Dynamic lag

Figure 8.22-d, on the other hand, gives an example in which the link dynamics lags behind the value development. In this example, the boundary proceeds outward... 

This paper extends previous studies on the control of a polystyrene reactor by including (1) a dynamic lag on the manipulated flow rate to improve dynamic decoupling, and (2) pole placement via state variable feedback to improve overall response time. Included from the previous work are optimal allocation of resources and steady state decoupling. Simulations on the non-linear reactor model show that response times can be reduced by a factor of 6 and that for step changes in desired values the dynamic decoupling is very satisfactory. 

Fuel injection, diesel, 70 60-61 Fuel injection systems, 70 51 Fuel injector detergents, 72 408 409 Fuel metering system dynamic (lag time), 70 50... 

There is a first-order dynamic lag of t minutes between a change in the signal to the steam valve and vapor boilup. The low base-level override controller pinches the reboiler steam valve over the lower 25 percent of the level transmitter span. 

These findings validate the approach of Krier et al. (53) when they adopted the collapsed A/PA—GDF model to predict low frequency instability behavior of composite solid propellants at normal rocket pressure. Since m = 1.5 X 10 5 sec. at these pressures, their quasi-steady treatment of the O/F flame reaction time is valid for low freqeuncies above about 5000 c.p.s., the dynamic lag of the O/F flame must be taken into account—the dynamic lag of the A/PA flame need be considered only when frequencies approach 100 k.c.p.s. 

However, there is an important dynamic effect as the size of the heat exchanger is increased. The larger holdup in the heat exchanger introduces more dynamic lag in the heat transfer process, which could degrade dynamic performance. We observed this in the jacket-cooled system discussed in Section 3.1.5. The smaller the thickness of the jacket, the better the temperature control. 

For an area of 58.1 m2 (the area of a coil), the volume of the tubes is 0.641 m3. This should be compared with the volume of the coil (1.1 m3). So the external heat exchanger has less volume (because of the smaller diameter tubes) and should introduce less dynamic lag. 

The purity of the product xPC undergoes a sharp drop when the ratio structure is used because of the step change in the reflux. This performance is improved by inserting a dynamic lag in the ratio loop, as the dotted curves in Figure 3.39 illustrate. 

Some rudimentary controllers can be used with the RBatch (see Fig. 4.31) reactor, but they are less realistic than those found in Aspen Dynamics. Lags and deadtimes cannot be... 

The second difference is the dynamic response to disturbances or changes in manipulated variables. In a perfectly mixed CSTR, a change in an input variable has an immediate effect on variables in the reactor. In a tubular reactor it takes time for the disturbance to work its way through the reactor to the exit. Therefore there are very significant dynamic lags and deadtimes between changes made at the inlet of the reactor and... 

When control of the outlet temperature is attempted, it does not work. Figures 6.61 and 6.62 demonstrate that with either a high controller gain Kc = 10) or with a low controller gain (Kc = 1), the system is unstable. This is due to the large dynamic lag this system and the pinch between the process and coolant temperatures at the exit end of the reactor. 

In addition, there is a need to handle the dynamic changes in load in a safe manner. If there is an increase in demand, the airflow should be increased before fuel flow. If there is a decrease in demand, the airflow should be decreased after the fuel flow. This is achieved by the use of some simple dynamic lags and selectors, as illustrated in Figure 8.3. 

Had we started to assign the DIB column base level control first, we would have ended up with the same inventory control structure. The reason is as follows. Assume we had chosen the DIB column base valve to control base level. After resolving the purge column inventory loops, we would have found that we needed to control the purge column base or reflux drum level with the fresh feed flow to the DIB column. The dynamic lags associated with these loops would have forced us back to the control strategy as described above. 

In addition to the basic continuous column model assumptions of equilibrium stages and adiabatic operation, dynamics-related assumptions are made for the batch model. Distefano (1968) assumed constant volume of liquid holdup, negligible vapor holdup, and negligible fluid dynamic lag. Although different solution strategies may be employed, the fundamental model equations are the same. 

