Analysis of a Model of the Triceps Surae Muscle Reflex Control System

Limit-cycle oscillations of two models of the triceps surae muscle stretch reflex system are analyzed, using previously derived criteria for single sign integral pulse frequency modulated (SSIPFM) control systems. The muscle spindle (MS) is assumed to function as an SSIPFM encoder. The system´s stability and error correction ability are studied using the SSIPFM model together with published physiological data. It is shown that the loop gain, which in the model represents the decerebrate preparation, is close to the instability value, despite its relatively small magnitude. This observation and the steady-state error of the model concur with physiological phenomena of decerebrate preparations. In accordance with the adaptive control systems model in which the parameters can be modified, a simple pole is added at the origin of the forward transfer function for improved system performance. The new model is analyzed, and it is shown that higher gains are attainable without limit cycle oscillations and with improved steady-state error. A sensitivity study of the influence of system parameter variation on stability is carried out for both systems.