sigmoid pid equation in matlab

hai everyone , how do i write this sigmoid pid equation into matlab

[Star Strider]

MATLAB Academy

Answer 1

[Sam Chak]

Hi Shah

I'm curious to to see how your designed Kp looks like. What is the pid equation?

Edit: Kp is a nonlinear proportional gain shaped by the sigmoid curve that is bounded by and .

% 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')

[Shaz Shah]

hai sam chak

thank you for your response

PID equation is

Kpid(s) = Kp+Ki/s+Kds

after applied PID equation and sigmoid we will get base on equation on photo above but i just show for Kp only.

the parameter of K_low and K_high are lower and upper bounds of the coefficients, and e(t) is an error function

[Sam Chak]

Thanks for the clarification. Then I think it should look like this, where x is the error signal measured somewhere. In this plot the error is defined through linspace.

x = linspace(-5, 5, 1001);
Khigh = 5;
Klow = 3;
alpha = 1;
h = 1 + exp(-alpha*x);  
g = Khigh - Klow; 
f = g./h;
Kp = Klow + abs(f);
plot(x, Kp)

[Shaz Shah]

Thanks for your response

is it correct if i do the equation in direct straight line like this?

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

and can i know what is the problems in this error ?, i was stuck here

Error evaluating expression '1 e-5 ' for 'AbsTol' specified in the Configuration Parameters dialog for block diagram 'TRMS4SigmoidPID_simulink'.

[Sam Chak]

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]

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.

Answer 2

[Mohd Ashraf]

Hi Shah,

You may refer to this link:

https://drive.google.com/uc?export=download&id=1Ut-zX3cTKn3r_kepRDe7_A5WPlsW3qjs

for the detail of the sigmoid PID code.