barcode reading in asp.net Criteria for Good Control in Software

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Criteria for Good Control
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Before we can be satisfied with the response of a control system for a choice of control parameters, we must have some concept of what we want as an ideal response. Most operators of processes know what they want in the form of a
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CONTROLLER TUNING AND PROCESS IDENTRXATION
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response to a change in set point or load. For example, a response that gives minimum overshoot and $ decay ratio is often considered as a satisfactory response. In many cases, tuning is done by trial and error until such a response is obtained. In order to compare different responses that use different sets of controller parameters, a criterion that reduces the entire response to a single number, or a figure of merit, is desirable. One criterion that is often used to evaluate a response of a control system is the integral of the square of the error with respect to time (ISE). The definition of ISE is as follows:
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Integral of the square of the error (ISE) m
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ISE =
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(19.1)
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where e is the usual error (i.e., set point - control variable). For a stable system for which there is no offset (i.e., e(m) = 0), Eq. (19.1) produces a single number as a figure of merit. The objective of the designer is to obtain the minimum value of ISE by proper choice of control parameters. A response that has large errors and persists for a long time will produce a large ISE. For the cases of P and PD control, where offset occurs, the integral given by Eq. (19.1) does not converge. In these cases, one can use a modified integrand, which replaces the error r(t) - c(t), by c(w) - c(t). Since c(m) - c(t) does approach zero as t goes to infinity, the integral will converge and serve as a figure of merit. %vo other criteria often used in process control are defined as follows:
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Integral of the absolute value of error (ME)
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(19.2)
Integral of time-weighted absolute error (ITAE)
ITAE =
m [ejt dt
(19.3)
Each of the three figures of merit given by Eqs. (19.1), (19.2), and (19.3) have different purposes. The ISE will penalize (i.e., increase the value of ISE) the response that has large errors, which usually occur at the beginning of a response, because the error is squared. The ITAE will penalize a response which has errors that persist for a long time. The IAE will be less severe in penalizing a response for large errors and treat all errors (large and small) in a uniform manner. The ISE figure of merit is often used in optimal control theory because it can be used more easily in mathematical operations (for example differentiation) than the figures of merit, which use the absolute value of error. In applying the tuning rules to be discussed in the next section, these figures of merit can be used in comparing responses that are obtained with different tuning rules.
PROCESS APPLICATIONS
TUNING RULES Ziegler-Nichols Rules (Z-N)
These rules were first proposed by Ziegler and Nichols (1942), who were engineers for a major control hardware company in the United States (Taylor Instrument Co.). Based on their experience with the transients from many types of processes, they developed a closed-loop tuning method still used today in one form or another. The method is described as a closed-loop method because the controller remains in the loop as an active controller in automatic mode. This closed-loop method will be contrasted with an open-loop tuning method to be discussed later. We have already discussed the Ziegler-Nichols rules in Chap. 17 as a natural consequence of our study of frequency response. Ziegler and Nichols did not suggest that the ultimate gain (K,,) and ultimate period (PJ be computed from frequency response calculations based on the model of the process. They intended that K,, and P, be obtained from a closed-loop test of the actual process. When the rules were first proposed, frequency response methods and process models were not generally available to the control engineers. The rules are presented below, and are in the form that one would use for actual application to a-real process. 1. After the process reaches steady state at the normal level of operation, remove the integral and derivative modes of the controller, leaving only proportional control. On some PID controllers, this requires that the integral time (~1) be set to its maximum value and the derivative time (7~) to its minimum value. On modern controllers (microprocessor-based), the integral and derivative modes can be removed completely from the controller. 2. Select a value of proportional gain (K,), disturb the system, and observe the transient response. If the response decays, select a higher value of K, and again observe the response of the system. Continue increasing the gain in small steps until the response first exhibits a sustained oscillation. The value of gain and the period of oscillation that correspond to the sustained oscillation are the ultimate gain (K,,) and the ultimate period (Pu). Some very important precautions to take in applying this step of the tuning method are given in the next section. 3. From the values of K,, and P, found in the previous step, use the ZieglerNichols rules given in Table 19.1 to determine controller settings (Kc,TI,TD). This table is the same as Table 17.1 in Chap. 17. Although variations in the tuning rules given in Table 19.1 are used by industry, the same approach of using K,, and P, to obtain controller parameters is used. The Ziegler-Nichols rules generally provide conservative (and safe) controller settings. The Z-N settings should be considered as only approximate settings for satisfactory control. Fine tuning of the controller settings is usually required to get an improved control response. The experimental determination of K,, and P, described in step 2 can be replaced by a computation using frequency response methods if an accurate model of the process, valve, and measuring element is known. This type of calculation was done in Chap. 17.
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