How can I get/build a current controller/amplifier?
simulate this circuit &ndash; Schematic created using CircuitLab

Class D audio amplifier would be a good choice. The one that you can eliminate the blocking capacitor at the input. Your current requirement seems to be a close match for what an D class amp is made for. 

But, the audio amp would amplify the voltage in certain relation. It compares input voltage and feedback voltage at amps output. Not a voltage to current converter.

You should put a shunt resistor in series to a load, then measure this current and close the loop with a P controller - supposing that you have successfully eliminated the DC blocking capacitor at the input. You would need an opamp, a small dual power supply and couple of resistors.

EDIT:

The current is measured with Rsh. A voltage drop is created on this resistor Vsh=I*Rsh. This voltage is then filtered with a low pass filter 1kohm + 100nF. Without R6 mounted, the loop gain is very high and could make the whole thing unstable, you should adjust the gain. You could use also one another opamp to separate the LP filter and gain setting.

IRAUDAMP9 no blocking capacitors at input signal



This is a schematics of IRAUDAMP with IRS2092, you will find many cheap boards with this setup, most of them require strictly the voltage power supply as declared.
Instead of the speaker, you should attach your load. The ground has to be the same for IRAUDAMP and for the P controller.







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Fixed LP filter and separate gain setting:







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EDIT2 :

Supposing the input and output voltages are out of phase by 180 degrees. You can see that both are summed by inverting input of opamp in IRS2092, so the conclusion is that they are shifted, and so the current is also shifted. The P controller has to get new shape:







simulate this circuit

You might need to attenuate the +/-10V setpoint value to a lower value also to fit to the amplifier input voltage:







simulate this circuit