I am looking for an analog device that will adjust the output to keep the difference between the inputs at zero.
This is, almost to the letter, an op-amp. However, there are some caveats to be followed. In particular, an op amp should meet your goals in your current schematic as long as:
- It is connected in negative feedback - i.e. as the setpoint increases, either the voltage to the inverting input increases, or the input to the non-inverting input decreases. With the way it's wired, V_setpoint would need to increase as V_feedback increases.
- The load on it is within the limit of the output drivers, i.e. an op amp will gladly drive a 100k resistor network, but probably not a motor or large lamp.
- V_measured and V_setpoint are both within its valid common-mode range (i.e. between +1.1V and +3.6V if it's a rail-to-rail input op amp)
- It has rail-to-rail output so it can achieve the output range you're asking for
- The system between V_setpoint and V_feedback does not include delays/lags that cause overshoot and oscillations, or you add sufficient compensation for them to keep it stable.
- The op amp is a low-voltage model that will operate on a supply of +2.5V.
- You're willing to relax the criterion of "linear fashion".
- The 1.1V and 3.6V rails are actually power rails with low impedance sources and can provide the op amp's necessary supply current without sagging or jumping.
Addressing a misconception:
The opamp applications that I know output zero or an offset voltage when the 2 inputs are equal.
Right, this is one simplistic way to model an op amp in open-loop configuration, but the op amp still meets your goals.
Suppose you had an op amp with no offset and an open-loop gain of 1 million. If you input 1.00000 V into both inputs, you'll get 0 V out. However, if you configure it as a unity-gain buffer and apply 1.00000 V to the non-inverting input, the output and the inverting input will end up at 0.999999, for a difference of 1 uV, which is pretty darn close to the goal of finding an output so "inputs are equal", and well within your ability to measure error.