I understand the need for flyback diodes when trying to change inductor current abruptly with a mechanical switch or when using a BJT/MOSFET as a switch.
Now, assume I (linearly) control the voltage across a coil with this op-amp circuit:
It seems to me that a flyback diode should not be needed at all with this circuit, even if we imagine that the op-amp has no internal diodes between its output terminal and its power terminals.
Let's say the circuit is steady at Vin = 4V so the coil current is 6A (from right to left). Let's then step Vin to 7V, which should decrease the stored energy in the coil. In my mind the op-amp should simply reduce current flowing through the lower transistor of its output stage at a rate which causes the EMF of the coil to result in 7V at the op-amp's output (when Vin is stepped the 6A through R1 mean that the right side of L1 is at 4V so the induced EMF across L1 would make it's left side 3V higher than the right side at that instant). This current change then ends when 3A are going through the inductor.
My question is: Is my understanding correct and theory dictates that a flyback diode is not needed for this circuit? If yes, is there anything missing from this simplified model which would require a flyback diode in real applications?
Note that this is more of a theoretical question aimed at improving my understanding and mental model of op-amps, so answers along the line of "just throw a diode in there to be safe" are unnecessary. This is a simplified version of my actual circuit which has dual-supplys and regulates current (using a current sense resistor between inductor and ground), so any explanation which allows extrapolation to more complex circuits is welcomed.