A simple yet challenging benchmark problem is proposed inspired from a particular class of DC motors presenting an underdamped resonant mode. Such resonant mode causes significant limitation to standard PI control and leads to important chattering for both first-order sliding-mode (FOSM) and super-twisting algorithm (STA) controllers. A well tuned standard PI controller serves as a comparison basis. Then, two methods for chattering alleviation based on the introduction of an ideal sliding-mode loop into the controller are chosen. Their efficiency is discussed in simulation and experimental tests. The results suggest interesting challenges for developing more efficient chattering alleviation techniques, particularly so for higher-order sliding mode (HOSM) based control which cannot be considered as a chattering alleviation technique per se.