Steady State Errors for Proportional
Control
For the following Plant transfer function:
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Use MATLAB to generate a time plot of a closed-loop,
proportional-only control, step response with this plant.
You may find
it helpful to start from the example file
pid_control_rev.m, uploaded to
the files section of Canvas. You will have to change the plant constants and
the loop control constants. Be sure to add comments at the top with your name
and descriptions of the revisions you made.
Observe the time response for a wide range of positive values
for the gain constant Kp
Note the steady-state error that exists. I.e. notice that
after the system settles out, that the closed-loop output never quite gets to
the same level as the step input set point signal.
Also note that the closed-loop system goes unstable for a
large enough value of Kp.
For this
first part, turn in:
·
a table of observed steady-state
errors for various Kp values, and
·
a graph of observed steady-state
errors vs Kp
Next, use block-diagram algebra techniques to compute a
closed-loop transfer function with a simple proportional control using Kp.
Use the final-value theorem to figure out what the
theoretical, final-value, steady-state outputs should be as a function of Kp.
This should be an astonishingly simple function! :-)
Plot this theoretical steady-state error vs Kp.
Do your
observations agree with your theoretical predictions
Steady State Errors for Proportional Control For the following Plant transfer function: Use MATLAB to generate a time plot of a closed-loop, proportional-only control, step response with this plant. You may find it helpful to start from the example file pid_control_rev.m, uploaded to the files section of Canvas. You will have to change the plant constants and the loop control constants. Be sure to add comments at the top with your name and descriptions of the revisions you made. Observe the time response for a wide range of positive values for the gain constant Kp Note the steady-state error that exists. I.e. notice that after the system settles out, that the closed-loop output never quite gets to the same level as the step input set point signal. Also note that the closed-loop system goes unstable for a large enough value of Kp. For this first part, turn in: • a table of observed steady-state errors for various Kp values, and • a graph of observed steady-state errors vs Kp Next, use block-diagram algebra techniques to compute a closed-loop transfer function with a simple proportional control using Kp. Use the final-value theorem to figure out what the theoretical, final-value, steady-state outputs should be as a function of Kp. This should be an astonishingly simple function! :-) Plot this theoretical steady-state error vs Kp. Do your observations agree with your theoretical predictions