Neuromorphic processing promises high energy efficiency and rapid response rates, making it an ideal candidate for achieving autonomous flight of resource-constrained robots. It can be especially beneficial for complex neural networks as are used for high-level visual perception. However, fully neuromorphic solutions also need to tackle low-level control tasks. Remarkably, it is currently still challenging to replicate even basic low-level controllers such as proportional-integral-derivative (PID) controllers. Specifically, it is difficult to incorporate the integral and derivative parts. To address this problem, we propose a neuromorphic controller that incorporates proportional, integral, and derivative pathways during learning. Our approach includes a novel input threshold adaptation mechanism for the integral pathway. This Input-Weighted Threshold Adaptation (IWTA) introduces an additional weight per synaptic connection, which is used to adapt the threshold of the post-synaptic neuron. We tackle the derivative term by employing neurons with different time constants. We first analyze the performance and limits of the proposed mechanisms and then put our controller to the test by implementing it on a microcontroller connected to the open-source tiny Crazyflie quadrotor, replacing the innermost rate controller. We demonstrate the stability of our bio-inspired algorithm with flights in the presence of disturbances. The current work represents a substantial step towards controlling highly dynamic systems with neuromorphic algorithms, thus advancing neuromorphic processing and robotics. In addition, integration is an important part of any temporal task, so the proposed Input-Weighted Threshold Adaptation (IWTA) mechanism may have implications well beyond control tasks.