Page 299 - Control Theory in Biomedical Engineering

272 Control theory in biomedical engineering

C_pu_LnðÞ ¼ P L step length desiredÞ step length nðÞÞ
ð
ð
+I L C_pu_Ln 1ðð ÞÞ (6)
+D L step length nðÞ step length n 1ðð ÞÞ
Impulse n +1Þ ¼ Impulse nðÞ + C_pu_LnðÞ (7)
ð
In these equations, P L , I L , and D L are the step length controller’s coef-
ficients, and C_pu_L is control variable to change Impulse result in step
length regulation. It is important to note that the traditional “neural signals
controller” method includes only P and D coefficients. In this study, the I
coefficient was added to improve the controller performance.
Similarly,thesteptimecontrollerformulationsareexplainedinEqs.(8),(9).

C_k_TnðÞ ¼ P T step time desiredðð Þ step time nðÞÞ
+I T C_k_Tn 1ðð ÞÞ (8)
+ D T step time nðÞ step time n 1ðð ÞÞ
ð
kn +1Þ ¼ knðÞ + C_k_TnðÞ (9)
In these equations, P T , I T , and D T are step time controller’s coefficients,
and C_k_T is control variable to change k result in step time regulation.
Depending on the walking parameters to be controlled, we designed four
control system models. The first control system model contains controllers
for step length and time referred to as c_TL.
The step velocity can be regulated by changes in step time and/or step
length. In order to increase/decrease step velocity, it is required to increase/
decrease step length and/or decrease/increase step time. Thus, in the second
control system model, a controller for velocity was designed and added to
c_TL by Eqs. (10)–(13). This control system model, which controls step
length, time, and velocity, is named as c_TLV.

ð
ð
C_pu_VnðÞ ¼ P VL treadmill velocity desired velocityÞ step velocity nðÞÞ
+I VL C_pu_Vn 1ðð ÞÞ (10)
+D VL step velocity nðÞ step velocity n 1ðð ÞÞ
Impulse n +1Þ ¼ Impulse nðÞ + C_pu_LnðÞ + C_pu_VnðÞ (11)
ð

C_k_Vn ðÞ ¼ P VT treadmill velocity desired velocityÞ step velocity n ðÞð ð Þ
+I VT C_k_Vn 1ðð ÞÞ (12)
+D VT step velocity nðÞ step velocity n 1ðð ÞÞ

ð
kn +1Þ ¼ knðÞ + C_k_TnðÞ + C_k_VnðÞ (13)