TI TPS57160-Q1 step-down converter outputs sawtooth-like voltage at high input voltages
This is a current mode controller, and therefore the output zero is important.

The output pole varies with load; i.e it is \$\frac {1} {2\pi R C_o}\$; as R = \$ \frac {V_o} {I_o}\$, then the output pole becomes \$\frac {I_o} {2\pi V_o C_o}\$.

This is an important point for this type of controller.

The output zero is fixed at \$\frac {1} {2\pi ESR_o C_o}\$

We normally use the output zero to give us some phase boost at 0dB, but a ceramic 47\$\mu\$F capacitor has a typical ESR of a few m\$\Omega\$, and the output zero is too far up the frequency range to help, so we need to add a zero to give us some phase boost.

In this situation, I normally add a small capacitor Cp across R6. I would size it so that it achieves 45 degrees at \$\frac {F_o} {10}\$ where \$F_o\$ is the loop crossover frequency.

The zero formed is at \$F_z = \frac {1} {2\pi C_p R6}\$

For this case \$Cp = \frac {1} {2\pi 0.1F_o R6}\$; I find that a 100pF capacitor is a good starting point in general.

What you are seeing is almost definitely loop instability; note that as you increase \$V_i\$, the duty cycle decreases, generating different frequency artefacts into the control loop, so it perfectly possible that a mixture of varying loads and Vin to Vout changes are causing instability.

An in-depth look at a particular architecture (but widely applicable to current mode controllers) may be found here

I do note that the controller datasheet indicates the use of ceramic capacitors is fine, but I always add a position for this capacitor (Cp) as a 'get out of jail free' item for the vagaries of layout induced issues.

Note that for a current mode controller, the loop crossover frequency can vary with load, which makes figuring these things out non-trivial.

[Update]

I just noticed the the pole setting capacitor at the compensation pin is 4.3pF; this can easily be much larger simply due to track capacitance (1.1pF per inch on 0.004" tracks with 0.004" to plane) or other layout effects and could easily have a much higher effective capacitance thereby changing the frequency response of the compensation network.

In general, if a design calls for a &lt; 10pF capacitor, great care needs to be taken in layout.