The informal commands follow the present tense subjunctive
Negative informal command and formal commands use the present tense subjunctive endings.
Why don't you ask for it? Que lo pidas. (¿Por qué no lo pides?)
Let's sleep now. Que durmamos ahora
The "exhortations" aren't what's normally referred to as informal commands.
The negative, informal command is formed by using the 2nd person, singular, informal, present tense subjunctive ending.
No lo pidas. (Don't ask for it) tú
The formal command (affirmative or negative) uses the 3rd person, singular and plural forms of the present tense subjunctive.
No lo pida. (Don't ask for it) usted
Now, to get back to your original question.
The reason that you see the stem changes in this mood is because the present subjunctive tense is formed by taking the 1st person, singular of the present tense indicative as the verb stem. This 1st person, singular form (indicative) contains stem changes so they likewise appear in the imperative mood.
Confusing, so let me repeat it. The imperative mood form is based on the present tense, subjunctive mood which, in turn, is based on the 1st person, singular of the indicative mood. Since this indicative mood form has stems changes, the subjunctative mood does also, which makes them subsequently appear in the imperative mood.
Clear as mud?
pongo=1st person, singular, present tense, indicative mood
pongas=2nd person, informal, singular, present tense, subjunctive mood
ponga=3rd person, informal, singular, present tense, subjunctive mood
pon=affirmative, informal, imperative (singular)
pongas=negative, informal, imperative (singular)
ponga=positive & negative, formal, imperative (singular)