Nonlinear and Adaptive Control

A: A looks boring, which is why it wins today. Anti-windup plus rate limiting directly targets the failure cause in the DFMEA: integrator windup under saturation. B tempts people who want 'adaptive' on the slide deck, but implicit handling of saturation is how you get parameter drift when the actuator rails. C assumes you know friction and inertia; you don't even have datasheets, so cancellation error becomes the new failure mode. D feels safe because of invariance, yet boundary layer sizing off worst-case friction trades chatter for tracking error, and that error feeds back into the hazard severity you're trying to shave.

A: Start from the 80 ms time constant. That's about 12.5 rad/s. A keeps adaptation slow enough that the plant dynamics settle before parameters move. B is a classic controls exam answer, but in hardware it turns sensor noise into parameter motion. C sounds safe, yet with that speed the adaptation never reacts within a maneuver, so the benefit vanishes while complexity stays. D ignores physics; CPU rate isn't the stability limit, excitation and noise are.

A: A is the quiet failure everyone misses. Lyapunov gives boundedness, not zero error, once the adaptation law is clipped. B would require the Lyapunov conditions to be broken entirely; saturation alone doesn't do that. C feels intuitive, but most designs remain stable, just wrong. D is backwards; quantization plus saturation is how limit cycles are born.

A: A is conservative and that's the point before SOP. The derivative of sin is cos, bounded by 1. B sneaks in a small-angle assumption, but observers care about bounds, not approximations. C misreads the math: cos(x) peaks at 1, not 0.88, in that interval. D is wishful thinking; linearization doesn't erase the nonlinearity in the real plant.