PID controller stabilization of a single-link biomechanical model with multiple delayed feedbacks

In this paper we address the problem of PID controller stabilization of a single-link inverted pendulum-based biomechanical model with force feedback, two levels of position and velocity feedback, and with delays in all the feedback loops. The motivation for this work arises from considering the postural stabilization problem in biomechanics where the human body is modeled as a neuro-musculo-skeletal system. The proprioceptive feedback from muscle spindle and Golgi tendon organ generates short, medium, and long latency responses from the central nervous system (CNS), consisting of the brain and the spinal chord. Of these responses the first two are included in the formulation. The Hermite-Biehler Theorem is used to derive stability results, leading to necessary and sufficient conditions for existence of stabilizing PID controllers for the model. An algorithm for selection of stabilizing gains is developed.