> This sounds like an on-off controller with a predictive model. Well, not exactly. At the startup, yes, but that's because the goal is to get to stable point

> This sounds like an on-off controller with a predictive model. Well, not exactly. At the startup, yes, but that's because the goal is to get to stable point as soon as possible. Think of this move like suicide burn made by SpaceX boosters coming back to Earth:) The most efficient burn would be done at 100% of thrust with minimum margins. In case of heater obviously the fastest way to get to temperature is to use 100% of heating power immediately and calculate when exactly to turn it off (or to transition to idle power). But later the controller switches to maintain the temperature by producing power setting for the heater. The controller produces the desired power level as a value between 0 and 1 and this is then mapped (dithered) to turn the heater on/off for half cycles of AC power. The heater is only turned on/off on zero crossing to reduce emitted interference. For this I built a separate controller board equivalent to a solid state relay. I have actually used SCR diode pair + opto isolator + mechanical relay for safety (because SCRs may fail causing dead short). > If you're doing predictions, I'm not sure the estimator is technically called an MHE since MHEs only estimate the current state, not future states (it cannot because one technically cannot know future measurements). I guess this is why it is called estimator. Not only it estimates future, but also a parameter that cannot be directly measured. I test the controller against modified portafilter with a precise temperature sensor in it, but in normal operation, obviously, I don't get this. In some sense this is an open loop controller. Yes, I am using MHE to estimate current state (including model parameters) and use it to feed predictive model. The current state of the system is quite complex, and it is possible to describe it in many different ways. I like to think about it as various pulses of energy traveling through the system. One of my approaches to build predictive model was to measure effect of step pulses on the system (for example with the cold machine I apply 10s of full power, then measure the change over time). Then I tried to divide the operation of the machine into separate pulses (for example 1s of 70% of power) and superimpose predicted effects of those past pulses on future evolution. This is quite easy if you are just heating but quickly gets complicated when you also try to move water through the system. But I found it fun and gained some understanding of the thermal system.