Signal inversion inside an interval

Hi folks,

I have a dynamic system with triggered logic.

Statement: as soon as x is between two values, do not alter y. At the limit x = x_min or x = x_max, invert the signal of y. The variable x has a saturation function on x = x_min and x = x_max.

Attempt: I have tried to use the Interval test block. This block has inverted logic and triggers only if the value is outside the predefined interval. Hence, if one defines an infinitesimal epsilon near to the boundary, as soon as x is epsilon of it, inverts the signal y.

Problem: If the next integration step results also on a value inside this epsilon-interval, which makes the signal invert very quickly.

If there is an ellegant way to solve it, I thank sincerely.

Answer 1

[sanidhyak]

Hi @Bruno Peixoto,

I understand that you are trying to implement a triggered logic system in MATLAB where “y” should remain unchanged when “x” is within a specific range and invert only when “x” reaches “x_min” or “x_max”.

Your current approach using the “Interval Test Block” causes rapid toggling due to repeated integration steps inside the “epsilon” threshold. To resolve this issue, I suggest two solutions:

Solution 1: MATLAB “Function Block” Approach

You can use a MATLAB “Function Block” with a persistent variable to ensure “y” toggles only when “x” reaches “x_min” or “x_max”. Kindly refer to the following function:

function y = control_logic(x, y_prev, x_min, x_max) 
% Define a persistent variable to store the previous state of y 
persistent y_state; 
if isempty(y_state) 
    y_state = y_prev; % Initialize y with the given previous value 
end 

% Check if x is at the boundaries and invert y 
if x <= x_min || x >= x_max 
    y_state = -y_state;  
end 

% Output the updated y value 
y = y_state; 
end 

This code retains the previous value of “y” using a persistent variable and toggles “y” only at “x_min” or “x_max”, preventing rapid oscillations.

Solution 2: Stateflow Chart Approach

Alternatively, you can use a “Stateflow Chart” for a more structured approach. Follow these steps:

1. Open Simulink and add a “Stateflow Chart”.
2. Define three states:

- "Hold" (when “x” is within bounds).

- "Invert_Positive" (when “x = x_max”).

- "Invert_Negative" (when “x = x_min”).

3. Set up transitions:

- If “x = x_max”, switch to "Invert_Positive" and set “y = -y”.

- If “x = x_min”, switch to "Invert_Negative" and set “y = -y”.

- Otherwise, stay in "Hold".

This would prevent rapid toggling by ensuring the inversion occurs only at strict boundary conditions and remains stable during integration.

Kindly refer to the following MATLAB documentations for further references:

• https://www.mathworks.com/help/simulink/ug/what-is-a-matlab-function-block.html
• https://www.mathworks.com/help/stateflow/getting-started.html

Cheers & Happy Coding!