# Scalar in terms of multiple variables, Nyquist & Bode Plot

• YoshiMoshi
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.
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

## 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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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

## 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

## 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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