Sine-wave testing

The main disadvantage of direct sine-wave testing is that it can be very time-consuming when applied to typical large time-constant chemical process equipment. The steadystate oscillation must be established at each value of frequency. It can lake days to generate the complete frequency-response curves of a slow process. 

When the test is being conducted over this long period of time, other disturbances and changes in operating conditions can occur that can affect the results of the test. Therefore direct sine-wave testing is only rarely used to get the complete frequency response. 

One of the most useful and practical methods for obtaining experimental dynamic data from many chemical engineering processes is pulse testing. It yields reasonably accurate frequency-response curves and requires only a fraction of the time that direct sine-wave testing takes. 

J. The frequency-response data given below were obtained from direct sine-wave tests of a chemical plant. Fit an approximate transfer function to these data. 

Even if the manipulated variable seems to follow the controller ontput, there could be a problem with the actuator. Estimates of the actuator deadband and dynamic response are required to determine if the actuator system is performing properly (both of which can be determined by a block sine wave test). This test is shown in Figure 15.21. A block sine wave is a series of eqnally sized step changes that approximate a sine wave. For the test shown in the figure, the amplitude... 

FIGURE 15.21 Results of a series of block sine wave tests to determine the deadband of the actuator. Note that the signal to the actuator and the measured value of the flow rate are plotted on different scales. 

The performance of a closed-loop system can be assessed by the settling time, closed-loop deadband, and the variability of the controlled variable evaluated over an extended period of time. The settling time and the closed-loop deadband can be determined using a closed-loop block sine wave test. For a closed-loop block sine wave test, the setpoint for the control loop is applied in the form of a block sine wave, and the amplitude of the block sine wave is varied until the deadband is determined. During these tests, the settling time of the controller can also be estimated. An accurate determination of the variability of a controlled variable generally requires an extended period of operation. An evaluation of the variability based on a short period of time may not be representative of true system performance. 

Step 1. Determine the deadband of the final control element using a series of block sine wave tests. Result the deadband of the final control element was less than 0.4%, and the dynamic response time of the final control element was 2 s therefore, the final control element was found to be functioning properly. 

If the input U does not provide enough excitation of the process over the important frequency range, the model fidelity is poor, particularly in processes with appreciable noise. This is why direct sine wave testing at a frequency near the ultimate frequency and relay feedback testing are such usefril methods. 

Direct sine wave testing is an extremely useful way to obtain precise dynamic data. Damping coefficients, time constants, and system order can all be quite accurately found. Direct sine wave testing is particularly useful for processes with signals that are noisy. Since you are putting in a sine wave signal with a known frequency and the output signal has this same frequency, you can easily filter out all of the... 

Direct Sine Wave Testing Pulse Testing... 

Specific numerical results depend on the modulation waveforms used and on the value of Ac. For example, assume Ac = 100 and that the modulating signal is a 1-kHz sine-wave test tone given by m(t) = 0.8 sin (27rl000r). Then Pm = rrf(t)) = = i0.8/ /2) = 0.320. 

The block diagram of the closed-loop calibration procedure is illustrated in Fig. 10 where the sine wave test signal from a generator is added to the closed-loop signal in the summation unit. The signal disturbance introduced into the closed-loop and the output response are measured by an external 2 channel analog-to-digital converter. 

The test voltage must be as close to a sine wave as practicable and frequency as noted in column 3 of Tables 14.1 and 14.2, for series II and Table 13.2 for series I voltage systems, and applied for one minute as follows ... 

Another modification to the slow strain-rate test involves the superimposition of a low amplitude sine wave ripple on the slow uniform extension (Fig. 8.47). In effect this produces higher strain rates (which appear to be more damaging for hydrogen embrittlement), while still giving a long test duration, with adequate time for the accumulation of hydrogen in the steeps. 

Purpose Generate data sets using mixed deterministic/stochastic models with N = 1. .. 1000. These data sets can be used to test programs or to do Monte Carlo studies. Five different models are predefined sine wave, saw tooth, base line, GC-peaks, and step functions. Data file SIMl.dat was... 

Fig. 15.18 SFJ test results obtained with a command signal composed of two sine waves, showing that the generated thrust follows the applied command signals through the gas generator pressure and the ramburner pressure.

The first term on the right-hand side of eqn. (11) decays away and, after a time approximately equal to 5t, the second term alone will remain. Note that this is a sine wave of the same frequency as the forcing function, but that its amplitude is reduced and its phase is shifted. This second term is called the frequency response of the system such responses are often characterised by observing how the amplitude ratio and phase lag between the input and output sine waves vary as a function of the input frequency, k. To recover the system RTD from frequency response data is more complex tnan with step or impulse tests, but nonetheless is possible. Gibilaro et al. [22] have described a short-cut route which enables low-order system moments to be determined from frequency response tests, these in turn approximately defining the system transfer function G(s) [see eqn. (A.5), Appendix 1]. From G(s), the RTD can be determined as in eqn. (8). 

In this section, the model in Equation (9.18) is used to develop an analysis/synthesis system which will serve to test the accuracy of the sine-wave representation for audio signals. In the analysis stage, the amplitudes, frequencies, and phases of the model are estimated, while in the synthesis stage these parameter estimates are first matched and then interpolated to allow for continuous evolution of the parameters on successive frames. This sine-wave analysis/synthesis system forms the basis for the remainder of the chapter. 

The braids were tested from — 100°C upwards at a heating rate of 1°C min 1 and a frequency of 1 Hz, using an inertial weight of 4.55 X 10 5 kg m2. The damped sine waves were processed by hand to give log decrement and modulus. The radius of the sample was calculated from the weight per unit length, as above, with the additional assumption that the sample was a right circular cylinder and that there were no voids in the sample. 

Coaxial cables used for data highways must be tested using sine-wave reflective testing techniques. Circuits involving intrinsically safe (IS) instmmentation must be tested (e.g., loop impedance, inductance, L/R [Inductance/Resistance] ratio) in accordance with the manufacturer s instmctions and approved by the customer. 

SlMl.dat Section 1.4 Five data sets of 200 points each generated by SIM-GAUSS the deterministic time series sine wave, saw tooth, base line, GC-peak, and step function have stochastic (normally distributed) noise superimposed use with SMOOTH to test different filter functions (filer type, window). A comparison between the (residual) standard deviations obtained using SMOOTH respectively HISTO (or MSD) demonstrates that the straight application of the Mean/SD concept to a fundamentally unstable signal gives the wrong impression. 

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