Background; Modeling; Position Controller Design - Quanser 6 DOF Hexapod Laboratory Manual

3 BACKGROUND

3.1 MODELING

The dynamics between the applied force to the linear position of each joint can be represented by the transfer function
where q(s) = [q(t)] is the Laplace of the joint position q(t), F (s) is the Laplace of the applied linear force, and M
is the total mass being moved by the motor (i.e., both pre-load and payload).

3.2 POSITION CONTROLLER DESIGN

The joint positions on the Hexapod system is controlled using a standard proportional-integral-derivative (PID) con-
trol. The PID control used has following structure:
where k is the proportional control gain, k is the integral gain, k is the derivative control gain, q (t)
setpoint or reference joint position (for all six joints), q(t)
F (t) is the force (i.e., control effort). The block diagram of the control is given in Figure 3.1.
In software implementation, the controller force is converted into motor current using
Thus the controller force is divided by the lead-screw radius, r, to get the torque and this is multiplied by the current
constant, k , to obtain the necessary motor current.
HEXAPOD Laboratory Guide
q(s) =
F (t) = k (q (t) q(t)) + k
Figure 3.1: Block diagram of Hexapod position control.
1
F (s)
M s
q (t) q(t)dt + k ( ˙ q (t)
is the measured joint position (for all six joints), and
F
τ =
r
τ
I =
k
˙ q(t))
is the
(3.1)
(3.2)
v 1.3