Are there any tips on how to properly cook brown rice using a portable induction burner? I use my standard ratio of 1 cup rice to 1 1/2 cup water bring to a boil, cover and reduce to low for 20 minutes, let stand for 10 minutes on the regular electric stove top. However my induction burner is labeled warm, simmer, boil and I have yet to achieve satisfactory results.
For what it's worth, I find it difficult to get brown rice cooked properly using any sort of regimented process. It seems sensitive to the variables involved, and it doesn't come out right without me being more involved in the cooking process.
So, I follow the procedure which (if I recall correctly) I found in Cook's Illustrated: cook the rice in a much larger volume of water than is needed (two-to-one, or even three-to-one if you can spare the room in the pot), stirring occasionally, monitor done-ness by tasting the rice periodically, and when the rice has the desired consistency (different people prefer different degrees of firmness), take it off the heat and drain it (e.g. in a chinois).
Even using this approach, it's important to maintain the heat relatively low, at a simmer. But it's a lot more forgiving than techniques that demand you get the rice-to-water ratio perfect, because you never run out of water, and the rice never sticks to the bottom of the pot.
The "simmer" setting on your hob should work well with this approach, but if the hob is so underpowered that "simmer" doesn't simmer, the "boil" setting might work out okay, if that setting doesn't in fact result in a very vigorous boil.
At the end of the day though, if your hob has only two cooking levels (plus the "warm" setting), it might just not be a hob worth using. There are plenty of other hob choices out there, which allow a more fine-grained control than choosing between "not quite warm enough to simmer" and "rolling boil", and with a better hob, cooking rice should be very easy, whatever technique you prefer.
I have learned to cook my rice (any kind) this way:
Cook for a set time in a lot of water, drain almost all of the water and let stand for 15 minutes with a closed lid (or other cover.)
If you live where it is not hot, cover the pan or keep it in a protected environment, under the covers of a bed or in a straw filled box will do nicely. In an office environment you can use an (old) winter coat.
For the rice I use 15 minutes of cooking time will do, with the additional 15 minutes resting time. But you can experiment to get the right time for you. You can regulate the water temperature a bit by adding a lid or leaving it off, throwing in a small handful of water if it is going too fast. The more covered, the more heat it retains and the more rolling the boil.
This method still allows you to over cook for a mushy, sticky, rice or under cook for rice needed to cook a bit in the next stage of food preparation. Just adjust the cook time and still drain and rest.
An other advantage of this cooking method is that it allows you to use your hob(s) for a sauce while the rice is resting.
Like with any burner you want to bring the water to a boil first and then cover and simmer. So you'll want the lowest setting on the burner, and if the burner is too hot on the lowest setting (so the water boils off and the bottom burns before it's cooked through and tender with just a bit of bite) then you can try offsetting the pot from the burner so maybe 2/3rds of the pot is on the burner (or less, depending on how hot your burner is). This works best with a pot with good conduction, such as a copper bottom.
You can also use more water to offset the extra water loss from evaporation. All rice needs a 1:1 ratio of water to rice to cook properly, but because of evaporation you generally need more water than this. The amount more depends on cooking method, pan surface to volume ratio, and other factors. I'd suggest adding 1/4 cup more water and see how you fare.
If you have a sous vide setup you can seal the water and rice in a bag (1:1 ratio) and it will come out perfectly. If you want to try this, cook at 200°F for the amount of time the recipe calls for for the type of rice.
First, you seem to be cooking by using a timer. Forget that. Time given in recipes tends to only be a rough guide for how to cook - you should cook until done, not until a timer goes off.
Second, the labels on your induction cooker don't matter. They could be called "S", "M" and "L" for what it's worth. Just because a setting is labeled "simmer" it doesn't mean that it will actually keep any pot with any amount of any food at a simmer.
So, what you have to do is to stop relying on settings and formulas and pay attention to your food. Place the rice in the cooking water, and reduce until it is at a constant simmer ("constant" here means averagely, over time - it is not a problem if you hear the bubble noise go up for a few seconds at the peak of the induction heat cycle). If it turns out that you don't have a setting that produces a constant simmer, you may even have to change settings once per minute, or pull the pot off the cooker for a few seconds, then back on, etc. (Since that's tiring, if it happens, try using a different pot or make a different-sized portion next time, and hopefully you will find a combination that works). You may want to start with less water than anticipated and add it during the cooking, or with more water and then throw it out, as Willeke suggested. And you stop when the rice is done - the decision is reached by tasting it, not by the clock.
When you have found a combination of pot, portion size, rice variety, rice/water ratio and cooker setting that works for you, you can write it down so you can leave it alone next time. You can also pre-emptively turn it off and let it sit the last minutes (probably longer than if it were still on the stove) as your current recipe suggests. But you will have to find out empirically what time works for your situation.