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A double pendulum model for human walking control 273
In these equations, P VL , I VL , and D VL are step velocity controller coef-
ficients and C_pu_V is control variable to change Impulse and step length
result in step velocity regulation. P VT , I VT , and D VT are step velocity con-
troller coefficients and C_k_V is a control variable to change k and step time
result in step velocity regulation.
In the third control system model, the position of human walking on the
treadmill, P n , was considered in the control system design. P n is calculated by
Eq. (14) (Dingwell and Cusumano, 2015).
ð
ð
P n ¼ P n 1ð Þ + step lengthð½ Þ treadmill velocityÞ step durationÞ (14)
The initial value of P n is set to 0, representing the middle of the treadmill
position. Similar to step velocity control, the position controller was
designed and added to c_TLV using Eqs. (15)–(18). This control system
model is referred to as c_TLVP.
C_pu_PnðÞ ¼ P PL treadmill desired position 0ðÞ step position nðÞÞ
ð
+I PL C_pu_Pn 1ðð ÞÞ (15)
+D PL step position nðÞ step position n 1ðð ÞÞ
Impulse n +1Þ ¼ Impulse n ðÞ + C_pu_LðnÞ + C_pu_VðnÞ + C_pu_Pn ðÞ (16)
ð
C_k_PnðÞ ¼ P PL treadmill desired position 0ðÞ step velocity nðÞð Þ
+I PL C_k_Pn 1ðð ÞÞ (17)
+D PL step position nðÞ step position n 1ðð ÞÞ
kn +1Þ ¼ knðÞ + C_k_TnðÞ + C_k_VnðÞ + C_k_PnðÞ (18)
ð
In these equations, P PL , I PL , and D PL are position controller coefficients
and C_pu_P is control variable to change Impulse and step length result in
step position regulation. P PT , I PT , and D PT are step velocity controller coef-
ficients and C_k_P is a control variable to change k and step time result in
step position regulation.
The fourth control system model contains only position and velocity con-
trollers (i.e., only C_k_V(n), C_pu_V(n), C_k_P(n), and C_pu_P(n)) and is
referred to as c_VP.
2.3 Experimental data
The experimental data (Dingwell et al., 2010) was used for comparing
the outcomes of the different control system models and are available at:
