Force-Controlled Tensile Test of Collagen Fibril by Using 2-DOF Control System With Modeling Error Compensation

Abstract

Collagen is a major structural protein in the human body. It not only provides connective tissues such as ligaments and tendons with toughness and strength but it also constitutes the biomechanical scaffold for cell attachment in the extracellular matrix. Collagen molecules aggregate to form collagen fibrils, which are fibers with a diameter of 10 \rm {nm} to 500 \rm {nm} and a length of up to a centimeter. Tensile tests on individual collagen fibrils reveal a strongly non-linear stress-response to deformation with the tensile modulus reaching the gigapascal range. But not only that, collagen fibrils have been found to be viscoelastic which means collagen fibrils have both elastic and viscous characteristics. However, direct measurement of viscoelastic material properties in tension is only possible with force-controlled tensile tests, which can not be conducted with state-of-the-art methods. In this paper, we report the first force-controlled tensile tests of individual collagen fibrils. To account for the non-linear material characteristics, high responsiveness in the force control and robustness about a property change of the collagen fibril are needed. Therefore, a two-degrees-of-freedom (2-DOF) controller is applied for force control with high responsiveness. The 2-DOF controller is composed of feedforward (FF) and feedback (FB) controllers. In addition, a modeling error compensation is implemented for robustness. The modeling error is calculated from the difference between the actual force response measured by the sensor and the ideal force response calculated from the plant model. The validity of the proposed control method is confirmed from simulation and experimental results.