What is the script code of the PI controller with saturation and rate limiter in the ode form?

I want to implement below box in the script form. How to do it? I converted the PI block in ode as

du/dt = Wt_rated - wt; 
B_ref = Kp *(Wt_rated - wt) + Ki *u

where wt is coming from another ode equation

dwt/dt= (Pt - Pg)/wt;

But I don't able to code saturation and rate limiter block.

Also how to code hysteresis comparator?

Answer 1

[Namnendra]

Hi,

Implementing control system components like saturation, rate limiter, and hysteresis comparator in a MATLAB script involves creating functions or logic that mimic the behavior of these blocks. Below is a guide on how to implement each component in a script form, along with an example for each.

1. Saturation Block

A saturation block limits the value of a signal to a specified upper and lower bound. You can implement this using simple conditional checks.

function y = saturation(x, lower_bound, upper_bound)
if x > upper_bound
    y = upper_bound;
elseif x < lower_bound
    y = lower_bound;
else
    y = x;
end
end

2. Rate Limiter Block

A rate limiter restricts the rate of change of a signal. You can implement this by checking the difference between current and previous values.

function y = rate_limiter(x, x_prev, max_rate, dt)
rate_of_change = (x - x_prev) / dt;
if rate_of_change > max_rate
    y = x_prev + max_rate * dt;
elseif rate_of_change < -max_rate
    y = x_prev - max_rate * dt;
else
    y = x;
end
end

3. Hysteresis Comparator

A hysteresis comparator toggles its output between two states based on input thresholds. It is useful for reducing noise in switching.

function state = hysteresis_comparator(x, threshold_high, threshold_low, state_prev)
% If the input exceeds the high threshold, turn on
if x > threshold_high
    state = 1;
    % If the input falls below the low threshold, turn off
elseif x < threshold_low
    state = 0;
    % Otherwise, retain the previous state
else
    state = state_prev;
end
end

Integrating with ODEs

You can integrate these functions into your ODE solver loop. Here's an example of how you might incorporate them:

% Parameters
Kp = 1; Ki = 0.1; Wt_rated = 100;
lower_bound = 0; upper_bound = 200;
max_rate = 10; dt = 0.01;
threshold_high = 1.5; threshold_low = 0.5;

% Initial conditions
u = 0; wt = 0; B_ref = 0;
state_prev = 0; x_prev = 0;

% Example ODE solver loop
for t = 0:dt:10
    % Calculate control signal u
    du_dt = Wt_rated - wt;
    u = u + du_dt * dt;
    
    % Apply PI controller
    B_ref = Kp * (Wt_rated - wt) + Ki * u;
    
    % Apply saturation
    B_ref = saturation(B_ref, lower_bound, upper_bound);
    
    % Apply rate limiter
    B_ref = rate_limiter(B_ref, x_prev, max_rate, dt);
    x_prev = B_ref;
    
    % Calculate system dynamics
    dwt_dt = (Pt - Pg) / wt; % Assuming Pt and Pg are defined elsewhere
    wt = wt + dwt_dt * dt;
    
    % Apply hysteresis comparator
    state = hysteresis_comparator(wt, threshold_high, threshold_low, state_prev);
    state_prev = state;
    
    % Output or store results as needed
    % e.g., store B_ref, wt, or state for plotting or analysis
end

Notes

- Ensure `Pt` and `Pg` are defined in your script as they are used in the `dwt/dt` equation.

- Adjust parameters like `Kp`, `Ki`, `lower_bound`, `upper_bound`, `max_rate`, `threshold_high`, and `threshold_low` based on your specific application needs.

- The example assumes a simple discrete-time integration using Euler's method. For more accurate results, consider using MATLAB's built-in ODE solvers like `ode45`.