Here are some good ways to fix that sentence:
- As a principal, I must balance the budget.
- As a principal, it is your role to balance the budget.
- As a principal, you should give all your teachers big fat bonuses.
Phrases that begin with a preposition ("as") and end with a noun ("principal") that answer the question, who? or what? are called prepositional adjectival phrases. They begin with prepositions and act as adjectives. If you write "As a principal, the budget must be balanced," then the adjectival phrase appears to modify "budget" and clearly the budget is not the principal.
The error is easy to see in this example because I've written a very short sentence to demonstrate the problem. As an editor, I see much more complex sentences in which the logic error is more difficult to spot. (Did you notice that when I begin the sentence "As an editor," I need to follow it immediately with the subject "I"?) How about this one: "Juggling many demands including paperwork, medication schedules and meals, regular rounds are necessary for a busy nurse to ensure patient care is maintained."
Who is doing the juggling? In this case, the sentence seems to imply that the rounds are juggling many demands because the subject of the introductory phrase should be the same as the subject of the main sentence. I would fix this sentence by changing the subject of the main clause: Juggling many demands including paperwork, medication schedules and meals, a busy nurse needs to do regular rounds to ensure patient care is maintained."
Any time you introduce a sentence with an adjectival prepositional phrase, ensure the subject of the sentence is the noun you intend to modify with the introductory phrase.