Deadtime algorithm

Theoretically it is possible to automatically adapt the tuning of the deadtime algorithm based on measured gas flows but this is complex and prone to error if there are multiple fuel gas consumers and producers. It is likely to be more practical to locate the analyser close enough to the heater so that dynamic compensation is not required. 

As our final minimal-prototype controller, let us consider the Dahlin algorithm. The basic notion is to specify a desired step setpoint response that looks like a deadtime followed by an exponential rise up to the setpoint. See Fig. 20.4. 

The design of the valve, process, and measurement should be made such as to minimize deadtime in the loop while providing a reliable, more linear response, then the controller can be tuned to provide the best performance, with an acceptable operating margin for robustness. The PID controller is the most widespread and applicable control algorithm, which can be tuned to provide near optimal responses to load disturbances. PID is an acronym for Proportional, Integral, and Derivative modes of control. 

To compute Dahlin s algorithm we assume that the closed-loop deadtime is equal to the process dead time plus one sampling period to account for the delay in the sampling and holding operations (i.e., 6 = 2+1=3 seconds). Also, we assume that the desired response has a time constant ji = 2. Then from the design eq. (30.14) we take... 

In a simulation study, Leffew and Deshpande [62] have evaluated the use of a dead-time compensation algorithm in the control of a train of CSTRs for flie emulsion polymerization of vinyl acetate. In this study, monomer conv ion was controlled by manipulating the initiator flow rate. Experiments indicate that there is a period of no response (dead-time) between the time of increase in the flow of initiator and the response of monomer conversion. Dead-time compensation attempts to correct for this dead-time by using a mathematical model of the polymerization system. Reported results indicate that if the reactor is operated at low surfoctant concentration (where oscillations are observed), the control algorithm is incapable of controlling monomer conversion by the manipulation of either initiator flow rate or reactor temperature. The inability of the controller to eliminate oscillations is most probably due to the choice of manipulated variable (initiator flow rate) rather than to the perfotmance of the control algorithm (deadtime conq)ensation). 

The result of this method produced a transfer function identical to that of a PID algorithm. Rarely does this occur with other process models. Eor example, if we introduce deadtime into the process, then the target trajectory becomes... 

We should also remember that the tuning has been based on the assumption that the process is first order plus deadtime. It is theoretically possible to implement a second order equivalent of the lead-lag algorithm but this would require the identification of second order models for the DV and MV, and the calculation of additional tuning constants. It is unlikely therefore to be practical. It would be easier to fine tune the dynamic compensation. This also takes account of any abnormalities in the way in which the DCS vendor may have coded the lead-lag algorithm. 

This is the equation for the proportional-on-error, derivative-on-error noninteractive controller. We can however choose coefficients to produce almost any control algorithm. For a first order plus deadtime processes we use... 

The performance of the Dahlin algorithm is similar to that of the Smith predictor and IMC. It is equally sensitive to the accuracy of the deadtime (6) used in deriving N and hence the value of j). It too can be extended to higher order models. 

The algorithm was originally developed for use when the controller scan interval (ts) is signihcant compared to the process dynamics. This makes it suitable for use if the PV is discontinuous, such as that from some types of on-stream analysers. Analysers are a major source of deadtime. They may located well downstream of the MV and their sample systems and analytical sequence can introduce a delay. An optimally tuned PID controller would then have a great deal of derivative action. However this wUl produce the spiking shown in Figure 7.6. 

Figure 8.10 shows the first of the decouplers. When PIDi takes corrective action, the decoupler applies dynamic compensation to the change in output (AOPi) and makes a change to MV2 that counteracts the disturbance that the change in MVi would otherwise cause to PV2- Dynamic compensation is provided by a deadtime/lead-lag algorithm. 

We apply dynamic compensation in the form of a deadtime/lead-lag algorithm. This is tuned in exactly the same way as described in Chapter 6 covering bias feedforward. By performing open loop steps on the MV we obtain the dynamics of both the inferential and... 

Dynamic compensation is likely to be necessary to ensure that the reflux and steam flows are adjusted at the right time. The method for tuning these deadtime/lead-lag algorithms is described in Chapter 6. Part of this procedure involves steptesting the DV, in this case feed rate, to obtain the dynamic response of the PV, in this case tray temperature. This can present a problem on some columns. 

As an alternative other algorithms, such as bias feedforward and deadtime compensation, can be implemented in the MVC - depending on which approach is better for operator understanding and what back-up scheme is necessary if the MVC is out of service. It is also possible to move averaging level control from the DCS to the MVC. This should only be considered if it is desirable to let the MVC select which flow to manipulate (i.e. vessel inlet or outlet) depending on where the process is constrained. The DCS controller will still be required as back-up. 

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