Multivariable System Identification of Human Postural Control. A Subspace Method Approach

Abstract: In order to analyse the human postural control system single-stimulus multi-response measurement experiments are made, where the body sway due to an induced disturbance on the calf muscles are recorded with force platforms, Selspot systems or EMG-equipments. The measured outputs are usually analysed one by one as for a Single-Input Single-Output system. In this study a Single-Input Multi-Output approach, consisting of a subspace state-space algorithm, is used to map the stimulus-response relation. A generated Pseudo-Random-Binary-Sequence signal was used to induce sway to the test subject. A six axis contact force-state was measured by a force platform and the position of the body mass centre was recorded with a Diode-CCD-camera system. Tests were made on seven normal subjects with large and small amplitude calf stimulation and the subjects tested both with closed and open eyes. Of the nine recorded outputs (three contact forces, three torques and three space coordinates) three were found to be relevant in the identification of calf muscle stimulation. These were the sagittal shear force, the torque around the lateral axis and the sagittal position coordinate of the body mass centre. A linear dependence between shear force and torque was found, and there was a strong correlation between all the three outputs. The subspace algorithm can acceptably identify the postural control system of closed eyes, but not the system of open eyes. The subspace method is able to analyse disturbed systems, but lacks of correct noise model. The white noise assumption made in the algorithm is not justified. This leads to difficulties in locating a correct model order, balanced model reduction approximation or statistical residual tests together with system simulation can be used as a method of model validation.