Control System Expert for Overhead Crane Simulation

I need an expert in control systems and nonlinear dynamics to help me explain and justify simulation results for an Overhead Crane (cart–pendulum) anti-sway system implemented in MATLAB/Simulink.

I have already designed and implemented multiple controllers:

a linear controller based on local tangent linearization around the equilibrium, and

nonlinear controllers (Backstepping and Sliding Mode, with several variants).

In many nominal and moderately perturbed cases, the linear controller clearly outperforms the nonlinear ones — not slightly, but significantly, even though the system is inherently nonlinear.
However, when I increase the system masses by a large amount (trolley and/or payload), the performance of the linear controller degrades strongly, and the nonlinear controllers can then outperform it. I want to understand, explain, and rigorously justify these behaviors.

Your tasks:

Use the provided MATLAB/Simulink files and system model documentation.

Design rich and well-chosen simulation scenarios by strongly varying:
masses (trolley/load), cable length, damping/friction, initial conditions, disturbances/noise, and actuator saturation.

Clearly identify scenarios where:

the linear controller is superior, and

the nonlinear controllers become superior.

For each scenario, provide plots/results and a clear technical justification explaining:

why this controller wins in that case,

why the others perform worse (e.g. validity range of linearization, nonlinear coupling effects, parameter sensitivity, robustness, saturation, disturbance structure).

Deliver a concise technical report summarizing scenarios, explanations, and conclusions.

Strong experience with MATLAB/Simulink, nonlinear control, and overhead crane / pendulum systems is required.