1. Given the following feedback control diagram:
a. Derive the transfer function that relates changes in Disturbance 1
[D1'(s)] to the regulated state variable [X'(s)].
b. Derive the transfer function that relates changes in Disturbance 2
[D2'(s)] to the regulated state variable [X'(s)].
2. Using SIMULINK, create the following control system block diagram.
We will explore how well a simple proportional-only (P-only) controller can
regulate this system. Simulate the behavior of the control system to a 1 unit
increase in the setpoint using the following different controller transfer
What choice of controller gain sign should be chosen for this system
b. Assume the controller in this case is a simple proportional-only (P-
Explore a range of different Kc values. Is there a range of Kc values
where the system behaves better or in a more stable manner? Is
there an ultimate gain for this system and if so what is your estimate
Write down the closed loop transfer function for setpoint tracking in
What is the characteristic equation for this system?
Plot the root locus diagram for this system. You can plot it by hand,
using Excel, and/or using MATLAB, but be sure to show some
important values of Kcon the plot.
f. What is the ultimate gain for this system based on your root locus
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