Introducing English Linguistics

Table 5.6. Primary and modal auxiliaries in English
Auxiliary Type
Primary
Present Tense
Past Tense
be/been/being
do(es)
did
am/are/is
was/were
has/have
had
Modal
Central
Phrasal
may/might
can/could
will/would
be going to
shall/should
ought to/need to
must
have to

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However, while will and is going to are interchangeable in this context, in
other contexts they are not.
Unlike primary auxiliaries, modal auxiliaries are typically not marked
for either number or tense. The modal must, for instance, has the same
form whether its subject is singular or plural:
The machine must serve the customer, not the other way around. 
(ICE-GB W2E-009 084)
The machines must ...
In addition, the difference between modals such as can and could is usu-
ally one of meaning, not of tense. In the example below, substituting
could for  can does not change the tense in the sentence but instead the
meaning: