Scalar in terms of multiple variables, Nyquist & Bode Plot

In summary, the task is to find the discrete equivalent model for a scalar with a given step time, determine the stability of the closed loop with a controller input, and obtain the transfer function using the Bode plot. The solution involves creating a 1x1 ABCD matrix and utilizing MATLAB for the calculations.
  • #1
YoshiMoshi
228
8

Homework Statement



A scalar is given by

upload_2018-3-3_20-42-37.png


It is controlled by

upload_2018-3-3_20-43-2.png


With step time h = 0.2 s

1. Find the discrete equivalent model
2. Check the stability of closed loop (K = +1)
3. Obtain the
upload_2018-3-3_20-44-11.png
via the Bode plot

Homework Equations

The Attempt at a Solution



So for question 1. This is where I'm struggling.

I know how to discrete a transfer function in terms of matrix A, B, C, and D through MATLAB easily. However how do I do that for a scalar, where I don't have matrix A, B, C, and D but just single values? Also how does the controller effect this?

I tried searching on google a bit, and can't find a solved example that is similar to this problem.

I know that question 2, I can get once I have the answer to question 1 by easily plotting the Nyquist plot.

I know that question 3, is very easy with MATLAB.

THANKS FOR ANY HELP!
 

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  • #2
YoshiMoshi said:

Homework Statement



A scalar is given by

View attachment 221400

It is controlled by

View attachment 221401

With step time h = 0.2 s

1. Find the discrete equivalent model
2. Check the stability of closed loop (K = +1)
3. Obtain the View attachment 221402 via the Bode plot

Homework Equations

The Attempt at a Solution



So for question 1. This is where I'm struggling.

I know how to discrete a transfer function in terms of matrix A, B, C, and D through MATLAB easily. However how do I do that for a scalar, where I don't have matrix A, B, C, and D but just single values? Also how does the controller effect this?

I tried searching on google a bit, and can't find a solved example that is similar to this problem.

I know that question 2, I can get once I have the answer to question 1 by easily plotting the Nyquist plot.

I know that question 3, is very easy with MATLAB.

THANKS FOR ANY HELP!

You're overthinking it...
you do have an ABCD matrix.

Your A matrix is a 1x1.
Your B matrix is a 1x1.
Your C matrix is a 1x1.
Your d matrix is a 1x1
 

Related to Scalar in terms of multiple variables, Nyquist & Bode Plot

1. What is a scalar in terms of multiple variables?

A scalar in terms of multiple variables refers to a single quantity that is independent of direction or coordinate system. This means that it only has magnitude and no direction, unlike vectors which have both magnitude and direction.

2. How is a scalar represented on a Nyquist plot?

A scalar is represented as a single point on a Nyquist plot. The point is located on the real axis and its distance from the origin represents the magnitude of the scalar value.

3. What is the purpose of a Bode plot?

A Bode plot is used to graphically represent the frequency response of a system. It shows the magnitude and phase of the system's output as a function of frequency, providing valuable information about the system's stability and performance.

4. How do you interpret a Nyquist plot?

A Nyquist plot is used to analyze the stability of a system. It plots the imaginary part of the system's transfer function against the real part, and the plot's shape and location can indicate whether the system is stable, marginally stable, or unstable.

5. What is the relationship between a Bode plot and a Nyquist plot?

A Bode plot and a Nyquist plot both provide information about the frequency response of a system. However, a Bode plot shows the magnitude and phase of the system's output, while a Nyquist plot shows the stability of the system. They can be used together to fully analyze the performance of a system.

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