Analysis, computers dead time

In this computer age, one may question why nobody would write a program that can solve for the roots with dead time accurately Someone did. There are even refined hand sketching techniques to account for the lag due to dead time. However, these tools are not as easy to apply and are rarely used. Few people use them because frequency response analysis in Chapter 8 can handle dead time accurately and extremely easily. 

With frequency response analysis, we can derive a general relative stability criterion. The result is apphcable to systems with dead time. The analysis of the closed-loop system can be reduced to using only the open-loop transfer functions in the computation. 

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. 

For faster reactions the speed with which reactants can be mixed is a hmitation the mixing time must be less than the half-time. Stopped-flow techniques have been developed that permit remarkably short kinetic analysis times. Beckwith and Crouch described a stopped-flow kinetic analysis apparatus, with a mixing and dead time of less than 0.01 s, capable of analyzing 1000 phosphate samples per hour with a relative standard deviation of about 1%. Sample handUng, mixing, and gathering and evaluation of data were automated with the help of on-Une computer systems. 

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