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The Art of the Helicopter John Watkinson - Karatunov.net

The Art of the Helicopter John Watkinson - Karatunov.net

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Fig. 7.28 In PCM or digital signalling, <strong>the</strong> position <strong>of</strong> a control is sampled periodically and <strong>the</strong> sample is<br />

expressed as a discrete number.<br />

Those who are not familiar with digital signalling may worry that sampling takes away<br />

something from a signal because it is not taking notice <strong>of</strong> what happened between <strong>the</strong><br />

samples. This would be true in a system having infinite response rate, but no real control<br />

system can be like this. All control signals from joysticks, actuators, gyros etc., have a<br />

distinct limit on how fast <strong>the</strong>y can change. If <strong>the</strong> sampling rate is high enough, a control<br />

waveform can only change between samples in one way. It is <strong>the</strong>n only necessary to<br />

carry <strong>the</strong> samples and <strong>the</strong> original waveform can be reconstructed from <strong>the</strong>m.<br />

Figure 7.28 also shows that each sample is also discrete, or represented in a stepwise<br />

manner. <strong>The</strong> value <strong>of</strong> <strong>the</strong> sample, which will be proportional to <strong>the</strong> control parameter,<br />

is represented by a whole number. This process is known as quantizing and results in an<br />

approximation, but <strong>the</strong> size <strong>of</strong> <strong>the</strong> error can be controlled until it is negligible. If, for<br />

example, we were to measure <strong>the</strong> height <strong>of</strong> humans only to <strong>the</strong> nearest metre, virtually<br />

all adults would register 2 metres high and obvious difficulties would result. <strong>The</strong>se are<br />

generally overcome by measuring height to <strong>the</strong> nearest centimetre. Clearly <strong>the</strong>re is no<br />

advantage in going fur<strong>the</strong>r and expressing our height in a whole number <strong>of</strong> millimetres<br />

or even micrometres.<br />

<strong>The</strong> point is that an appropriate resolution can also be found for a control system, and<br />

a higher figure is not beneficial. If a conventional pushrod control system is considered,<br />

each bearing and joint in <strong>the</strong> system has some backlash and <strong>the</strong> cyclic stick on a typical<br />

helicopter can always move some small distance before any motion is detected at <strong>the</strong><br />

swashplate. If <strong>the</strong> movement step size <strong>of</strong> a digital system is <strong>of</strong> <strong>the</strong> same order as <strong>the</strong><br />

backlash <strong>of</strong> a mechanical system, both systems have <strong>the</strong> same accuracy.<br />

<strong>The</strong> advantage <strong>of</strong> using whole numbers is that <strong>the</strong>y are not prone to drift. If a whole<br />

number can be carried from one place to ano<strong>the</strong>r without numerical error, it has not<br />

changed at all. By describing control parameters numerically, <strong>the</strong> original information<br />

has been expressed in a way that is better able to resist unwanted changes. <strong>The</strong> amount<br />

<strong>of</strong> backlash in a mechanical system increases with <strong>the</strong> number <strong>of</strong> ball joints and bell<br />

cranks in a control run. <strong>The</strong> accuracy <strong>of</strong> a mechanical signalling system would decline as<br />

Control 293

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