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Frequency response refers to graphing the dynamic response of output from a machine or process with a sine wave as the command input. Test equipment is available for testing a physical system, and analytical techniques and tools exist that allow using a completely theoretical approach. Here, we'll take a brief look at the frequency response method as a test procedure and summarize what the system designer can glean from the procedures and results.
The frequency response test method can be applied to anything, quite literally, if the device can be stimulated with a sinusoidal test signal and its output measured. Frequency response is most often encountered in electrohydraulic motion control in the data that manufacturers publish for servo and proportional valves. In fact, one compelling reason why I advocate servo and proportional valves for control - rather than other kinds of valves — is because so much frequency response data exists for servo and proportional valves, and almost none for other devices. Having this information puts us in a much better position to predict the performance of the system before we build it.
The frequency response test is quite simple and can easily be understood after a few minutes of observing the test. This is in contrast to months of study in a purely academic environment. It is one method for measuring the dynamic response of a component, such as a valve.
Another popular dynamic test procedure is to measure the output response to a step input. The frequency response and step response are related, because they come from the same system. However, the frequency response method is more reliable than the step response, because of the way in which distortion and noise are inherently rejected in the frequency response test when using a frequency response analyzer.
The test, represented in Figure 1, involves applying a controlled-amplitude sinusoidal wave shape to the input that causes the tested device, say — a valve — to cycle back and forth. Meanwhile, the output will cycle, too, at the same frequency. However, the amplitude of the output and command input will not necessarily be the same as the command input. In the case of the valve, input (current) and output (flow rate) aren't even in the same units of measure. Furthermore, output will, in most real physical dynamic processes, undergo a phase lag. That is, the output must necessarily lag behind the input. The test operator records the frequency, output amplitude, and the amount of phase lag between input and output (measured in degrees).
Next, frequency is increased while the input sine wave is maintained at a constant peak-to-peak amplitude. The phase is normally plotted in degrees and the amplitude is given in deciBels (dB) by this equation:
A = 20 log | On÷Ol |, where
A is the amplitude of the valve's frequency response
On is the output at any frequency, and
Ol is the output at the lowest frequency. Thus, we see that the frequency response test data for a servo valve always begins at 0 dB for the lowest frequency of a test.
With higher test frequencies, an attendant higher phase lag normally occurs, and the output amplitude changes. It is normal with any kind of machine that the output amplitude will be less able to keep up with the input amplitude with increasing frequency. That is, there will always be some frequency where the input command is vibrating so fast that the output cannot keep up at all. Therefore, the output amplitude tends to diminish with increased frequency, and the phase lag between input and output tends to increase.
There are exceptions. When resonances exist within the tested system, the output amplitude can increase with frequency over some narrow frequency band or range. Resonances occur when the potential energy stored in a spring or other flexible member is exchanged with the kinetic energy of a moving mass. Resonances occur in the hydraulic system when the kinetic energy of masses interacts with the potential energy stored in the internal compressed fluid.
When resonances occur, they are sometimes revealed as rises in the output amplitude for increasing frequency. That is the case for the servo valve frequency response data shown in Figure 2. At 30 Hz there is about a 0.8-dB rise above the 0-dB reference level. The existence of the resonant rise indicates that there is a tendency for the valve to be slightly springy, and its output will tend to "ring" at approximately that frequency if tested with a step input. The rise indicates that the designers of the valve tuned its response to be under-damped. Most servovalves are tuned to have no resonant rise. However, there are some exceptions. The property of being under-damped is accompanied by a resonant rise. One way to describe this would be, "Under-damped means there are overshoots and resonant rises."
The frequency response graph in Figure 2, typical of many servo valves, at the very least can be used to compare the response of one valve to another. The important "benchmark" frequency for any valve is the frequency at which the phase lag reaches 90°. Note in the referenced valve that frequency is about 50 Hz. It should be obvious that if there is another valve with a 90° phase lag frequency higher than 50 Hz, that valve will respond faster than the one plotted in Figure 2.
The 90° phase lag frequency should always be used when comparing one valve to another. The frequency is called the valve frequency, valve frequency response, or the valve bandwidth. All terms are more or less synonymous. In any event, this frequency is useful in predicting how well the valve response matches the required performance of the application system into which it will be placed. Some designers use the 3-dB roll-off frequency; however, as a benchmark for comparison, it is unreliable. It also has no value in assessing how well the valve will perform with the rest of the componentry in the final system. The most important feature of the 90° phase lag frequency is that it allows us to compare the valve frequency to the hydromechanical resonant frequency, which is the resonance that occurs because of fluid compressibility (hydraulic capacitance, or compliance) interacting with the load mass at the actuator.