Starting from total reflux conditions, the distillate rate is incremented from zero to D, thereby lowering the reflux rate to Lq - D. Since negligible fluid dynamic lags are assumed, all the liquid rates are instantly lowered to Lj - D. The vapor rates are maintained at Vj. These flow rates and the steady-state total reflux mole fractions are used to calculate the mole fraction derivatives by Equations 17.29 through 17.31. The molar holdups in these equations are calculated from the assumed constant volume holdups multiplied by calculated molar densities. 

To include information about process dynamics, lagged variables can be included in X. The (auto)correlograms of all x variables should be developed to determine first how many lagged values are relevant for each variable. Then the data matrix should be augmented accordingly and used to determine the principal components that will be used in the regression step. 

EXAMPLE 4.1. Consider the two blending systems shown in Fig. 4.8. The flow rate or composition of stream 1 is the disturbance. The flow rate of stream 2 is the manipulated variable. In Fig. 4.8a the sensor is located after the tank, and therefore the dynamic lag of the tank is included in the feedback control loop. In Fig. 4.8h the sensor is located at the inlet of the tank. The process lag is now very small since the tank is not inside the loop. The control performance in part h, in terms of speed of response and load rejection, would be better than the performance in part a. In addition, the tank now acts as a filter to average out any fluctuations in composition. ... 

Usually, the additional control for splitting the vapor and liquid products is the condensate temperature (or composition, if an analyzer is available). The temperature measurement point should be as close to the condenser as possible to avoid the dynamic lag associated with the reflux drum (which is commonly 5 to 10 minutes). It has been recommended (68) to locate the thermocouple in the liquid line just beneath the condenser and above the reflux drum. Figure 17.8a-d shows the common control schemes. It is frequently preferred to manipulate the condensation rate by varying the coolant rate. 

In summary, analyzer control has the advantage of directly controlling product purity, and in many cases, providing better composition control. However, analyzers tend to be troublesome suffer from dynamic lags, high downtime, and low reliability and are expensive. For these reasons, they are only used for composition control in applications where improved composition control is highly beneficial and the above limitations are not overly restrictive. 

Controlling bottom impurity by an analyzer located in the nest column overhead did not woric because of excessive dynamic lags. 

Guideline 12. Select measurement points that minimize time delays and time constants. Large time delays and dynamic lags in the process limit the achievable closed-loop performance. These should be reduced, whenever possible, in the process design and the selection of measurements. 

This last loop is the unusual element in the control structure. The tuning of most conventional level loops is simple because we use a proportional controller with a gain of 2. The level loop in the proposed stmcture is not conventional. In this application, we want fairly tight level control because the distillate/temperature loop depends on the vapor/level loop. In addition, the dynamics of the vapor/level loop contain some dynamic lags because the pressure loop is involved, that is, increasing reboiler heat input increases pressure, and the pressure controller increases condenser heat removal, which affects reflux-drum level. 

The default mode is Constant duty in which heat-transfer rates Qc in the condenser and 2r in the reboiler) are set immediately with no dynamic lags. These heat-transfer rates are directly manipulated in the dynamic model and their effects are immediately felt by... 

DYNAMIC LAG AND MAGNETIC SWITCH REPEATABILITY. In establishing the effect of the scalers dynamic lag and repeatability of the magnetic switch, the following information is used as obtained from actual test runs ... 

The errors introduced as a result of the scalers dynamic lag and magnetic switch repeatability may be directly attributed to the failure to register the initial increment of weight for the first actuation and the over-registration of a second incremental weight for the final actuation. These gravimetric incre-... 

The total gravimetric error due to the dynamic lag and magnetic switch repeatability will then be... 

It is seen that the error due to the dynamic lag of the scale and the magnetic switch repeatability increases with flow rate. 

It should be noted that there are page tabs for flie condenser and reboiler. Since the dynamics of these heat exchangers are usually much faster than those of the column, the default setting is to assume these units have instantaneous responses (no dynamic lags). 

Deadtime and Lags. Most temperature and composition controllers need to be tuned because the dynamics lags in these loops carmot be neglected. Deadtimes and lags degrade dynamic performance, so not including realistic dynamic lags in the simulation of these loops can lead to a prediction of dynamic performance that is unrealistically better than what will actually be seen in the plant. 

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