Core Strength is the foundation to every exercise. The key to strengthen your core is to take your time. Rushing will not help. If a plank on your knees BURNS, then stick with it. Why jump to your feet where your core is not strong enough to handle and your back starts compensating? This makes total sense when we read it but for some reason I still see SO many people RUSHING to get to the "top".
I promise if you just practice CONSISTENCY over INTENSITY you will win.
Hope that helps you get a new perspective on how you should train.
In any event, here are different plank variations that you can do / modify to meet you core's ability.