I would like to be able to run this motor clockwise and counter-clockwise and speed control.
I have 3 phase power 380 volts (AC) and this is a 110 V DC motor (max 40 amps).
What is the correct type of controller for this?
There are a lot of DC motor controllers on the market. You start by selecting one with output voltage and current ratings suitable for the motor.
The motor's torque rating appears to be 15 Newton-meters. The torque constant is 0.5 N-m per amp. That would mean the controller must supply 15 / 0.5 = 30 amps.
You need to determine if the motor requires a separate power supply for the field. Since that isn't marked on the nameplate, the motor probably is a permanent-magnet motor and requires no separate field supply.
The nameplate indicates the motor has a tachometer generator that produces 20 volts per 1000 RPM or 40 volts for the 2000 RPM rated motor speed. The controller will need to accept that.
Since the motor apparently does not have a wound field, it can be reversed only by reversing the polarity of the armature voltage. That can be done electronically, by using contactors, or even by using a switch. Electronic reversing is likely preferable and the method most likely to be included in some available controllers.
You will probably need a transformer to reduce the available 380 volts to the voltage required by available controllers.
Find what is available for sale in your part of the world and review the features and specifications for suitability with your motor and operational requirements.