Change symbol used for anti-windup gain

[Richard Murray]

On 14 Nov 2018, at 6:53 , Karl Johan Astrom [e-mail] wrote:

Richard,

Have made a slight modification of stability of anti-windup schemes and example, one small thing I would have a slight preference to change $k_\text{f}$ to $k_\text{t}$ because it is called a tracking gain, but I let you decide, global change is necessary.

Karl

[Richard Murray]

See commit 319315e.

[Richard Murray]

Reverted back t o$k_\text{t}$ in commit 8cee139.

Comments to Karl via e-mail:

We are already using k_f for the feedforward gain in the state feedback work, so I think we probably want to avoid that particular symbol.

Having said that, I am not that big a fan of k_t since it doesn’t really link to anything (we don’t use the term “tracking gain” in the text => the ’t’ is not that natural). A couple of options:

• We could use some other symbol, like k_a or k_{aw} (for antiwindup). This might be in conflict with what is used in the standard PID literature, though.

• We could change to k_f and just note the conflict with the state space notation. Is there something that ‘f’ stands for that we should point out so that students can remember it?

• We could leave as is (k_t).

For now I am included to either leave as k_t or change to k_a (but only if you think this won’t cause confusion).

[Richard Murray]

There is now a macro \awsub that should be used for the anti-windup subscript. This currently expands to \text{aw}.

[Richard Murray]

Subscript changed to \awsub in all locations.