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The tail current of the input diff pair should be larger than the sum of currents created by the two PMOS of the folded cascode stage minus tha NMOS currents. That rest current goes trough the transistor with its gate to vcmp. Since the gate is fixed, Vgs makes the source of that transistor fix too. In that way, the common node of the diff pair is fixed and then both inputs.
Now, comments: I don like that circuit AT ALL. It's very difficult to control, specially with only 1.8V. If you just want to make it for educational purposes, fair enough. But if you want to produce it, I wont go that way.
You have to make sure that the remaining current is enough in every corner and mismatch situation otherwise the control transistor hasn't got gain enough to control the cm. You also have to take care of the output impedance of the tail current source. Remember that you are moving that node, if with that you reduce the current you could face that problem again.
PS. How are you controlling the cm of the two small opamps? Same way? )
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