Scalar in terms of multiple variables, Nyquist & Bode Plot

[YoshiMoshi]

Homework Statement

A scalar is given by

It is controlled by

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

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!

 

[donpacino]

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