Question

In: Electrical Engineering

Derive the equation of motion for the system and obtain its transfer function of Controller for...

Derive the equation of motion for the system and obtain its transfer function of Controller for Propeller Driven Pendulum showing the steps .

Solutions

Expert Solution

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.


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