After few hours spend on reading about control theory and PID controllers in particular I came to the conclusion, that PID controller is not suitable for my oven project mostly because it's on/off device. Although you can set temperature on most ovens, there is no simple way for me to control the knob on the panel - this is obvious. So instead SSR (a relay) is used, transforming the oven into on/off device. In a PID controller I is used to speed up the process increasing the overall value (lets name it u, where u = P + I + D). So lets assume, that setpoint (SP) equals 100°C, and PV (actual temperature) equals 20°C. Thus the error (e) is 80, and hence P > 0, the u becomes 1, oven starts to heat up. I increases every Dt (delta t), because it accumulates the past errors, but heating cannot be speed up : you cannot turn it on more. Similar consideration goes to D.

So for now I think, that the best solution will be to implement a on/of (bang-bang) controller with deadband (deadband dependent on thermal capacity of the oven used).

Fixed some issues with thermocouple.