Page 302 - Control Theory in Biomedical Engineering

A double pendulum model for human walking control 275

Table 2 Controller parameters for step length and time.
Step length Step time
controller Values controller Values

2 0.03
P L P L
0.02 0.03
I L I L
0.03 0.002
D L D L

Table 3 Controller parameters for step length and time.
Step velocity Step position
controller Values controller Values

0.02 0.001
P VL P PL
0.01 0.02
I VL I PL
0.001 0.001
D VL D PL
1 0.001
P VT P PT
0.02 0.02
I VT I PT
0.05 0
D VT D PT
In these equations, η and γ are coefficients of added noises and rand is the
equivalence of probability density functions that generate a random number
between 0.5 and 0.5. The controllers’ coefficients, shown in Tables 2 and 3,
and η and γ values were set manually in the c_TLVP model in order to pro-
duce similar standard deviations (SD) of stride length and time in both model
and experimental data. In this way, the η and γ were set to 0.0008 and 0.0037,
respectively.
In the next step and to evaluate the effect of each controller, the control
variables were removed step by step and the other control system models
(i.e., c_TLV by deletion of position controller, and then c_TL by deletion
of velocity controller) were simulated and the results were compared to
those of experiments. The same approach was used for c_VP by deleting
stride length and time controllers.

3Results

First, we set length (desired) to 0.55, step time (desired) to 0.5, and treadmill
velocity to 1.1, and transient responses of the four models were computed.