PID Control Case Study - Balanced beam demonstration

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PID Control Case Study – Balanced beam demonstration

1.0        Introduction

In order to demonstrate  the capabilities of the AN20, a PID (Proportional, Integral Differential) control loop has been created to balance a weighted beam.The balanced beam consists of a Perspex bar (beam) pivoted roughly in the middle.  (See Diag.1).  At one end a mass is attached, and at the other a metal disc. When current flows in the coil, the disc accelerates, causing the angle of the beam to change.  An LED and photodiode are used to sense the position of the beam.

Diag.1 - Balanced beam.

The control loop, is required to force the correct current, in order to exactly balance the beam.

2.0        Control theory

In order to stabilise the beam, a loop-filter must be designed and placed, as shown below (Diag.2).  In order to establish what properties the loop-filter requires, it is necessary to calculate the gain of each element within the loop.

Remember that the time dependant variable in this loop is position.

Diag.2 – Control loop

Position sensor:  This consists of an LED source, pulsed at 100 KHz and a photodiode detector.   The photodiode current is input to a trans-impedance amplifier and rectifier,  to generate a dc voltage.  The input quantity to this block is position, and the output quantity is voltage.  The relationship between the two is linear (to 1st order) and thus the gain Ks is a constant.  

V->I converter:  In order to drive the coil (which requires 1-2 Amps) a voltage to current converter is required.  This has voltage input and current output.  The o/p current is proportional to the input voltage, thus the gain Kv->I is a constant.

Coil:  This is an electromagnet, which attracts the metal disk attached to the beam.  The I/P quantity to this block is current , and the O/P quantity is position. A current in the coil, produces a force, and thus an acceleration of the disk towards the coil.  The O/P position, is the second integral of the I/P current, and thus the coil acts as a double integrator.  The S-domain gain (to 1st order) is  Kc/S2.

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The Open loop gain of these three blocks is thus K/S2.  where K = Ks.Kc.Kv->I

This is a double pole at DC, which from an open loop perspective, causes the gain to fall off at 40dB's per decade.  In order to close the loop and make it stable, the roll off must be 20dB's per decade as the loop gain passes through unity.  This helps to define the requirements of the loop filter.  To lessen the roll off to 20dB’s per decade, a differentiator is required, (to cancel a pole) along with some proportional control. 

The ...

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