The great promises of neuromorphic sensing and processing for robotics have led researchers and engineers to investigate novel models for robust and reliable control of autonomous robots (navigation, obstacle detection and avoidance, etc.), especially for quadrotors in challenging contexts such as drone racing and aggressive maneuvers. Using spiking neural networks, these models can be run on neuromorphic hardware to benefit from outstanding update rates and high energy efficiency. Yet, low-level controllers are often neglected and remain outside of the neuromorphic loop. Designing low-level neuromorphic controllers is crucial to remove the standard PID, and therefore benefit from all the advantages of closing the neuromorphic loop. In this paper, we propose a parsimonious and adjustable neuromorphic PID controller, endowed with a minimal number of 93 neurons sparsely connected to achieve autonomous, onboard altitude control of a quadrotor equipped with Intel's Loihi neuromorphic chip. We successfully demonstrate the robustness of our proposed network in a set of experiments where the quadrotor is requested to reach a target altitude from take-off. Our results confirm the suitability of such low-level neuromorphic controllers, ultimately with a very high update frequency.