Critical Damping Conditions for Third Order Muscle Models: Implications for Force Control

Abstract

Experimental results presented in the literature suggest that humans use a position control strategy to indirectly control force rather than direct force control. Modeling the muscletendon system as a thirdorder linear model, we provide an explanation of why an indirect force control strategy is preferred. We analyzed a thirdorder muscle system and verified that it is required for a faithful representation of muscletendon mechanics, especially when investigating critical damping conditions. We provided numerical examples using biomechanical properties of muscles and tendons reported in the literature. We demonstrated that at maximum isotonic contraction, for muscle and tendon stiffness within physiologically compatible ranges, a thirdorder muscletendon system can be underdamped. Overdamping occurs for values of the damping coefficient included within a finite interval defined by two separate critical limits (such interval is a semiinfinite region in secondorder models). An increase in damping beyond the larger critical value would lead the system to mechanical instability. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved; thus resulting in an oscillatory free response of the system, independently of the value of the damping. Under such condition, combined with high muscle activation, oscillation of the system can be compensated only by active control.