I think what you are describing is akin to "split range," not "cascade," control. Split range control is when there are multiple systems to effect control of the Process Variable (PV) via a single feedback control loop (e.g. the PID), and the Controlled Variable (CV) output of the loop varies the output of each of the multiple control systems over a different portion of it's total range. One form of split range control is when one control system is heating and the other is cooling, and to control the system at any given time either might be required e.g. heat reactants initially (total output CV range of 50-100% corresponds to heating system output of 0-100%) then cool to remove heat from an exothermic reaction (total output CV range of 0-50% corresponds to cooling system output of 100-0%), or heat a building at night and cool it during the day.
In the case of this thread, 0-100% of the soak burner might correspond to 0-20% of the PID CV, and 0-100% of the main burner might correspond to 20-100% of the to PID CV, the soak burner would operate at 100% when the PID CV is above 20%, and the main burner would operate at 0% when the PID CV is below 20%. The actual breakpoint would not be 20%, but would depend on the relative process gains of the two burners.
I would think it would be easier to implement a simpler approach with two modes:
- Startup mode: run the main burner at 100% output until the measured temperature is "close" to setpoint,
- Soak mode: then switch to PID control using the soak burner.
This way the added complication of the relative gains of the two burners does not make the system tuning more difficult. Presumably the main burner is there to minimize the time it takes to add the necessary sensible heat to the initial materials at ambient temperature to get them to the soak temperature, in which case it makes sense to always run the main burner at 100%. The truck will be determining the temperature at which to transition from startup to soak mode: too low and time is wasted while the smaller soak burner completes the startup temperature rise; to high and the m main burner causes temperature overshoot.
Cascade control would have the measured temperature as the PV, plus a target setpoint (SP) to the primary PID, and the controlled variable (CV) output of that primary PID would connected , or cascaded, to the SP of a secondary PID, perhaps with measured fuel flow as its PV, and the secondary PID's CV output would be the valve position. That way any non-linearity in the valve characteristic would not affect the tuning parameters in the primary PID.