How can you identify a process's dead time and time constant from a step test?

• A. Drive the input with a step, record output; dead time is the delay before output begins to respond.
• B. Dead time is the delay before the output begins to respond; τ is the time to reach 63% of final value after dead time.
• C. Dead time is the delay before the output begins to respond; τ is the total time to reach final value.
• D. τ is the dead time; dead time is time to reach final value.

Answer: (B)

In a step test, a process often behaves like a first-order system with a pure delay: nothing happens for a while (dead time), then the output rises exponentially toward a final value. The dead time is the interval from the step application to when the output first starts to respond. The time constant is how long it takes after that delay for the output to reach about 63% of its final value. So you measure the onset of movement to get the dead time L, then find the time when the output reaches 63% of its final steady-state value; that time minus the dead-time gives the time constant T (since t63% = L + T). This 63% point is the standard marker for the exponential approach.

In practice, if the final value is, say, 10 units and the output reaches 6.32 units after the delay, then the time from step to 6.32 units is L + T, and T = (time at 63% final) − L. The total time to reach the final value is not a fixed finite point for a first-order system; using the 63% criterion provides a consistent way to identify the time constant.