How to plot the Eular Transformation?

Question

Hardik 2022-12-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1883422-how-to-plot-the-eular-transformation

回答： Sulaymon Eshkabilov 2022-12-24

hello below is my question I have derive the bilinear TF but when I try to do the Euler transformation part I am not able to do that. I want to implement forward type but i dont know where to start.

below is my Question

Use sampling period of 0.10 Sec Euler transformations to convert the compensated systems into digital (discrete). Provide the overall closed loop transfer function (indiscrete domain) andraw the step responses of the systems obtained

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Paul 2022-12-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1883422-how-to-plot-the-eular-transformation#answer_1134682

在 MATLAB Online 中打开

The Control System Toolbox, for unknown reasons, doesn't support the forward or backward Euler transformations. I'm not aware of any other toolboxes that do either.

You can implement them with a bit of work, see this answer for one approach illustrating the forward method.

Or, you can go back and forth with the Symbolic Math Toolbox, which would be pretty straightforward.

Also, instead of using bilinear, you can use c2d and save a few keystrokes:

num = [1.5 60 600];
den = [1 15 83 210.5 300 700];
Qc  = tf(num,den);
Fs  = 10; % 1/0.1=10
Qp  = c2d(Qc,1/Fs,'tustin')
Qp =
 
  0.0003777 z^5 + 0.001133 z^4 + 0.001133 z^3 + 0.0003777 z^2
  -----------------------------------------------------------
    z^5 - 3.739 z^4 + 5.558 z^3 - 4.098 z^2 + 1.5 z - 0.218
 
Sample time: 0.1 seconds
Discrete-time transfer function.

2 个评论
显示无隐藏无

Paul 2022-12-22

Show what you've tried so far .... even on paper (you can click the image icon in the Insert menu to upload an picture if you need to).

Paul 2022-12-23

That expression for for Hf is incorrect, it should use the tf command.

There is no such function c2d_eular.

There is a function c2d in the Control System Toolbox and in the System Identification Toolbox, but neither supports forward or backward Euler tranformation.

So you'll have to implement something yourself.

Do you know the relationships between s and z for forward and backward Euler?

请先登录，再进行评论。

Answer 2

Sulaymon Eshkabilov 2022-12-24

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1883422-how-to-plot-the-eular-transformation#answer_1135352

在 MATLAB Online 中打开

num = [1 2];

den = [1 2 3 4];

Qc = tf(num,den);

ts = 0.1; % Sampling time

Qd_zoh = c2d(Qc,ts,'zoh') % Continuous - to - Discrete with zero-order-hold

Qd_zoh = 0.004988 z^2 + 0.0009038 z - 0.004083 ------------------------------------- z^3 - 2.79 z^2 + 2.612 z - 0.8187 Sample time: 0.1 seconds Discrete-time transfer function.

Qd_foh = c2d(Qc,ts,'foh') % Continuous - to - Discrete with zero-order-hold

Qd_foh = 0.001664 z^3 + 0.005284 z^2 - 0.003778 z - 0.001362 --------------------------------------------------- z^3 - 2.79 z^2 + 2.612 z - 0.8187 Sample time: 0.1 seconds Discrete-time transfer function.

step(Qc), hold on

step(Qd_zoh)

step(Qd_foh)

xlim([0, 15])

legend('toggle')