英语中补语的问题，求助！

Question

是这样：
我知道补语有宾语补足语和主语补足语。
如 he always keeps the room clean. cleam就是宾补，这个我知道。
主补是被动语态中宾补就变成了主补
比如
i asked him to read the text.
he was asked to read the text by me. to read the text成了主补，知道我也知道。

我想问的是：
比如i am busy (in)doing my homework.
(in)doing my homework有人说是补语，我不明白就在这：这个是主-系-表结构，没宾语也不是被动语态，(in)doing my homework怎么就成补语了？
也就是补语在什么情况下能出现？
还是说(in)doing my homework不是补语，那是什么成分？

初学，高手详细说下，满意一定追加！

Answer 1

有六种宾语的补语，其实这个语法点如果你不是英语专业的话是不用掌握的很清楚的，重要的是动词搭配，像第一句例句Father will not allow us to play on the street. ，虽然是考补语，但主要的考点还是allow sb. to do sth.，把动词搭配搞清楚，就做得了题目了。
1.不定式(to do)
Father will not allow us to play on the street. 父亲不让我们在街上玩耍。
We believe him to be guilty. 我们相信他是有罪的。
We made him copy the sentence.
He is made to copy the sentence.
I felt my hands tremble.

2.名词
At the meeting we elected him monitor.
I think your brother is a clever boy.

3.形容词
What you said made Xiao Wang angry.
I found the classroom empty

4.副词
Please call the students back at once.
He was seen to take his cap off.

5.现在分词
We hear him singing in the hall.
I found him lying in bed, sleeping.

6.过去分词
He saw his face reflected in the water.
I heard it spoken of in the next room.

Answer 2

补语就是起到补充说明的作用
在这个句子里面，in doing my homework 就是起到补充说明busy、的
所以是补语。

Answer 3

我认为(in)doing my homework是介词短语作原因状语。doing my homework是in的动名词短语宾语。