For reference here and because it may change, the circuit you are currently asking about is:
This is supposed to regulate output current, but the complaint is that it is unstable. R1 is meant to be a high side current sense resistor. You say this is for charging 12 V lead acid batteries. You don't say what current, but probably a few amps. In that case 100 mΩ seems rather large. Note that at 5 A it will dissipate 2.5 W.
However, the large current sense resistor should only make measuring the current easier. It looks like your intent is that OA2 provide a ground-referenced voltage proportional to the current thru R1. That concept is good, but the implementation is flawed.
What you need is a "diff amp" that has some finite gain. The differential part eliminates the common mode voltage on R1, but the finite gain part is also important. As it is now, OA2 is being used open loop as a comparator. It's output will quickly switch between full high and full low as the current goes slightly above and below the regulation threshold.
Another problem is that the top of M3 is not connected anywhere, so it can't source any current onto R7. I don't know what that dashed line is supposed to show. Usually if things are connected to it like that it means a conductive case, but you show nothing else connected to it. A case is usually grounded, which is certainly not what you want the source of M3 (strange designator for a FET) connected to. It also makes no sense that you need to buffer the output of OA2 amplifier. I didn't look up a LM358, but if that does not have a push pull output stage, get one that does.
All in all, I'd lose the wierd current sense amp circuit as it is now. There are diff amp chips that do what you want directly. Sometimes they are called instrumentation amplifiers. These have a truly differential input, finite and sometimes adjustable gain, and the output can be referenced to some other voltage like ground.
Once you have a reasonable ground-referenced voltage proportional to the output current, you can feed it into the negative input of OA1 as shown. However, you have to make sure that the controller (OA1 in this case) is slower than everything else in the system. I mentioned this already in another one of your questions. Put a cap between the output and the negative input of OA1 to slow it down. This may require a resistor between the current sense amplifier output and the negative input of OA1 so that the cap has some impedance to work against. Do not under any circumstances attempt to slow down the current sense circuit. That will only make things worse.
jippie's right. D2 is your problem. On the reverse cycle, you've got no regulation on the voltage/current from D2.L3's top is at "virtual ground". L3's bottom is at positive 23 volts or so. This forward biases D2. The output is the cathode side of D2 I assume. That means you've only got regulation on 1/2 of your cycle (through D1). Your regulator sees the high voltage and tries to shut it down, but the power isn't coming from the regulator side. It's coming from D2 so all it's effort to shut the voltage down is in vain.
In short, you want the cathode of D2 connected to the cathode of D1. This will force both sides of your transformer to go through the voltage regulator circuit you've created.
Best Answer
For an ideal op amp, which has zero input offsets and infinite gain, nothing happens.
For real op amps, the output will change slightly with changes in the power supply voltages. The ratio between the supply changes and the output changes is called the Power Supply Rejection Ratio (PSRR)or Supply Voltage Rejection Ratio (ksvr). The ratio will vary with op amp, and to make things more complicated the number for any op amp will vary with frequency. Higher frequency supply variations will produce a greater output variation than lower frequencies.
In general, for low frequencies, the rejection ratio will be on the order of 80 to 100 dB.