15.3 Control System

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The two primary functions of the shaker control system in vibration testing are (1) to guarantee that the

specified excitation is applied to the test object and (2) to ensure that the dynamic stability (motion

constraints) of the test setup is preserved. An operational block diagram illustrating these control

functions is given in Figure 15.12. The reference input to the control system represents the desired

excitation force that should be applied to the test object. In the absence of any control, however, the force

reaching the test object will be distorted, primarily because of: (1) dynamic interactions and

nonlinearities of the shaker, the test table, the mounting fixtures, the auxiliary instruments, and the test

object itself; (2) noise and errors in the signal generator, amplifiers, filters, and other equipment; and (3)

external loads and disturbances acting on the test object and other components (for example, external

restraints, aerodynamic forces, friction). To compensate for these distorting factors, response

measurements (displacements, velocities, acceleration, and so on) are made at various locations in the

test setup and are used to control the system dynamics. In particular, the responses of the shaker, the test

table, and the test object are measured. These responses are used to compare the actual excitation felt by

FIGURE 15.11 An instrumented hammer used in

bump tests or hammer tests.

Excitation

Input

(Reference)

Feedback Paths

Drive

Signal

Shaker

Response

Test

Table

Test

Object

Test Object

Response

Test Table

Exciter Response

(Shaker)

(Ram)

Controller

and

Amplifier

FIGURE 15.12 Operational block diagram illustrating a general shaker control system.

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the test object at the shaker interface, with the desired (specified) input. The drive signal to the shaker is

modified, depending on the error that is present.

Two types of control are commonly employed in shaker apparatus: simple manual control and

complex automatic control. Manual control normally consists of simple, open-loop, trial-and-error

methods of manual adjustments (or calibration) of the control equipment to obtain a desired dynamic

response. The actual response is usually monitored (on an oscilloscope or frequency analyzer screen, for

example) during manual-control operations. The pretest adjustments in manual control can be very

time-consuming; as a result, the test object might be subjected to overtesting, which could produce

cumulative damage, is undesirable, and could defeat the test purpose. Furthermore, the calibration

procedure for the experimental setup must be repeated for each new test object.

The disadvantages of manual control suggest that automatic control is desirable in complex test schemes

in which high accuracy of testing is desired. The first step of automatic control involves automatic

measurement of the system response, using control sensors and transducers. The measurement is then fed

back into the control system, which instantaneously determines the best drive signal to actuate the shaker

in order to get the desired excitation. This may be done by either analog or digital methods.

Primitive control systems require an accurate mathematical description of the test object. This

dependency of the control system on the knowledge of test-object dynamics is clearly undesirable.

Performance of a good control system should not be considerably affected by the dynamic interactions

and nonlinearities of the test object or by the nature of the excitation. Proper selection of feedback signals

and control-system components can reduce such effects and will make the system robust.

In the response-spectrum method of vibration testing, it is customary to use displacement control at

low frequencies, velocity control at intermediate frequency, and acceleration control at high frequencies.

This necessitates feedback of displacement, velocity, and acceleration responses. Generally, however, the

most important feedback is the velocity feedback. In sine-sweep tests, the shaker velocity must change

steadily over the frequency band of interest. In particular, the velocity control must be precise near the

resonances of the test object. Velocity (speed) feedback has a stabilizing effect on the dynamics, which is

desirable. This effect is particularly useful in ensuring stability in motion when testing is done near

resonances of lightly damped test objects. On the contrary, displacement (position) feedback can have a

destabilizing effect on some systems, particularly when high feedback gains are used.

The controller usually consists of various instruments, equipment, and computation hardware and

software. Often, the functions of the data-acquisition and processing system overlap with those of the

controller to some extent. As an example, consider the digital-controller of vibration testing apparatus.

First, the responses are measured through sensors (and transducers), filtered, and amplified

(conditioned). These data channels may be passed through a multiplexer, whose purpose is to select

one data channel at a time for processing. Most modern data acquisition hardware does not need a

separate multiplexer to handle multiple signals. The analog data are converted into digital data using

analog-to-digital converters (ADCs). The resulting sampled data are stored on a disk or as a block data in

the computer memory. The reference input signal (typically, a signal recorded on an FM tape) is also

sampled (if it is not already in the digital form), using an ADC, and fed into the computer. Digital

processing is done on the reference signal and the response data, with the objective of computing the

command signal to drive the shaker. The digital command signal is converted into an analog signal, using

a digital-to-analog converter (DAC), and amplified (conditioned) before it is used to drive the exciter.

