other analysis methods that guide in the selection of control loops and suggest tuning constants for the relatively simple controllers normally employed [PI, PID, I-only. P-only, lead-lag compensation, etc. (P = proportional, PI = proportional-integral, PID = proportional-integral-derivative)]. Conventional control approaches attempt to build the smarts into the system (the process and the controllers.) rather than only use complex control algorithms. 

Notice that the TCI controller does not hold the T35 temperamre at 101 °C during the period when the feed is ramping down or up. A PI controller will produce offset when subjected to a ramp disturbance. This offset occurs in all control structures during the ramp load disturbances. This offset problem could be reduced by using a lag-compensated PI controller for TCI. 

W. L. Luyben, Fed-batch reactor control using lag compensation and gain scheduling, Ind. Eng. 

Figure 2.17. Temperature-time profile of the Mettler DSC before and after compensation for the thermal lag. In the figure, = furnace temperature, 7 = reference temperature, Ts = sample temperature, = program temperature, = melting point, ATiag = extent that reference temperature lags behind furnace temperature, and tiag = tau lag compensation of the furnace temperature. The tau lag compensation synchronizes the program temperature with the reference and sample temperatures. [From Mettler Toledo (2004) courtesy of Mettler Toledo.]...

Figure 2.18. Melting points or extrapolated onset calibration temperatures for tau lag adjustment factor after compensation as a function of heating rate. The extrapolated onset temperatures (Tinset) are determined from calibration standards note that there is no change with heating rate after the tau lag compensation has been applied. [From Mettler Toledo (2004) courtesy of Mettler Toledo.]...

Given a process whose dynamics consist of first-order lags, = 3 min and T, = 1 min For conditions of rand q, both at 50 percent, what is the integrated area per unit load change with an uncompensated forward loop What is the Integrated area with lead-lag compensation, if the lead time is 2.5 min and the lag time is 1 min ... 

Design experience with flooded reboilers is limited but indicates that typical time constants are of the order of 2—5 minutes. Simulation studies show that substantial improvement in response speed may be achieved by lead-lag compensations with transfer functions such as ... 

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