3. Design Strategies¶
3.1 Proportional Control¶
For simple systems, a loop gain can often be chosen which is high enough to give acceptably small errors, low sensitivity and compliance (see Section 4.1.4) an adequate speed of response and yet good stability. When these specifications cannot be satisfied simultaneously a more sophisticated strategy is required.
3.2 Phase Lag Compensation¶
The lag compensator
and proportional-plus-integral (PPI) compensator
are used either to increase the loop gain at low frequencies, and so reduce the errors and the sensitivity, or to reduce the loop gain at higher frequencies (specifically around the region of \(180^\circ\) phase lag (phase cross-over frequency \(\omega_\pi\) ) to reduce the band-width and improve stability. PPI action may be preferred for the former (it increases system type number by 1 and so eliminates steady state-errors) and a lag compensator for the latter. In any case the phase lag is incidental and since it is a destabilising influence it should be used well below the unity loop gain frequency (gain cross-over frequency \(\omega_1\)). When there is nothing else to choose between the two, the smaller phase lag of the lag controller (PPI is always \(90^\circ\) at zero frequency) and its freedom from ‘warm-up’ problems will lead to its use.
3.3 Phase Lead Compensation¶
The lead compensator
is used to reduce the phase lag around the gain cross-over frequency (unity loop gain frequency) \(\omega_1\). It is therefore used to increase stability without reducing bandwidth. Naturally it may also permit the use of a higher proportional gain than would otherwise be possible. The gain of the lead compensator at high frequencies is a destabilising influence so that it should be used at the highest effective frequency and \(\alpha\) should not be reduced below \(0.1\). The high gain will also amplify any noise in the measurement sensor, which may be a problem.
3.4 The Three-Term Controller¶
This combines the effect of both phase lag and phase lead compensation. A special case is the proportional + integral + derivative (PID) compensator
3.5 Parallel Compensation¶
Parallel compensation (seen in this course as velocity feedback) can be used to produce the same stabilising effect as phase lead compensation without amplifying the measurement noise. For this reason it may be possible to introduce a little more phase advance. Note that velocity feedback will reduce the bandwidth a little.
3.6 Feed-forward Control¶
Feed-forward control is used when the compliance is too high but when the disturbances can be measured. If the load disturbances can be measured, feeding the measurement ‘forward’ to the error comparator can reduce compliance errors. It does not affect the stability.