The nature of the control components depends to a large extent on the nature and objectives of the

particular test to be conducted. Some of the basic components in a shaker controller are described in

the following subsections.

15.3.1 Components of a Shaker Controller

15.3.1.1 Compressor

A compressor circuit is incorporated in automatic excitation control devices to control the excitationinput

level automatically. The level of control depends on the feedback signal from a control sensor and

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the specified (reference) excitation signal. Usually, the compressor circuit is included in the excitationsignal

generator (for example, in a sine generator). The control by this means may be done on the basis of

a single-frequency component (e.g., the fundamental frequency).

15.3.1.2 Equalizer (Spectrum Shaper)

Random-signal equalizers are used to shape the spectrum of a random signal in a desired manner. In

essence, and equalizer consists of a bank of narrow-band filters (for example, 80 filters) in parallel over

the operating frequency range. By passing the signal through each filter, the spectral density (or the mean

square value) of the signal in that narrow frequency band (for example, each one-third-octave band) is

determined. This is compared with the desired spectral level, and automatic adjustment is made in that

filter in case there is an error. In some systems, response-spectrum analysis is made in place of power

spectral density analysis. In that case, the equalizer consists of a bank of simple oscillators, whose

resonant frequencies are distributed over the operating frequency range of the equalizer. The feedback

signal is passed through each oscillator, and the peak value of its output is determined. This value is

compared with the desired response spectrum value at that frequency. If there is an error, automatic gain

adjustment is made in the appropriate excitation signal components.

Random-noise equalizers are used in conjunction with random signal generators. They receive

feedback signals from the control sensors. In some digital control systems, there are algorithms (software)

that are used to iteratively converge the spectrum of the excitation signal felt by the test object into the

desired spectrum.

15.3.1.3 Tracking Filter

Many vibration tests are based on single-frequency excitations. In such cases, the control functions

should be performed on the basis of the amplitudes of the fundamental-frequency component of the

signal. A tracking filter is simply a frequency-tuned band-pass filter. It automatically tunes the center

frequency of its very narrow-band-pass filter to the frequency of a carrier signal. Then, when a noisy

signal is passed through the tuned filter, the output of the filter will be the required fundamental

frequency component in the signal. Tracking filters also are useful in obtaining amplitude – frequency

plots using an X – Y plotter. In such cases, the frequency value comes from the signal generator (sweep

oscillator), which produces the carrier signal to the tracking filter. The tracking filter then determines the

corresponding amplitude of a signal that is fed into it. Most tracking filters have dual channels so that two

signals can be handled (tracked) simultaneously.

15.3.1.4 Excitation Controller (Amplitude Servo-Monitor)

An excitation controller is typically an integral part of the signal generator. It can be set so that automatic

sweep between two frequency limits can be performed at a selected sweep rate (linear or logarithmic).

More advanced excitation controllers have the capability of an automatic switch-over between constantdisplacement,

constant-velocity and constant-acceleration excitation-input control at specified

frequencies over the sweep frequency interval. Consequently, integrator circuits should be present

within the excitation controller unit to determine velocities and displacements from acceleration signals.

Sometimes, integration is performed by a separate unit called a vibration meter. This unit also offers

the operator the capability of selecting the desired level of each signal (acceleration, velocity, or

displacement). There is an automatic cut-off level for large displacement values that could result from

noise in acceleration signals. A compressor is also a subcomponent of the excitation controller. The

complete unit is sometimes known as an amplitude servo-monitor.

15.3.2 Signal-Generating Equipment

Shakers are force-generating devices that are operated using drive (excitation) signals generated from a

source. The excitation-signal source is known as the signal generator. Three major types of signal

generators are used in vibration testing applications: (1) oscillators, (2) random-signal generators, and

(3) storage devices. In some units, oscillators and random-signal generators are combined. We shall

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discuss these two generators separately, however, because of their difference in function. It also should be

noted that almost any digital signal (deterministic or random) can be generated by a digital computer

using a suitable computer program; the signal eventually can be passed through a DAC to obtain

the corresponding analog signal. These ‘digital’ signal generators along with analog sources such as

magnetic tape players (FM) are classified into the category of storage devices.

The dynamic range of equipment is the ratio of the maximum and minimum output levels (expressed

in decibels) at which it is capable of operating without significant error. This is an important specification

for many types of equipment, particularly for signal-generating devices. The output level of the signal

generator should be set to a value within its dynamic range.

