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The two measurement modes account for various linear correction factors like the moment of inertia of the arm, linear sources of friction, and the non-uniform magnetic field.
The magnetic flux of the coil can be determined independently in both measurement modes.
The two measurement modes allow us to relate pseudo electric power and pseudo mechanical power
EXPERIMENTAL SETUP:
Device Diagram:
The Watt balance resembles an ordinary straight arm balance.
Under each mass pan hang two permanent magnets above 3000 turns of magnetic wire. Each pair of magnets are oriented anti-parallel.
A compact laser triangulation displacement sensor measures the displacement of the balance arm.
In the force mode the blue coil is driven sinusoidally, and the induced emf is measured in the red coil.
In the velocity mode a mass is placed on the mass pan and a current is applied to the red coil to balance the arm.
Building a Lego Watt Balance
Michael Laraia and Jack Hirschi
University of Minnesota - Methods of Experimental Physics II
INTRODUCTION:
As of May 20, 2019, all SI units have been redefined with fundamental constants of the universe. The Kilogram’s new definition is in terms of Planck’s constant, and the relationship can be measured with a Watt Balance. In this project we built a Watt Balance device to measure this relationship.
THEORY:
Velocity Mode Force Mode
A Watt balance balances an electromagnetic force with a mechanical force.
In the velocity mode the balance arm is driven sinusoidally and an emf is induced.
In the force mode a current creates an electromagnetic force that balances an object’s weight
PID Controller:
A PID algorithm is a control loop feedback to continuously modulate control.
The algorithm calculates the optimal output to return the input to a defined setpoint.
The input is the position sensor, the output is the current in the red coil.
Algorithm’s response governed by three parameters: Proportional gain, Integral gain, and Differential gain.
Several outputs of a PID controller with a blue setpoint [1]
KP: Proportional gain, used to minimize rise time and reduce the steady state error.
KI: Integral gain, corrects for steady state error.
KD: Derivative gain, improves stability of system and dampens large changes.
RESULTS:
In the velocity mode the blue coil is driven with a sinusoidal wave. This motion induces an electromotive force in the red coil.
When the amplitude of the oscillation is small, the induced emf is proportional to the velocity of the magnet.
The BL factor depends on the position of the magnets. The magnets must be centered at the same height as in the force mode measurement.
The velocity BL factor was measured to be within 7.5% (0.6σ) of the force mode BL factor.
In the force mode a mass is placed above the red coil. The PID algorithm acts to balance the arm by applying a current. A current measurement was made when the balance has settled within 1% of the set point.
CONCLUSIONS:
The relative difference between the BL factors can be attributed to slight deviations from the setpoint in the velocity mode data.
Future experiments of this type can hopefully account for this systematic error and, for example, calculate local gravitational constant g.
REFERENCES:
PID controller. (2019, May 02). Retrieved from https://en.wikipedia.org/wiki/PID_controller
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