Is there a mathematical way to match the effect of 13 amps (or any other) output with on/off switching? Or is it strictly based on empirical experiences with just longer off to on ratio?
Manual control could easily be implemented by setting the on/off ratio over a repetitive time interval. So in essence, this is PWM but at a much lower frequency that's compatible with the SSR-40DA (or equivalent) relay.
Examples:
Emulated ± 1 amp control ( 0 amp to 23 amp maximum), 24 steps.
Use 0 to 23 second ON time range and 23 second interval, where:
AMPS ON(sec) OFF(sec)
0 0 23
1 1 22
2 2 21
etc, up to
23 23 0
Emulated ±1% control ( 0 amp minimum to 23 amp maximum), 101 steps.
Use 0 to 100 second ON time range and 100 second interval, where:
% ON(sec) OFF(sec)
0 0 100
1 1 99
2 2 98
etc, up to
100 100 0
If the 100 second interval is too long, then you could still get ±1% control with 20 second interval, where:
% ON(sec) OFF(sec)
0 0.0 20.0
1 0.2 19.8
2 0.4 19.6
etc, up to
100 20.0 0.0
For control, the existing pot could be re-used and connected to an analog input.
For automatic control you'll need a temperature probe and that can be monitored at another analog input. The existing pot could then be used to set the required temperature.
If higher resolution is required, there could be more adjustment (timing) steps added.
If better performance (temperature regulation, etc) is required, PID mathematics could be used.