In: Electrical Engineering
Derive the equation of motion for the system and obtain its transfer function of Controller for Propeller Driven Pendulum showing the steps .
Propeller pendulum can be described as a motorized propeller at the end of the pendulum so that it
can be lifted up or down by driving motor. Thrust force can be produced by driving propeller and
pendulum can be stabilized at any desired angular position by using different control methods such
as PID method, sliding modes method or fuzzy logic methods [1-4]. Propeller pendulum is a
nonlinear system and can be controlled by classical control system after linearization.
The axis of rotation is fixed and the pendulum is actuated by four thrust force which is produced
by propeller mounted at the free end of the pendulum. Four motorized propeller pendulum is
capable of holding the pendulum any desired angular position on two planes by means of varying
magnitude of thrust force. In literature, one or two motorized propeller pendulum systems exist.
The angular position of the pendulum on a single plane is balanced against gravity for any desired
position by means of brushed or brushless motor powered propeller [4]. The brushed or brushless
motor can be controlled by PWM signals, so that pendulum system control behaviors such as
stability, rise time overshoot etc. are adjusting
Mathematical model of single propeller pendulum
When viscous damping and disturbance torque of propeller are neglected, according to Newton’s
law and angular momentum, the equation of motion of single propeller pendulum is derived as
follows:
The vertically driven pendulum is an inverted simple pendulum whose pivot oscillates up and
down with amplitude A and frequency v . As with the simple pendulum, the driven
pendulum only has one degree of freedom, and so its position at any time t can be described
just with the angle ? that the pendulum makes with the vertical reference line.