Technical Note

An Advanced Sinusoidal Control Algorithm

Control Methods used by the SD2550 Family of Shaker Control and Analysis Systems

The SD2550 Shaker Control System employs an advanced swept-sine generation feature that results in an analog-quality sweeping sine wave. This sine wave generator creates a sine wave and associated cosine wave for band-pass filtering of input signals. A "true" tracking filter implementation, the band-pass filter always centers on the sweep frequency, regardless of the sweep rate. Implementing this design requires a high-performance hardware platform and control algorithm expertise not commonly available with competitive systems.

The multi-processor architecture and advanced control algorithms of SD2550 systems provide superior control for swept-sine testing. For test articles with sharp resonances, Sine insures precise control with 0.1 dB (approximately 1%) attenuation steps in the drive signal. Dedicated processors on each channel provide programmable rms and tracking filters. They also prevent performance degradation for multi-channel control.

An Advanced Control Algorithm

The SD2550 continuously calculates the equalization transfer function (ratio of response and drive signals) so that the system can adaptively react to test load dynamics. Measurement of the transfer function at full excitation level assures fast and accurate adjustments for non-linearities and changing test article dynamics.

Many competitive systems measure the equalization transfer function at low level and assume that the transfer function characteristics remain the same as the excitation level changes. This assumption is often incorrect and causes inaccurate control or even loss of control stability.

An additional advantage of the SD2550 control algorithm is a "feed-forward" method. Simply stated, this method allows the system to anticipate changes to the transfer function as the sweep frequency changes. Feed-forward tracks and adjusts the drive amplitude based on the rate of change, or derivative, of the error in the control amplitude. This method provides smoother and more accurate control compared to available competitive methods.

The block diagram shows the swept-sine control loop processing used by SD2550 Systems.

Superior Control Accuracy

The output subsystem design utilizes a 16-bit Digital-to-Analog Converter (DAC) coupled with digital smoothing filters and a 24-bit amplitude attenuator. Smoothing filters protect signal purity and minimize harmonic distortion. The 24-bit attenuator allows the SD2550 to adjust the full-scale output voltage range in steps as fine as 0.1 dB over the full span from 0 dB to -80 dB.

This fine amplitude control provides accurate control when sweeping through resonances. At a resonance the drive signal is likely to be fully compressed; that is, the high response at resonance demands that the drive signal be drastically reduced. This requires reducing the DAC voltage range to the minimum level. In the SD2550 even at the minimum level, 1 milliVolt, the system gives full 16-bit resolution to provide accurate amplitude adjustments of small drive signals.

Other systems employ either no attenuators or larger steps than 0.1 dB. These systems typically exhibit "hunting" at resonance on the order of the correction steps. Systems with a 16-bit output DAC but no attenuators typically see these oscillations on the order of + 0.3 dB. Those employing 12-bit DACs will see oscillations on the order of + 3 dB.

Inherent Control Loop Stability

Setting the bandwidth of the detector too low for the correction rate (feed-back gain) causes control instability. This instability results from the control system correcting faster than the input system is able to measure the subsequent changes, much like an inexperienced driver at the wheel of an automobile.

The SD2550 System control loop design eliminates this problem. It has a table of the highest feedback gain possible for a particular bandwidth. A user can set the feedback gain lower than this maximum but not higher.

RMS and Tracking Filter Processing

SD2550 Systems offer both RMS (Root Mean Square) and tracking filter processing. Both the RMS and tracking filter processes employ a Zero Hertz Intermediate Frequency (0-Hz I.F.) detection technique. This technique employs a low-pass filter to extract a term at DC that either represents the RMS or the real and imaginary components of its AC amplitude. These low pass filter bandwidths determine the control speed as well as the narrowness of the synthesized band-pass filters. Digital Signal Processors (DSPs) in the input hardware adjust these bandwidths, as a function of frequency, to optimize both the control speed and accuracy.

RMS control involves measuring the input signal's RMS energy between DC and 20 kHz. For this reason it is the most noise sensitive control technique. If the ambient noise's RMS exceeds the desired system response's RMS, successful control cannot be accomplished. It is, however, a conservative test policy since it controls to the total energy seen at the control point.

Fundamental control, on the other hand, uses a narrow band-pass filter centered about the sweeping sine frequency for estimation of the input signal amplitude. For this reason it is the most noise tolerant method. By its nature, it filters out the effects of ambient noise for the amplitude estimate. It also measures the relative phase between control signals making it possible to do phase-tracked resonance dwells.

Advantages of "True" Tracking Filters

The SD2550 System actually synthesizes a digital filter that represents a band-pass filter centered about the sweep frequency. This filter smoothly follows the sweeping drive signal frequency during the test.

In contrast, many competitive systems employ a FFT approach which in effect keeps a band-pass at fixed frequency during the measurement. This approach inherently assumes that the input signal is at a fixed frequency and at a constant amplitude. Neither of these assumptions are satisfied during a swept-sine test. This approach, although resulting in "pretty" response plots, exhibits input amplitude errors of unknown magnitude that depend greatly on the nature of the input signal and sweep rate. If the frequency changes by an octave during the acquisition time, possible at low frequencies and/or with high sweep rates, an amplitude error of at least 6 dB can develop. Thus, the usage of an FFT for swept-sine testing is totally inappropriate and is only employed due to its simplicity of implementation.

Accurate Transfer Function Measurements

The use of a tracking filter results in transfer function estimates that do not suffer from the FFT induced errors such as resolution and leakage. The resolution can be set up to 2000 samples per sweep versus FFT resolutions that involved prohibitively long buffers for better resolution. These longer buffers create additional errors due to the change in frequency during the buffer duration.

Tracking filtering produces results that are free from leakage effects. The sweeping heterodyne frequency used in the 0-Hz I.F. detectors guarantees that the tracking filters are always centered at the sweep frequency. FFT methods used by most competitors suffer from leakage due to the effects of using an essentially constant heterodyne frequency. The SD2550 multi-processor architecture facilitates this computation intensive tracking filter approach. The architecture used by many competitive systems forces the use of the inappropriate FFT approach.

An Advanced RMS Time Integration Feature

On SD2550 Systems the RMS detection method employs a 0-Hz I.F. detection approach. This approach squares the input signal, producing a term at DC that is proportional to the instantaneous RMS of the input signal. This squared signal is then filtered by a subsequent low-pass filter with a cut-off frequency of f_cutoff. This cutoff frequency, f_cutoff, is a function of the sweep frequency f_sweep. The time-constant of the resultant RMS detector is given by 1/(2f_cutoff), and is a measure of the averaging time of the detector. A longer time-constant gives more accurate RMS measurements but at the expense of control responsiveness.

The control system design optimized both factors to result in the fastest compression rate (drive correction rate) possible at any sweep frequency. It allows for the correction of control errors, at the highest compression rate, within a quarter cycle. Simpler approaches require a full cycle as they measure the RMS by calculating the standard-deviation of an input buffer one cycle long.

Conclusion

SD2550 Systems offer "analog-quality" sine test capability with the accuracy and flexibility of digital processing and control. The high fidelity output and fine amplitude adjustment capability provide superior control accuracy particularly when highly resonant structures are involved. The choice of RMS or "true" tracking filter processing gives the user the needed test method flexibility and makes it possible to meet today's demands for accurate tests and precise measurement collection.