Lecture Notes 18
Lecture 18 - Transfer Functions
Lecture 18 builds on the discussion of Laplace Transforms to work with Transfer Functions. Transfer Functions are a compact form to display Input / Output relationships in an algebraic relationship in the s-domain. They can be combined in series or parallel and are convenient to use in block diagrams.
Discussion Questions
Test the lecture's ideas before or after class - commit to an answer first, then check it with a classmate or an AI tutor.
- A transfer function is defined as Y(s)/U(s) with zero initial conditions. Why does this definition quietly assume the model is linear and in deviation variables - and what "transfer function" would a truly nonlinear process have?
- Set s = 0 in any transfer function. What physical quantity do you get, and why is this the fastest sanity check on any block-diagram reduction you (or an AI) perform?
- Two first-order processes in series give a second-order transfer function. When you multiply the blocks, what physical assumption are you making about the connection between the units, and when does it fail in real equipment?
- The poles of G(s) belong to the process; the input only contributes its own terms. What does that separation tell you about which features of a response you can change by choosing a different input, and which you cannot?
"Quiz me with 4 questions, one at a time, on transfer functions: the definition as output over input in deviation variables with zero initial conditions, what the steady-state gain check at s=0 verifies, how series and parallel blocks combine and what loading assumption that requires, and what the poles of a transfer function determine about the shape and speed of the response. Grade my answers and list my misconceptions."
App: The Two-Tank Level Control Studio is two first-order blocks in series that you can watch: step the pump and see the second tank respond with the slower S-shaped second-order response that the product of the two transfer functions predicts.
