feedback linearization

Feedback linearization is a trick for taming a system whose behaviour is nonlinear — meaning its response is lopsided and changes depending on where it is, like a pendulum that feels heavy near horizontal but light near the bottom. Such systems are hard to control because the simple, reliable tools we have work best on linear systems, where doubling the input always doubles the output. Rather than give up that simplicity, feedback linearization wraps the messy system in a layer of cleverly chosen feedback (control commands computed from the system's measured state) that cancels the nonlinear lumps. To the outside controller, the combination then looks and acts perfectly linear.

The recipe is: model the nonlinear forces, then at every instant compute and inject exactly the counter-command that erases them, leaving a clean target relationship of your choosing — typically 'whatever I ask for, the output simply follows.' It is like driving a car whose accelerator pedal behaves wildly at different speeds, but with a smart assistant who silently adjusts the throttle so that, from the driver's seat, the pedal feels perfectly ordinary at every speed. Once the system feels linear, you can design the actual steering with all the well-understood linear methods and proofs.

The price is honesty about your model: the cancellation only works if you know the nonlinear terms accurately, and it can demand large control effort or break down near singular configurations where the math blows up. So engineers often combine it with robust or adaptive layers to absorb the inevitable mismatch between the model and the real machine.