15.3.2.1 Oscillators

Oscillators are essentially single-frequency generators. Typically, sine signals are generated, but other

waveforms (such as rectangular and triangular pulses) are also available in most oscillators. Normally,

an oscillator has two modes of operation: (1) sweeping up and down between two frequency limits and

(2) dwelling at a specified frequency. In the sweep operation, the sweep rate should be specified. This can

be done either on a linear scale (Hz/min) or on a logarithmic scale (octaves/min). In the dwell operation,

the frequency points (or intervals) should be specified. In either case, a desired signal level can be chosen

using the gain-control knob. An oscillator that is operated exclusively in the sweep mode is called a sweep

oscillator.

The early generation of oscillators employed variable inductor-capacitor types of electronic circuits to

generate signals oscillating at a desired frequency. The oscillator is tuned to the required frequency by

varying the capacitance or inductance parameters. A DC voltage is applied to energize the capacitor

and to obtain the desired oscillating voltage signal, which subsequently is amplified and conditioned.

Modern oscillators use operational amplifier circuits along with resistor, capacitor, and semiconductor

(SC) elements. Also common are crystal (quartz) parallel-resonance oscillators, used to generate voltage

signals accurately at a fixed frequency. The circuit is activated using a DC-voltage source. Other

frequencies of interest are obtained by passing this high-frequency signal through a frequency converter.

The signal is then conditioned (amplified and filtered). Required shaping (for example, rectangular

pulse) is obtained using a shape circuit. Finally, the required signal level is obtained by passing the

resulting signal through a variable-gain amplifier. A block diagram of an oscillator, illustrating various

stages in the generation of a periodic signal, is given in Figure 15.13.

A typical oscillator offers a choice of several (typically six) linear and logarithmic frequency ranges and

a sizable level of control capability (for example, 80 dB). Upper and lower frequency limits in a sweep can

be preset on the front panel to any of the available frequency ranges. Sweep-rate settings are continuously

DC Voltage

Oscillator

Frequency

Specification

Frequency

Converter

Filter/

Amplifier

Shaper

Periodic

Signal

Frequency

Counter

Fixed-Frequency

Signal

Variable-Gain

Output

Amplifier

Signal

Specification

Level

Specification

FIGURE 15.13 Block diagram of an oscillator-type signal generator.

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variable (typically, 0 to 10 octaves/min in the logarithmic range, and 0 to 60 kHz/min in the linear range),

but one value must be selected for a given test or part of a test. Most oscillators have a repetitive-sweep

capability, which allows the execution of more than one sweep continuously, for example, for mechanical

aging and in product-qualification single-frequency tests. Some oscillators also have the capability of

varying the signal level (amplitude) during each test cycle (sweep or dwell). This is known as level

programming. Also, automatic switching between acceleration, velocity, and displacement excitations at

specified frequency points in each test cycle can be implemented with some oscillators. A frequency

counter, which is capable of recording the fundamental frequency of the output signal, is usually an

integral component of the oscillator.

15.3.2.2 Random Signal Generators

In modern random-signal generators, SC devices (e.g., zener diodes) are used to generate a random

signal that has a required (e.g., Gaussian) distribution. This is accomplished by applying a suitable DC

voltage to a SC circuit. The resulting signal is then amplified and passed through a bank of conditioning

filters, which effectively acts as a spectrum shaper. In this manner, the bandwidth of the signal can be

adjusted in a desired manner. Extremely wideband signals (white noise), for example, can be generated

for random-excitation vibration testing in this manner. The block diagram in Figure 15.14 shows the

essential steps in a random-signal generation process. A typical random-signal generator has several

(typically eight) bandwidth selections over a wide frequency range (for example, 1 Hz to 100 kHz). A

level-control capability (typically 80 dB) is also available.

15.3.2.3 Tape Players

Vibration testing for product qualification may be performed using a tape player as the signal source.

A tape player is essentially a signal reproducer. The test-input signal that has a certain specified response

spectrum is obtained by playing a magnetic tape and mixing the contents in the several tracks of the tape

in a desirable ratio. Typically, each track contains a sine-beat signal, with a particular beat frequency,

amplitude, and number of cycles per beat, or a random-signal component with a desired spectral

characteristic).

In frequency modulation (FM) tapes, the signal amplitude is proportional to the frequency of a carrier

signal. The carrier signal is recorded on the tape. When played back, the actual signal is reproduced, based

on detecting the frequency content of the carrier signal in different time points. The FM method is

usually favorable, particularly for low-frequency testing (below 100 Hz).

