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In the late 1950s there was much tall; of extensive tests on processes using frequency-response analysis. In fact some tests were conducted 011 reactors, heat exchangers, and distillation columns. Although a certain amount of information was obtained using this method, two major objections stand out: 1. The tests are unbelievably time-consuming. 2. They assume that the process is linear and invariant. The first objection rules out testing in most plants because of the unwillingness of operating personnel to tolerate upsets for long intervals and because of the expense of manpower and equipment. The second
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objection indicates that the results of tests on a process with nonlinear elements may be not only invalid, but also misleading. Frequency response is only suitable for fast, linear devices like instruments, controllers, amplifiers, etc. The author has been called upon many times to invest,igate a process which was in trouble. In these instances it, was impossible to bring a,n extensive array of test, equipment or to spend days gathering information. In most cases the process was nonlinear in some respect and not well understood by the operating people-ot,herwise it would not have been in trouble. A simple test procedure was decided on, independent of linearity, from which the dominant properties of the system could be determined. A properly conducted test should pinpoint problem areas with a minimal upset to the process. To keep testing to a minimum, all available knowledge of the process must be employed. The volume of vessels and flow rates are always available, from which time constants may be calculat ed. The length and diameter of piping runs can serve to locate dead-time elements. By identifying all the known or knowable elements in this way, any tests will be of more value in defining the unknown elements which make up the balance of the loop. The author has always reacted strongly to any test procedure that is based upon knowing nothing about a process. JIany things about an unfamiliar process can be learned by observing the vessels and piping, examining the chemistry and physics involved, and talking to the operators. Preliminary information like this is of inestimable help in indicating what to look for and where. It is surprising how much can often be learned about a particular process without even making a t est. Occasionally the tests will not substantiate the expectations, which provides a challenging opportunity t,o learn.
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Before describing how to conduct a test, it is important to point out how not to conduct a test, in order to avoid some serious pitfalls. 1. Do not test for steady-state gain. In Chap. 1 it was pointed out that the steady-state gain of a single-capacity liquid-level process is not constant. It varies with both flow and level. Yet t,he dynamic gain is constant. Because the process is in a control loop, only the dynamic gain-the loop gain at To--is of real consequence. 2. Do not test for time constants. There arc several methods available for finding the time constants in a linear system. But, as in the singlecapacity level process, the time constant may vary with flow without affecting dynamic gain. The likelihood of a nonlinear element in a
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troublesome process is extremely high, rendering these tests meaningless. The tests also require the process to come to rest after a disturbance. A non-self-regulating process will not come to rest and therefore cannot be treated in this way. Furthermore these tests require the control loop to be open until a new steady state has been reached, which could be a long time. Fortunately there is a quick and easy method for obtaining enough information to suggest corrective measures in most instances. The method consists of one open-loop and one closed-loop test. In the latter case, the proportional mode of a controller serves as the test instrument. The procedure is as follows: 1. With the cont,roller in manual, step or pulse the cont rol valve sufficiently to produce an observable effect . Pleasure the time elapsed between the disturbance and the first indication of a response. This i.s the dead time Ed. 2. Transfer control to automatic, with minimum derivative and maximum reset time. Adjust the proportional band to develop nearly undamped oscillation. Note the period of oscillation 7O and the proportional band setting. In this test, it was onIy necessary to leave the loop open (manual control) long enough to measure the dead time. Any other type of open-loop test would consume more time. The closed-loop test describes the process under those conditions that are of great,est significance, that is, at the natural period. Two complete cycles are enough to measure TV. If it is not practical to induce uniform oscillations, damped oscillations will suffice, although the proportional band reading should be corrected for the damping. E rom the data obt,ained, a represent,ation of the dynamic elements in t he process may be const ructed: If rO/rd = 2, the process is pure dead time. If 2 < ~0/7~~ < 4, dead time is dominant. If T /T~ = 4, t here is a single dominant capacity. If r /ird > 4, more than one capacity is present. l urthcrmorc, the setting of proport,ional band responsible for uniform oscillation equals the gain product of the other elements in the loop at TV. When these bits of information are combined with the characteristics of the known elements, a remarkably accurate picture of the process can he asscmblcd. Icor example, if the process is known t,o contain one principal capacity, and TJ~,~ = 4, no other time constants need be sought . If t he time constant of this capacity is known, its dynamic gain G1 at 7O can be calculated. Combining this with known values of transmitter and valve gain, together with the controller proportional band, yields
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