Should the verb after "Чтобы" be infinitive or in the past tense?

Question

When do I use an infinitive after Чтобы and when do I use the verb in the past?

This is confusing me when Чтобы is used to express the purpose of one action by another. I mean sentences like these:

I woke up early to catch the train.

I woke up early so that we catch the train.

I'm inclined to think that the absence of a subject in the subordinate clause after чтобы is why the infinitive is used. Maybe when the subject is clear from context?

Я проснулся рано чтобы успеть на поезд.

Я проснулся рано чтобы мы успели на поезд.

Are these sentences correct?

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In other usages of Чтобы, things seem clearer to me:

Скажи ему чтобы не переживал.

У меня нет времени чтобы играть.

Are these correct? Did I miss anything of relevance?

Answer 1

All four sentences are correct, however for some of them better version exists stylistically-wise.

Subject is inferred from verbs' case. When you say чтобы успеть, subject is you unless stated otherwise чтобы ему успеть, when you said чтобы успел, subject is not you unless stated explicitly чтобы я успел.