Controlling the position of a motorized cart x(t) with a remote control slider position p(t):
engineering
Description
Controlling the position of a motorized cart x(t) with a remote control slider position p(t):
As described in past notes, the velocity v(t) of a motorized cart (m/sec) can be modeled as
where m = 100 kg is the mass, b = 20 N sec/m is the coefficient of a friction or drag force that
opposes the motion (proportional to the velocity), and f(t) is the externally applied force to the
cart (in N). The position x(t) of the cart is related to the velocity by
The force produced by an electric motor and a transmission system is related to the position of a
mechanical slider p(t) (cm) for remote control by
where a = 1 sec-1 is the “lag coefficient” and g = 10 N / (cm-s) is a gain that describes the
conversion from slider position to force applied to the cart (through the transmission system that
converts the motor torque to translational force).
The slider position can be positive or negative, resulting in force applied in the positive or
negative direction. This is like a remote-controlled car, where negative force will slow down the
car if it is moving in the positive direction.
