Tuning parameter in Sliding Mode Control

You haven't provided many details but if you are using an analog output then use a tanh function. For a simple motion controller I would use u=10*tanh(k*s) where: u is the control output

If you have a digital on-off system then you try different boundary layers until satisfied.

First thing first. Do you know how to compute the constants for the error and each derivative of error that is used to compute s?

Peter Nachtwey

Thank you for your reply.

I compute the s using the definition

S = (d/dt + lambda)^(n-1) * ( X - Xd)

where n : order of the system (in my case n=2) X : state variable Xd: desired state lambda is a design parameter and is a kind of cutoff frequency.

In Slotine's book, the control output is suggested

u = un - k(x) sat(s/phi)

where un : estimate of the control output using the known k : gain phi : boundary layer thickness

It was my fault that I had not provided the details.

And I'm still wondering about the relationship among the unmodeled mode, phi, and lambda.

Would anybody help me?

Thank you.

Thank Mr. Nachtwey for the reply.

I compute the s using the definition

S = (d/dt + lambda)^(n-1) * ( X - Xd)

where n : order of the system (in my case n=2) X : state variable Xd: desired state lambda is the sliding line slope and is like a kind of cutoff frequency.

In Slotine's book, the control output is suggested

u = un - k(x) sat(s/phi)

where un : estimate of the control output using the known k : gain phi : boundary layer thickness

It was my fault that I had not provided the details. And I'm still wondering about the relationship among the unmodeled mode, phi, and lambda.

Would anybody help me?

Thank you.