Performance of a tape player is determined by several factors, including tape type and quality, signal

reproduction and recording circuitry, characteristics of the magnetic heads, and the tape-transport

mechanism. Some important specifications for tape players are (1) the number of tracks per tape

(for example, 14 or 28); (2) the available tape speeds (for example, 3.75, 7.5, 15, or 30 in./sec);

(3) reproduction filter-amplifier capabilities (for example, 0.5% third-harmonic distortion in a 1 kHz

signal recorded at 15 in./sec tape speed, peak-to-peak output voltage of 5 V at 100 V load, signal-to-noise

ratio of 45 dB, output impedance of 50 V); and (4) the available control options and their capabilities

(for example, stop, play, reverse, fast-forward, record, speed selection, channel selection). Tape player

specifications for vibration testing are governed by an appropriate regulatory agency, according to a

Amplifier

Conditioning

Filters

Variable-Gain

Output Amplifier

Zener Diode

Noise Source

DC

Voltage

Band Width

Specification

Level

Specification

Gaussian

Random Noise

Random

Signal

FIGURE 15.14 Block diagram of a random signal generator.

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specified standard (e.g., the Communication and Telemetry Standard of the Intermediate Range

Instrumentation Group (IRIG Standard 106-66).

A common practice in vibration testing is to generate the test-input signal by repetitively playing a

closed tape loop. In this manner, the input signal becomes periodic but has the desired frequency content.

Frequency modulation players can be fitted with special loop adaptors for playing tape loops. In spectral

(Fourier) analysis of such signals, the analyzing-filter bandwidth should be several times more than the

repetition frequency (tape speed/loop length). Extraneous noise is caused by discontinuities at the tape

joint. This can be suppressed by using suitable filters or gating circuits.

A technique that can be employed to generate low-frequency signals with high accuracy is to record the

signal first at a very low tape speed and then play it back at a high tape speed (for example, r times

higher). This has the effect of multiplying all frequency components in the signal by the speed ratio (r).

Consequently, the filter circuits in the tape player will allow some low-frequency components in the

signal that would normally be cut off and will cut off some high-frequency components that would

normally be allowed. Hence, this process is a way of emphasizing the low-frequency components in a

signal.

15.3.2.4 Data Processing

A controller generally has some data processing functions, as well. A data-acquisition and processing

system usually consists of response sensors (and transducers), signal conditioners, an input – output

(I/O) board including a multiplexer, ADCs, etc., and a digital computer, with associated I/O

devices. The functions of a digital data-acquisition and processing system may be quite general, as listed

below:

1. Measuring, conditioning, sampling, and storing the response signals and operational data of test

object (using input commands, as necessary)

2. Digital processing of the measured data according to the test objectives (and using input

commands, as necessary)

3. Generating drive signals for the control system

4. Generating and recording test results (responses) in a required format

The capacity and the capabilities of a data-acquisition and processing systems are determined by such

factors as:

1. The number of response data channels that can be handled simultaneously

2. The data-sampling rate (samples per second) for each data channel

3. Computer memory size

4. Computer processing speed

5. External storage capability (hard disks, floppy disks, and so forth)

6. The nature of the input and output devices

7. Software features

Commercial data-acquisition and processing systems with a wide range of processing capabilities are

available for use in vibration testing. Some of the standard processing capabilities are the following:

1. Response-spectrum analysis

2. FFT analysis (spectral densities, correlations, coherence, Fourier spectra, and so on)

3. Frequency-response function, transmissibility, and mechanical-impedance analysis

4. Natural-frequency and mode-shape analysis

5. System-parameter identification (for example, damping parameters)

Most processing is done in real time, which means that the signals are analyzed as they are being

measured. The advantage of this is that outputs and command signals are available simultaneously as the

monitoring is done, so that any changes can be detected as they occur (for example, degradation in the

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test object or deviations in the excitation signal from the desired form) and automatic feedback control

can be effected. For real-time processing to be feasible, the data-acquisition rate (sampling rate) and the

processing speed of the computer should be sufficiently fast. In real-time frequency analysis, the entire

frequency range is analyzed at a given instant, as opposed to analyzing narrow bands separately. Results

are presented as Fourier spectra, power spectral densities, cross-spectral densities, coherence functions,

correlation functions, and response-spectra curves. Averaging of frequency plots can be done over small

frequency bands (for example, one-third-octave analysis), or the running average of each instantaneous

plot can be determined.

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