ABSTRACT

Books devoted to feedback system design show many different compensation techniques that can be used in different situations when the "bare bones" feedback system cannot be adjusted to meet specifications. In our present example, the technique called cancellation compensation4 turns out to be useful. This can also be interpreted as proportional plus derivative control. Here we include in our system a (usually electronic) dynamic compensator of so-called lead-lag form, (r1s + 1)/(r2s + 1) (see Fig. 7-13b for one way to actually build such a device). We choose the number r1 to match (and thus cancel) the time constant of the mechanical system, and make r2 much (as much as 10 times) smaller. I tried one such compensator in the system and still could not meet specifications. I then added a second compensator as shown, and by adjusting amplifier gain, got the acceptable response of Fig. 7-13c. Note that because of the "cancellation" effect, the two compensators in cascade with the mechanical system have an overall transfer function of 8/(0.05s +I); thus the feedback system "thinks" it is controlling a mechanical system with this transfer function, not the actual mechanical system. This cancellation compensation trick is used to speed up the response of many practical open-loop and closed-loop systems, including sensors5 such as hot-wire anemometers and thermocouples. Since such compensators are approximate differentiators, they may not be usable in real systems unless the level of random noise (present in every real system) is sufficiently low. Noise problems can be studied at the design stage with simulation and verified by lab testing once actual hardware is in hand.