The ability of humans to stand upright and maintain balance in the presence of disturbances is achieved through the postural control system. Postural control consists of both postural steadiness associated with the ability to maintain balance during quiet standing, and postural stability that is associated with the response to applied external disturbances and volitional postural movements [1
]. The postural control system makes use of information from the visual, vestibular, and somatosensory systems [2
Balance is achieved when the subject’s center of gravity (COG) remains within the base of support. The COG is the vertical projection of the center of mass onto the base of support. It is a whole body characteristic that is difficult to directly measure, so typically the center of pressure (CoP) is used instead. The CoP is the location of the vertical ground reaction force on the surface upon which the subject stands. CoP movements are used to control the horizontal displacements of the center of mass. In general the CoP varies about the COG, but with higher amplitude and higher frequency content [3
]. Using a single force plate, it is the net CoP from both feet that is measured [4
]. Over an extended period of time of quiet stance, the average of the CoP must equal the average of the COG [5
During quiet standing, humans sway to maintain balance; and this motion can be measured using the anterior–posterior (AP) and the medial–lateral (ML) components of the CoP. Different control mechanisms and different muscle groups are used to control AP and ML motion [3
]. Most mathematical models of the postural control system are biomechanical and employ a 1-D or 2-D inverted pendulum structure [6
]. Some look at the contributions of each leg separately and, therefore, include a pair of inverted pendulums [4
]. Others are more refined and include an articulated chain of links interconnected by joints to model the effects of the ankles, knees, hips, shoulders, elbows, and neck [5
]. One control system strategy suggests that high ankle stiffness accounts for most, but not all, of postural steadiness [10
]. Another approach employs continuous linear feedback including proportion plus derivative (PD) and proportional plus integral plus derivative (PID) control [14
]. Both of these approaches achieve asymptotic stability with the residual sway movements being noise driven. Another control system representation has been proposed that relies on an intermittent controller that becomes activate when the sway motion moves outside of a small dead zone [7
]. Here the persistent sway patterns are not noise driven but result from the limited resolution of the controller.
Most of the control system model focus on the question of postural steadiness or the ability to maintain balance during quiet standing. This paper focuses on the development of a control system model that characterizes postural sway when human subjects are exposed to periodic disturbances whose frequencies and amplitudes vary [14
]. It is hypothesized that quiet standing motion can be represented mathematically as a noise-corrupted oscillation. A nonlinear phase-locked loop (PLL) structure is used to control both the frequency and the amplitude of the quiet standing oscillator when a periodic stimulus is applied [19
]. If the stimulus amplitude is sufficiently large and the stimulus frequency is sufficiently close to the quiet standing frequency, the oscillator will achieve phase lock with a well-defined phase angle between the periodic disturbance and the steady-state response. Measurements of the amplitude and the phase of the steady-state response are used to identify parameters of a PLL model.
To test this notion, subjects stood on an air bearing platform that was made to undergo sinusoidal AP motion in order to generate a periodic disturbance to the postural control system. The measured response was the CoP of the subjects along the direction of platform motion. Nine healthy young adults were tested to collect the experimental data used to develop and test the model. The results show that a PLL structure is highly effective in describing the experimental behavior observed in this study.