MOD NOTE: This post was originally in response to this thread.

Here is my treatment of the so-called PWM to const current device. I suppose a better description might be a Voltage Controlled Voltage Source because the voltage at Rsense controls the voltage at the output. 10mA flows through Rload as long as it is between 10-500Ω with about a 1% ripple.

The workings of the two 555 timers for PWM operation can be found in the NE555 datasheet:

9.2.2 Pulse-Width Modulation
The operation of the timer can be modified by modulating the internal threshold and trigger voltages, which is
accomplished by applying an external voltage (or current) to CONT. Figure 18 shows a circuit for pulse-width
modulation. A continuous input pulse train triggers the monostable circuit, and a control signal modulates the
threshold voltage.

The feedback loop is completed with the opamp which compares the voltage at Rsense to a 1mV reference voltage. The operation of the circuit is similar to a boost converter without an inductor. I haven't figured out how to prevent the voltage overshoot during startup yet. I challenge the pros to take a stab at it.



For Rload = 500Ω:





For Rload = 10Ω:

 

What seems to be rather "not found" in this post is a question or a statement of a problem to be solved. That is why there have not been any responses. Including any of mine.

 

The overshoot is because your control loop is under-damped - you've got the 'P' of PID, but no 'I' or 'D' ! Go read up about PID controllers - a little bit of 'D' will help.

 

Irv has provided exactly the correct explanation, and pointed at the solution.