Understanding electronic loads
There's nothing wrong with the conceptual circuit. It's a simple 1A current sink. If you simulate this with practically any op-amp and a MOSFET such as a 2N7000 it will work fine at relatively low currents (from uA up to say 100mA) 

In actual practice at the 1A level it might not be stable without compensation for the MOSFET gate capacitance loading, but that is highly dependent on the op-amp characteristics and on the MOSFET characteristics (in particular Cgs). Here is an op-amp designed to be stable with very heavy capacitive loads, but it's not hard to accomplish with ordinary op-amps by closing the loop for higher frequencies separately from the gate DC. The gate then charges through an isolation resistor but that's not really PI control, as Tim says. 







simulate this circuit &ndash; Schematic created using CircuitLab