Step response test

Process model is known An approximate model of the process may be obtained by the step response test noted earlier (see Section 12.4.2.4) (or from first prindples). When an approximate modd of the process is known we may obtain the tuning parameters directly. We use here the example of the first-order plus dead time process, since its dynamics are so representative of the polymer equipment dynamics. Here we have chosen for the tuning criteria to minimize the integral of the time-weighted absolute error (ITAE) [Eq. (96)] [7]. 

In contrast, the step response test is frequently performed in the process industries. A step response test uses a step input signal defined by... 

Figure 2.23 Step response test data from polymer reactor. Upper diagram initiator flow rate (ml/min) lower diagram fraction monomer conversion...

Simple first order plus delay models for this process were derived firom step response tests. For controlling the temperature of the outlet water stream, the manipulated input variable is the steam valve position and the process output variable is the outlet water temperature, measured at one of three thermocouples located at different distances from the tank outlet. The tests involved introducing a step change in steam valve position, with the temperature controller in manual, and observing the response in the outlet water temperature at each of the three thermocouples. Simple graphical methods were used to calculate the parameters of the first order plus delay models. 

The dynamic response of composition to a change in distillate flow exhibits considerable dead time, as is expected in a multicapacity process. But the presence of an additional feature is indicated by step-response tests. Figure 11.13 illustrates results which are typically encountered. The response is the sort which would be seen in a transmission line with... 

S ystem identiflcation is the term used to define a procedure to characterize the process response. In this case, system identification can be accomplished by adjusting the feed rate to the tank in steps, up and down, and then observing the tank level response on a strip chart. This is termed step response testing. 

Perform a series of steady-state runs to determine the amount of steam required to raise the temperature of the feed water stream to about 200°F (about 80°C). Then, switch to the dynamic mode of operation and perform step response testing by varying the inlet flow rate and feed temperature to determine the process response. Remember to use the strip charts to observe the important process variables. 

Repeat the step response testing done above to determine the time constant of the new system and use these results to calculate the dead time/time constant ratio. You will need to stop the sine-wave feed-temperature input and use a constant feed temperature. Record your results in Table W3.5. 

Add integral time to your controller, starting with = 1.0, and check that it eliminates offset for set-point changes, both with and without dead time in the system Interactively change the feed rate to determine how effective the controller is at disturbance rejection, i.e. step response testing. 

Hint How long does it take the controller to respond to a change in the feed temperature Can the warm water temperature be stabilized by manipulating the tuning constants How does the controller respond to changes in the feed rate, i.e. step response testing ... 

In principle, the step-response coefficients can be determined from the output response to a step change in the input. A typical response to a unit step change in input u is shown in Fig. 8-43. The step response coefficients are simply the values of the output variable at the samphng instants, after the initial value y(0) has been subtracted. Theoretically, they can be determined from a single-step response, but, in practice, a number of bump tests are required to compensate for unanticipated disturbances, process nonhnearities, and noisy measurements. 

A practical method of predicting the molecular behavior within the flow system involves the RTD. A common experiment to test nonuniformities is the stimulus response experiment. A typical stimulus is a step-change in the concentration of some tracer material. The step-response is an instantaneous jump of a concentration to some new value, which is then maintained for an indefinite period. The tracer should be detectable and must not change or decompose as it passes through the mixer. Studies have shown that the flow characteristics of static mixers approach those of an ideal plug flow system. Figures 8-41 and 8-42, respectively, indicate the exit residence time distributions of the Kenics static mixer in comparison with other flow systems. 

Long time constants in the system and zone-to-zone interaction of the heaters complicated the controller design and tuning. The time available for experimental measurements was limited by the schedule of other experimental work to be performed by the extruder. The classic step response methods of tuning controllers would take on the order of hours to perform, and frequently disturbances in the polymer feed or in the ambient room conditions would invalidate the test. Consequently, a mathematical rather than an empirical approach was desirable. 

To make use of empirical tuning relations, one approach is to obtain the so-called process reaction curve. We disable the controller and introduce a step change to the actuator. We then measure the open-loop step response. This practice can simply be called an open-loop step test. Although we disconnect the controller in the schematic diagram (Fig. 6.1), we usually only need to turn the controller to the manual mode in reality. As shown in the block diagram, what we measure is a lumped response, representing the dynamics of the blocks Ga,... 

Empirical tuning with open-loop step test Measure open-loop step response, the so-called process reaction curve. Fit data to first order with dead-time function. 

Question 2 Is my equipment somehow responsible That is sadly often the case. For example, some electronic loads can show weird glitches in the load profile they present to the converter under dynamic conditions. For example, if we are doing step load testing from 10mA to 200mA, all may be fine. But if we go from 0mA to 200mA, and see an output overshoot/undershoot, it could also be because of the electronic load. We may need to do... 

Figure 9-4 Too Little Phase Margin Shows Up in a Step-Load Response Test...

The most direct way of obtaining an empirical linear dynamic model of a process is to find the parameters (deadtime, time constant, and damping coefficient) that fit the experimentally obtained step response data. The process being identified is usually openloop, but experimental testing of closedloop systems is also possible. 

It would be interesting to test with other Rh(III) complexes, whether the direct oxidation of the base (by photo-electron transfer) could also be a primary step responsible for photocleavages. Indeed, as outlined before in Sect. 5, radiation studies have shown that the radical cation of the base can produce the sugar radical, itself leading to strand scission [122]. Moreover base release, as observed with the Rh(III) complexes, can also take place from the radical cation of the base [137]. Direct base oxidation and hydrogen abstraction from the sugar could be two competitive pathways leading to strand scission and/or base release. 

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). 

The dynamics of the system under study can, in fact, be recovered from a variety of stimulus response tests. These include impulse and step response experiments, and frequency response and cross-correlation techniques. Descriptions of these methods and the interrelationships between them are discussed in many references, see, for instance, refs. 22—25 and Sects. 3.2.1—3.2.4 of this chapter. 

The constants Kp, Kt, and Kd are settings of the instrument. When the controller is hooked up to the process, the settings appropriate to a desired quality of control depend on the inertia (capacitance) and various response times of the system, and they can be determined by field tests. The method of Ziegler and Nichols used in Example 3.1 is based on step response of a damped system and provides at least approximate values of instrument settings which can be further fine-tuned in the field. 

The data from step-change tests is modeled mathematically to fit one or more exponential time constants depending upon the curvature of the line. Each exponential time constant is related to a relaxation time in the sample response. Most rheometers have software that automatically fits the data to these models. 

A general point to remember when dealing with step change tests when compared to oscillation tests is that the linear response of a sample is quite often different for the two types of test. This is because the physical displacement of the structure of the material is much smaller in an oscillation test, with its forward and backward motion. A step change test is unidirectional and thus may cause more dislocation of a molecule, droplet, or particle, which in turn results in greater damage. ... 

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