Measurement lag

Temperature is the hardest parameter to control in a fractionation system. It exhibits high process and measurement lag. Temperature can also be ambivalent as a measure of composition. Pressure changes are reflected quickly up and down the column. Temperature changes are not. It is typical to provide three-mode controllers for all temperature applications. 

The ratio of the time constants, Xr/Xm, which for this case equals (k Xm) will determine whether C is significantly different from Cm. When this ratio is less than 1.0 the measurement lag will be important. If Xj/Xm >10, then Cm = Cr and the measurement dynamics become unimportant. 

The measurement lag for concentration in a reactor is depicted in Fig. 2.8. The actual reactant concentration in the reactor at any time t is given by C but owing to the slow response of the measuring instrument, the measured concentration, shown by the instrument, Cm, lags behind Cp as indicated in Fig. 2.9. 

Rat peritoneal mast-cell exocytosis (as monitored by membrane capacitance measurements) in response to either antigenic stimulation or to the intracellular perfusion with guanine nucleotides (for example, GTP[AS]), occurs after a measurable lag period which has been suggested to be due to the involvement of a GTP-binding regulatory protein [202]. In contrast, stimula-... 

Automatic primary coolant temperature control with inlet and outlet temperature measurement lags and associated control devices. 

Example The location of the best temperature-control tray in a distillation column is a popular subject in the process-control literature. Ideally, the best location for controlling distillate composition xa with reflux flow by using a tray temperature would be at the top of the column for a binary system. See Fig. 8.9o. This is desirable dynamically because it keeps the measurement lags as small as possible. It is also desirable from a steadystate standpoint because it keeps the distillate composition constant at steadystate in a constant pressure, binary system. Holding a temperature on a tray farther down in the column does not guarantee that x will be constant, particularly when feed composition changes occur. 

The span of the temperature transmitter is 100-200°F. Control valves have linear trim and constant pressure drop, and are half open under normal conditions. Normal condenser flow is 30 gpm. Normal jacket flow is 20 gpm. A temperature measurement lag of 12 seconds is introduced into the system by the thermowell. 

The control valve on the steam has linear installed characteristics and passes 500 Ibi min when wide open. An electronic temperature transmitter (range 50-250°F) is used, A lemp>efature measurement lag of 10 seconds and a heat trans fer lag of 20 seconds can be assumed. A proportional-only temperature contioller is used. 

Rearranging to find the openloop transfer function between reactor temperature and cooling water flowrate and including two first-order temperature measurement lags (tm) give... 

The two measurement lags are included so that reasonable controller tuning constants can be determined. The reactor itself is only net second-order (first-order polynomial in the numerator and third-order polynomial in the denominator), so the theoretical ultimate gain would be infinite if lags were not included. The linear model is used in the following section to explore stability. 

The one zero and the three poles of the openloop transfer function (not including the two poles from the measurement lags) for the two cases are given in Table 3.2. The 85% conversion case has two complex conjugate poles with positive real parts, so it is openloop-unstable. The 95% conversion case is openloop-stable. 

Figure 3.2 gives root locus plots for the two designs at reactor temperature of 350 K with the measurement lags included. You may remember that a root locus plot is a plot of the roots of the closedloop characteristic equation as a function of the controller gain Kc. The plots start (Kc = 0) at the poles of the openloop transfer function and end (Kc —> oo) at its zeros. 

The nonlinear model and the linear model are the same as those given in Section 3.1.1. For the Tr <— F0 control structure, the openloop transfer function required to design the temperature controller is TR(s)/F0 y Using Eqs. (3.12)—(3.16), solving for TR(s)/F(Ms) and including two first-order temperature measurement lags give... 

Two 1-min temperature measurement lags are included in the temperature control loop. A 50°C temperature transmitter span is used. Controller gain is 10, and integral time is 10 min. 

Dead time can result from measurement lag, analysis, and computation time, communication lag or the transport time required for a fluid to flow through a pipe. Figure 2.27 illustrates the response of a control loop to a step change, showing that the response started after a dead time (td) has passed and reaches a new steady state as a function of its time constant (t), defined in Figure 2.23. When material or energy is physically moved in a process plant, there is a dead time associated with that movement. This dead time equals the residence time of the fluid in the pipe. Note that the dead time is inversely proportional to the flow rate. For liquid flow in a pipe, the plug flow assumption is most accurate when the axial velocity profile is flat, a condition that occurs when Newtonian fluids are transported in turbulent flow. 

