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In engineering, any device that controls the speed of a machine or engine, usually by
regulating the intake of fuel or steam is called a governor.
A centrifugal governor is a specific type of governor that controls the speed of an
engine by regulating the amount of fuel admitted, so as to maintain a near constant
speed whatever the load or fuel supply conditions. It uses the principle of proportional
control.
It is most obviously seen on steam engines where it regulates the admission of steam
into the cylinder(s). It is also found on internal combustion engines and variously fueled
turbines.
The device shown is from a steam engine. It is connected to a throttle valve and to the
prime mover (not shown). The action of the governor is dependent on centrifugal force.
As the speed of the prime mover increases, the central spindle of the governor rotates
at a faster rate and the two masses move outwards, and this motion is translated by the
series of rods and arms to the throttle valve, reducing its aperture. The rate of steam
entering the cylinder is thus reduced and the speed of the prime mover falls. If the
speed of the prime mover falls, the reverse effect occurs and the throttle valve opens further.
In other words, when the engine speed increases too much, the balls fly out, and cause
the stem valve to close, so the engine slows down. The opposite happens when the
engine speed drops too much.
Problem Statement:
The governor mechanism shown above, has an initial angular velocity of 360 deg/s and
over 4 seconds, the ngular velocity increases to 1440 deg/s (the initial velocity is 360
deg/s). There is an uncompressed spring (this a modification of the original design),
which has a stiffness of k =0.9 N/mm (damper=0.1 N-sec/mm), and is connected from
the top center of the slider to the rotating collar where z = 345mm.
As the governor rotates, determine the distance z corresponding to the maximum
compression of the spring. (When the Fly balls are on the top)
Note: In order to add motion, use the following data.
A proportional control system is a type of linear feedback control system. Two classic
mechanical examples are the toilet bowl float proportioning valve and the fly-ball
governor.
The proportional control system is more complex than an on-off control system like a
thermostat, but simpler than a proportional-integral-derivative (PID) control system used
in something like an automobile cruise control.
An on-off control is like driving a car by applying either full power or no power to control
speed. The power would be on until the target speed is reached, and then the power
would be removed, so the car reduces speed. When the speed falls below the target,
full power would again be applied. It can be seen that this is poor control.
Proportional control is how most drivers control the speed of a car. If the car is at
target speed and the speed increases slightly, the power is reduced slightly, or in
proportion to the error (the actual versus target speed), so that the car reduces speed
gradually and reaches the target point with very little, if any, "overshoot", so the result is
much smoother control than on-off control.
Further refinements like PID control would help compensate for additional variables like
hills, where the amount of power needed for a given speed change would vary, which
would be accounted for by the integral function of the PID control.