How to write user logic to control SOPC DMA controller?

Yes you can write the registers directly. You can get their address from the register map. First get the component base address in SOPC builder, and then add to it the register's number multiplied by 4.

As an example if the component address is 0x00001000, you can access register 0 at address 0x00001000, register 1 at address 0x00001004, register 2 at address 0x00001008 etc...

This is the address that you must use on the Avalon memory mapped master interface.