In the conventional control loop, the measurement lag is only part of the total time lag of the control loop. For example, an air heater might have a total lag of 15 minutes. Of this lag, 14 minutes is contributed by the process lag, 50 seconds by the bulb lag, and 10 seconds by the control valve lag. Bypass control is often applied to circumvent the dynamic characteristics of heat exchangers, thus improving their controllability. Bypass control can be achieved by the use of either one three-way valve or two two-way valves. 

We next try a more aggressive heat recovery alternative as shown in Fig. 5.24. The heat input to the furnace is quite small and most of the heat is provided by the large feed-effluent exchanger. With, our choice of measurement lags (two 1-minute lags in series) and the lag in the furnace., this system cannot be stabilized by feedback control around the furnace if the quench controller is in manual. However, it is possible to stabilize the system with just the quench controller in automatic and the furnace controller in manual. Subsequent tuning of the furnace controller is then easy since the new system is open-loop stable. 

Temperature measurement lags (two Product composition controller... 

Pure delays in dynamic response impose fundamental bounds on achievable disturbance rejection, as discussed in Section II.B.2. Uncertainty imposes additional limitations. For example, if the measurement lag were accurately known, it could be canceled and would not limit control performance. But the measurement response is more complex than this and it is variable over time thus it cannot readily be canceled and combines with the delay to limit controller performance (see Sections V.A.3 and V.A.5). Limits on the reagent addition rate prevent the ideal delay-limited control bound from being achieved in some cases, even in the absence of uncertainty, as infinite actuator range is required (see Section V.A.5). However, these limits are not observed to have a major effect on PI control performance as the degree of transient overshoot is moderate compared to the steady-state control output change required. 

For typical values of F of 30-300 m /hr, the predicted optimal volumes of 10-30 m cotTespond to residence times of between 2 and 60 min. It should be economically attractive to achieve mixing near the achievable bound (see Section IV.D) with tanks of this size, so that = 10 s independent of tank volume. The main secondary lag in typical applications is the measurement lag. The value of this lag varies with installation conditions but is not dependent on tank volume and may be generally taken as less than 30 s. This gives an effective t l 25-30 s and a rigorous f,) = 10 s, with both values independent of tank volume. This shows that the two main assumptions of the above analysis... 

In Section V.A.4, we showed that optimal volume is proportional to t j and that there is a factor of about (1.5n ) " between the optimal volume with PI control (without uncertainty) and the volume required, assuming the performance bound is reached. The PI performance is governed by the effective delay it d — tJ4) rather than the actual pure delay. The maximum effective delay, assuming a mixing delay of 10 s, a probe lag of up to 30 s, and a CSTR with > td. , is 28.7 s. The measurement lag may therefore imply almost a threefold increase in the required volume, compared to that required with an instantaneous measurement response. 

Summary. The greatest scope for moving performance toward the ideal control bound lies in reducing measurement lag and improving understanding of meas-... 

The greatest potential for moving control performance toward the ideal delay-limited control bound lies in minimizing or compensating for pH measurement lags. 

The dominance of the flow effect suggests that flow information should be used directly to cancel this effect. This can be achieved by adding a flow measurement and controlling the ratio of the effluent and reagent flows based on the pH measurement (Section III.B.4). Despite the measurement lag and minor biases in flow measurement, this makes the concentration effect dominant. As only the two-tank configuration allows the concentration effect to be tolerated, we have two 12-m tanks with ratio control of reagent flow at the inlet to the treatment system as the starting point for the search for an effective plant. 

The outer-approximation algorithm (Section II.A) took six iterations to identify this solution, with a projection factor, e, of. 05 on the disturbance amplitude. Both vertex and nonvertex constraint maximizers were identified, confirming the need to consider nonvertex maximizers. The variables that contributed nonvertex maximizers were the step switching times (several times) and the measurement lags (once). Robustness was verified with respect to all vertex combinations of uncertain values and a random selection of interior points (ivert = 1, nrand y = 1000). 

The mixing delay is 10 seconds. The maximum measurement lag is 30 seconds. The reagent dynamics are complex, but the effective lag associated with the initial response is no more than 10 seconds (based on examination of time for 50% conversion of reagent using the model given above). The effective delay, calculated as f 4 (Section II.B.2), is therefore about 41 seconds. The estimated disturbance attenuation with PI control is 8 X 10 (Eq. 52). Transient control performance is not expected to be a problem for this system and a basic control scheme should be adequate. 

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