I fully agree. Now, what do you see as the unanswered questions to be discussed? My own thought is whether or not a simple on / off controller can do the job for you. If I recall correctly, the task was to produce a kettle that will heat water to some pre-set temperature near 100C (must have the ability to change this setpoint with reasiable precision, so needs a calibrated setpoint scale) and hold it there (well, within some specified tolerance of "there"). So one way is a relatively simple controller that uses temperature measured in the kettle water (or through the wall of the kettle via a surface sensor) to turn the kettle power supply on or off. Of course, the controller will need to be able to switch 15 A at 120 VAC, or whatever the supply is in your location.
The alternative, if that type of control cannot give acceptably close tolerance to the temperature setpoint, is to use a Proportional controller (more likely a PID controller without trying to optimize the Integral and Differential portions) for much smaller tolerance of temperature maintained once the setpoint is reached. The controller must still be capable of varying the voltage and current supplied to the kettle with a maximum of 15 A at 120 VAC (or locally appropriate). This type of controller MAY be slightly slower to reach setpoint because it will start to reduce the kettle current as setpoint is approached, but it can give you tighter tolerance.
The choice depends on how much tolerance you need on the temperature maintained. It also depends, to some extent, on the specific controller chosen, in that within each of these two types there is a range of sensitivity / tolerance that can be achieved, depending on the sensor and actuator technology employed.
The alternative, if that type of control cannot give acceptably close tolerance to the temperature setpoint, is to use a Proportional controller (more likely a PID controller without trying to optimize the Integral and Differential portions) for much smaller tolerance of temperature maintained once the setpoint is reached. The controller must still be capable of varying the voltage and current supplied to the kettle with a maximum of 15 A at 120 VAC (or locally appropriate). This type of controller MAY be slightly slower to reach setpoint because it will start to reduce the kettle current as setpoint is approached, but it can give you tighter tolerance.
The choice depends on how much tolerance you need on the temperature maintained. It also depends, to some extent, on the specific controller chosen, in that within each of these two types there is a range of sensitivity / tolerance that can be achieved, depending on the sensor and actuator technology employed.