Direct and reverse control

What is direct and reverse control?

Do you mean Direct and Indirect Acting Controllers (PID)?
If this is the case then this is the way the controller determines the Error.
Direct: Error = PV(process variable) - SP (setpoint)
Indirect: Error = SP - PV

For example: on a temperature controller if your PV is higher than the SP you want to increase cooling flow (open the valve). With a Direct Acting PV-SP gives you a positive Error which Increases the Output of the PID (open the valve)which will lower temp to SP. If it was indirect your error would be negative and the valve would close causing your temp to go higher.

The Other definition which is easier to remember is :

With increase in PV if MV increases: Direct Control

With increase in PV if MV decreases: Reverse Control

Direct Control - Output of controller increases as the process variable increases.

Reverse Control - Output of controller decreases as the process variable increases