Process Control: Modeling, Design, and Simulation

4.3. Integrator + Dead Time

An integrator + dead-time process has the input-output transfer function relationship

Equation 4.3

and the output response to a step input

Equation 4.4

with the response shown in Figure 4-5. The gain, k, can be found from the slope by solving

Figure 4-5. Estimating parameters for an integrator + time-delay model from a step input test.

and the time delay is clearly identified by the time required for a change in output. ...