Solution to the rattling clicking noise with Agattus/ PC and other pedelecs
I accidentally submitted my post before finishing it.
So here is the solution for all who have suffered from this problem:
1. My first thought was that why don't the owners of the S (speed versions) pedelecs of Kalkhoff have the same issue. In the French forum I often visit, the people who complain about this issue are always the owners of the e-bike which speed is limited to 25 km/h (be it Kalkhoff or BH). No owner of S pedelec has complained about the problem. The only difference between C and S version is that the S version has 41T chain-wheel (instead of 35T on C pedelecs) and, more importantly 11-13T motor sprocket instead of 9T one on C pedelecs. So I bought the 41T chain-wheel and 11T motor sprocket and tried them without changing anything else (I did not change the chain length). It instantly solved the problem. No clicking sound and no jumping of the chain.
One would probably conclude that it is the chain length issue as with larger chain-wheel and motor sprocket, the relative length of the chain is reduced. However, then the chain should not jump on the smaller gears (larger rear cogs are engaged in smaller gears with derailleur) as the tension is higher. However, this was not the case as it jumped the same with all the gears. Moreover, to test my assumption, I even added 4 links to (from 132 to 136 total links) to my chain to make up the increase in motor sprocket and chain-wheel size. Again, no rattling and clicking noise in any gear and everything is smooth. If I inspect the system more closely, I can see that because of the bigger motor sprocket, the chain engages a bigger part of the idler arm pulley and the chain is not slipping, jumping under the load any more.
2. Lubricating the chain properly/professionally. Personally I think that the 9T motor sprocket is not well adapted (in US they sell the 11T and 41T version of the same bike) to the new Panasonic system and makes the chain to slip on the idler arm pulley if the chain is not in the perfect condition (after rain, some links are a bit stiff etc.) That explains why there is no problem whatsoever when the motor is not engaged. Therefore, if you do not want to fiddle with the motor sprocket and chain-wheel, you should lubricate your chain so that it is in perfect condition and as smooth as a new chain. It is not easy to do it for the particles tend to get inside the links with casual chain lubricating processes. This will accentuate the problem. Every time I lubricated my chain, the problem got worse. So, after some research, I bought
Shop quality Finish Line chain cleaner and cleaned my chain with this. Then I let it dry over night and lubricated separately every joint as explained in Sheldon Brown's website with a wet lube that also contains some grease (Finish line cross country in my case). The I wiped off all the excess. That gave me the chain that is almost in the same condition as the one on the new bikes. And a miracle, even with original chain length and sprockets (9T motor and 35T chain-wheel), there is no clicking or rattling.
So, in conclusion, you have two solutions (or 3, if you consider roblee's one), either you change you motor sprocket and/or chain-wheel (to keep the same assisted cadence), or you lube and take care of your chain using professional methods/tools. I use them both at once because with 9T motor sprocket you only need some rain or a dusty road to have your chain slipping again on the idler pulley. And you do not have to be in illegality in doing so because if you change your rear cog or cogs (in case of derailleur) to the size that sets your maximum assisted speed to 25-27 km/h, everything is ok. For example, in case of derailleur, the smallest sprocket on the rear cog should not be smaller than 14T. In case of hub gears, you have to do the calculation yourself but it is easy to do and there are many calculators on the web. There is also a possibility to reduce your chain length, but, in principle, it will only work with hub gear versions and not with derailleur ones.
What amazes me is that my bike was taken back to Germany for 2 months in order to have my chain properly lubricated. And of course nobody communicated to me that this was the case because that would put the dealer (the biggest kalkhoff dealer in France) in shame. Nobody also communicates the fundamental weakness of the transmission of the 9T motor sprocket, although, as described above, there are alternative, more robust solutions adopted by Kalkhoff themselves on they speed bike line. I you adjust the size of you chain-wheel/rear cog(s) accordingly, you would still remain with the same assisted cadence/maximum speed with 25 km/h versions (C or Agattu line). It makes me wander about the quality of German engineering, otherwise very reputed. I also hope the technicians and dealers in UK are better than those in France and do not send the bike back to Germany with this issue that even I, an amateur e-biker, could solve with some common sense. Before I buy my next e-bike, I will weigh my options much longer and it is not sure it will be a Kalkhoff.
Best,
Vaasa