Ising integral

Usually the smallest square error ISE (Integral Square Error) is used as a measure of the quality of the control ... 

Describe an on-line tuning procedure for PI controllers which uses as criterion the ISE (integral square error). 

Regarding differential equations (18-23) are the mass balances (mg/l-h) of the aeration tanks (subscripts 1 and 2). They represent the rate of change of oxygen (c/, C2), biomass (x/, x ) and organic substrate (si, s ). Equations (24-29) are the mass balances for the two settlers (subscripts 1 and 2) where three layers of different and increasing biomass concentration (xdi, xbj, xri and xd2, xb2, xr2) are considered. Finally, equations 30 and 31 correspond to the integral term of the controller and to the ISE (Integral Square Error) measure respectively. 

In any given situation, there may be different levels of dependence between an operator s performance on one task and on another because of the characteristics of the tasks theraseb e.s. or because of the manner in which the operator was cued to perform the tasks. Dependence levels between the performances of two (or more) operators also may differ. The analyses should account for dependency in human-error probabilities. In addition, each sequence may have a set of human recovery actions that if successfully performed will terminate or reduce the consequences of the sequence. This information, coupled with a knowledge of the system success criteria leads to the development of human success and failure probabilities which are input to the quantification of the fault iices or event trees. With this last step, the HRA is integrated into the PSA, and Pl. ise 4 is complete. 

Time integral performance criteria (ISE, IAE, ITAE) Apply design relations derived from minimization of an error integral of the theoretical time-domain response. 

Flow-through sensors based on integrated optical detection and a liquid-liquid separation are relatively scant since the analytes are rarely determined by their photometric or luminescence properties. Thus, with few exceptions, these sensors use amperometric detection —as noted earlier, ISEs and ISFETs are dealt with separately in Section 4.6. 

Here e is the error (the deviation) e = rate setpoint minus measured rate. ISE is relatively insensitive to small deviations, but large deviations contribute substantially to the value of the integral. The result is small overshoots , but long ripple times because deviations occurring late contribute little to the integral. 

This is employed when the process is not well-known. The Model Reference Adaptive Controller contains a reference model to which the command signal or set point change is applied as well as to the process itself (Fig. 7.98)<4 ). The output of the reference model is postulated as the desired controlled process output and this is compared with the actual process output. The difference (or error) e , between the two outputs is used to adjust the controller parameters so as to minimise the relevant integral criterion. For example, if the ISE criterion is employed then the quantity... 

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