A thermal feedback was installed to the end PDH locking and it works well. There are no saturations 

As I said the feedback signal was sometimes saturated at the sum-amp because the drive signal going to the laser PZT was large at low frequency (below 1Hz).

So I made a passive low pass filter which filters the signal controlling the temperature of the laser crystal, and put it before the temperature drive input.

Now the amount of the feedback signal got reduced when it is locked, and there are no saturations. It's very good.

(thermal property of the crystal) 

According to the specification sheet for the 1W Innolight, the thermal properties of the crystal are:

  Response coefficient : 3GHz/K 

  Temperature control coefficient : 1K/V

  Thermal response bandwidth: 1Hz 

(filter circuit and actuator response)

In order to feedback the signal blow 1Hz, a low pass fiter is needed. 

The attachment:1 shows the filter circuit I made.

Since I found that the drive input had an input impedance of 100kOhm, so I put relatively big resistors to have a moderate gain.

The expected actuator responses are also attached.

The blue curve represents the response of the PZT, the green is the thermal response including the low pass filter and the red curve is the total response composed of both the responses.

I assume that the PZT response is 1MHz/V according to Mott's measurement.

Also I assume that the thermal response intrinsically has two poles at 1Hz according to the specification listed above.

In the total response, there is a little gain reduction around 2Hz due to the cancelation of each other, but it still looks okay.