Home  |  Classical Feedback Control   | 

Please refer to the beginning of this document for copyright information and use permissions.

4.3.3  Sensor noise at the actuator input

In the control system diagram in Fig. 4.26, the noise source N reflects the noise from the sensor and the noise from the pre-amplifier in the compensator. When the signal at the input of the saturation link is below the saturation threshold, the noise effect at the input of the saturation link is

.
 
Fig. 4.26  Noise source in a feedback system

Fig. 4.27  Noise level at saturation link input

With the typical responses of P and T shown in Fig. 4.26, |CAP| >> 1 at lower frequencies. At these frequencies the noise NA  N/P does not depend on C. On the other hand, at frequencies higher than fb, NA  NCA, and reducing |C| decreases the noise. With proper loop shaping, the noise NA is most prominent at the frequencies within 2 to 4 octaves above fb.

It is seen from Fig. 4.27 that the increase of the feedback from |T| to |T'| is attained at the price of increasing |CA| to |C'A|, i.e., at the price of a bigger noise effect at the input to the nonlinear link in Fig. 4.26. The noise amplitude and power increase not only because C' > |C|, but also because the noise power is proportional to the frequency bandwidth.

When the noise overloads the actuator, the actuator cannot transfer the signal. As a result, the effective gain of the actuator drops, the distortions of the signal increase, and the control system accuracy decreases. Hence, the noise effect at the input to the actuator must be bounded. This restricts the available feedback in the operational band by constraining |C|.

The optimal shape of the Bode diagram which provides maximum feedback bandwidth while limiting the noise effect can be found by experimenting with computer simulation. Typically, the responses which are best in this sense contain Bode steps.

   

Example 1. In an existing system, the bandwidth is limited by the noise at the input to the actuator. If a better amplifier and better sensors become available with half the noise mean square amplitude, the feedback bandwidth can be increased. Maintaining the same mean square noise amplitude at the actuator input, the feedback bandwidth can be increased 1.4 times (since the mean square amplitude of the white noise is proportional to the square root of the noise bandwidth).

Home  |  Classical Feedback Control   |