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2024 Summer Process Control Homework #2

发布时间：2024-06-01

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2024 Summer Process Control

Homework #2 (100)

Problem #1 (20)

Find the time function corresponding to each of the following Laplace transforms using partial- fraction expansions:

Problem #2 (30)

Solve the following ODEs using Laplace transforms:

Problem #3 (30)

Find the solution of the equation

Plot the solutions for 0 ≤ t ≤ 2 and values of ℎ = 1,10,100 and the limiting case of ℎ → ∞ (or ℎ(t) = δ(t)). Place all four plots on a single figure.

Problem #4 (20)

For the temperature profile on the figure, write function T(t) and Laplace transform T(s). Check the result in Matlab.

Bonus Problem (10)

For a stirred-tank heater, assume the transfer function between the heater input change u(t) (cal/sec) and the tank temperature change y(t) (°C) can be modeled as

a) find the steady-state response for a unit rectangular pulse change in the heating rate

b) repeat the calculation in (a) for a unit ramp