Why most of the author chosen the IAE, ITEA as fitness function.
Usually the most used performance index is the ISE criterion, because it's easy to compute (analytical derivative function) and it allows to discriminate overdamped from underdamped system. It allows small oscillations as the time goes. IAE produces slower response than ISE outputs but without a big oscillation over time. ITAE delivers an output that settles faster than the other two methods(because of the time integrated together the absolute value of the error). The downside of ITAE is that sometimes its outputs are lethargic. It's up to you decide which option is the best.
Good Q. Which criterion is best depends on the application. Usually tuning is tested with set point changes, servo mode, and deviations from the new set point are the measure of goodness. If overshoot and undershoot (too hot, too cold) material is blended down stream, then IE could be an appropriate measure. If either is bad (customer likes higher purity but producer knows it costs more, customer does not like low purity), then IAE could be the right measure. If small deviations are inconsequential, but large ones are detectably bad, then ISE is appropriate. ISE is my favorite of all of these sort of measures, because, when normalized by time, it represents the process variance during regulatory periods. ITAE and ITSE penalize persisting oscillations and would seek to improve settling time in servo mode.
Most of the time processes are not being changed, but regulated, kept at the same set point. Here, I think, a measure of controller performance would be ISE, because it relates to process variance, and how close the set point can be to product specifications. But, in this case testing would not be in response to set point changes. Choose the controller coefficient values, collect data in an extended regulatory period, long enough to experience the range of vagaries. Then tweak a parameter and observe the change in ISE from a similar period. Such an approach is predicated on sequential regulatory periods of expressing similar upsets to be regulated. If a spurious event happens in one period, it cannot be used by the optimizer as a rational performance comparison to other periods.
But, in the minimization of any of these, to my preference, the MV action is undesirably aggressive. Because of safety, propagation of upsets, thermal stresses, operator response, and robustness to process gain changes, I prefer controllers to be more temperate and move the process in an over-damped manner. I do not use any of those measures to define goodness of tuning.
Also in my preference, I want tuning to be a quick human directed process. I want it confidently done quickly. So I like to tune in response to set point changes, not automated with an optimizer, not from an extended regulatory period.
I do not use any of the standard tuning approaches (ZN Ultimate, lambda, controller synthesis, FOPDT model based), because they take too long, induce too large upsets, presume the controller coefficient settings are properly calibrated, and use the too aggressive QAD (quarter amplitude damped), IAE, ISE, ITAE sort of measures. I use a heuristic approach of increasing the gain until there are about 3 detectible MV movement directions in a set point change, then set the integral time to the half period of the oscillations. Then test and fine tune.
My favorite automated method is ATV (auto tune variation), which imposes a square wave on the controller output in MAN changing + to - when the set point is crossed, then uses ZN-Ultimate sort of rules to define controller coefficient values. This is relatively fast, and makes small perturbations. But is generally aggressive (in my preference), and presumes that the controller coefficients are properly calibrated.
The role of any controller is to reduce the error (including PID). Error may be positive or negative, but all the error needed to be accumulated. At that situation modulus ie absolute is calculated. Hence the error value alone is taking in to account. The objective of optimizing PID is to find the exact controller settings (it is different concept). The ultimate aim of PID controller is to reduce the error. the terminology is performance measure is used to find the process performance after designed and implemented PID controller.
it is not necessary to use IAE, ITAE to check the system performance. you can use any other methodology to check that. But PID controller optimization is entirely different one.
Hi. Take a look at the following paper, at Section 3.3:
Y. Karnavas, K. Dedousis, "Performance evaluation of evolutionary designed conventional AGC controllers for interconnected electric power system studies in a deregulated market environment", International Journal of Engineering, Science and Technology, vol. 2, no. 3, 2010, pp. 150-166.
https://www.google.gr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahUKEwiVjb6L4uDKAhWJCiwKHXEcBPkQFggsMAI&url=http%3A%2F%2Fwww.ijest-ng.com%2Fijest-ng-vol2-no3-pp150-166.pdf&usg=AFQjCNEtmsXKrtaakrtXlHhxHEg59q_06A&sig2=S0Soxxkq5zYeQjSJOP2dnw
I don’t think there is one answer can cover your question, because it really depends on the type of application. After reviewing the previous answers I would suggest to use the most well know fitness functions and compare their behaviour to see which is better fit to your application.
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