explain Any one of applications detail in digital control system ?
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13.4 Robustness of digital control systems
Digital control systems are subject to the same effects of coefficient variability and coefficient uncertainty as time-continuous controllers. Two additional effects deserve consideration for the design of robust digital control systems:
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Aliasing: Noise was identified as a broadband signal, which implies that the sensor noise, unless filtered, exceeds the Nyquist frequency. The filtering requirement becomes more stringent in digital control systems.
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Control period T: In Chapter 4, T was identified generally as the sampling period. Any digital control system requires computation time to prepare the value for the corrective action and apply it to the output. More specifically, therefore T is the period between two complete control actions (sensor readout, computation, update of the output). The control period is fundamental to the transfer function of a digital control system, and any variability of T affects the closed-loop transfer function.
Noise and its influence on a time-continuous control system was discussed in Section 13.3. In the example in Fig. 13.7, a first-order lowpass filter was proposed to reduce the spectral energy of the sensor noise. A first-order lowpass attenuates frequency components by a factor of 10 for a 10-fold increase of frequency. In the specific example, a lowpass of fc=8 Hz (ωc=50s−1) was used. If the sampling period of a hypothetical control system is T=6.25 ms (fs=160 Hz), then the noise magnitude at the Nyquist frequency is merely attenuated to 10% of the average noise spectral energy, and the entire spectral energy above fN=fs/2 is mirrored (aliased) into the frequency band below fN. The aliased noise spectrum adds to the passband noise spectrum and leads to a deterioration of SNR at the controller input. For this example with a factor of ten between filter cutoff frequency and Nyquist frequency, the signal with frequency components between fc and fN is more than two times larger than passband component with frequencies below fc, although this part of the spectrum is not subject to aliasing. The remaining spectral components, under the assumption of reasonable op-amp cutoffs, are roughly six times larger than the passband component, and this part of the spectrum is subject to aliasing.