- Linear State Space Models
- Introduction to Laplace Transforms
- Transfer Functions
- First-Order Behavior
- Integrating System
- Second-Order Behavior
- Lead-Lag Behavior
- Poles and Zeros
- Processes with Dead Time
- Padé Approximation for Dead Time
- Converting State Space Models to Transfer Functions
- Matlab and Simulink
- Student Exercises
3.10 Processes with Dead Time
Many processes have a delayed response to a process input, either due to transport lags (such as flow through pipes) or high-order effects. In Section 3.3.4 we found that a time-delay of q time units had a transfer function of e–qs.
A first-order process combined with a time-delay has the transfer function
Consider a process with kp = 1, tp = 10, and q = 5. A unit step input change at t = 0 yields the response shown in Figure 3-15. We see that the time-delay shifts the response of the output.
Figure 3-15. Response of a first-order + dead time process.