sigmoid pid equation in matlab

% parameters
x     = linspace(-6, 6, 1001);
Khigh = 5;  % upper bound
Klow  = 3;  % lower bound
alpha = 1;
% construction of sigmoid
h     = 1 + exp(-alpha*x);  
g     = Khigh - Klow; 
f     = g./h;
Kp    = Klow + abs(f);
% plotting the nonlinear gain Kp
plot(x, Kp, 'linewidth', 1.5)
grid on
xlabel('error')
ylabel('Kp')

5 个评论
显示 3更早的评论隐藏 3更早的评论

Sam Chak 2022-5-29

编辑：Sam Chak 2022-5-29

Hi @Shaz Shah

You did not comment about the suggested sigmoid in my previous post (edited to add an image of the plot). Anyhow, using the same parameters,

x = linspace(-6, 6, 1001);
Khigh = 5;  % upper bound
Klow  = 3;  % lower bound
alpha = 1;

I have fixed your code

Kp = Klow - (abs(Khigh - Klow)./(1 + exp(-alpha*x)));

and plotted it

plot(x, Kp, 'linewidth', 1.5)
grid on
xlabel('error')
ylabel('Kp')

but I don't see any straight line. Sigmoid should look like an 'S'-shaped curve. Furthermore, the upper and lower bounds are definitely incorrect. You are advised to sketch the 'S'-curve with the upper and lower bounds. Only then, I can give a proper advice on getting the desired Sigmoid curve.

Edit #1: I have made a minor modification. I think that your sigmoidal equation should look like this:

Kp = Khigh - (abs(Khigh - Klow)./(1 + exp(-alpha*x)));

Perhaps you mean this one:

Edit #2: I guess you want to enter the 'AbsTol' as

1e-5

without the space between '1' and 'e'.

Query:

Is there a reason for you to select the Logistic function as a sigmoid curve? Better performance?

By the way, technically, this should work already

Kp = Khigh - (Khigh - Klow)./(1 + exp(-alpha*x));

where abs(X) is unnecessary.

Shaz Shah 2022-5-31

Thank you for your response ,

now i need to compare between Simoid PID (advance controller) and PID by get better performance for sigmoid PID. i was did for PID last week and now progress for Sigmoid PID. But have some error that i need to solve.

请先登录，再进行评论。