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For deriving the tuning formula, the genetic algorithm based design method is applied to design PID controllers for a variety of processes.
The relationship between the controller parameters and the parameters that characterize the process dynamics are determined and the tuning formula is then derived.
Since the PID tuning formula of Ziegler-Nichols step test, perhaps the best known, the process control literature is still showing lots of PID control schemes to improve the closed-loop stability.
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The provided simple tuning formulae have physically meaningful parameters.
The tuning formulae are simple enough and the method guarantees satisfaction of performance specifications.
The tuning formulas for PI/PID controllers are analytically derived and are generally applicable to stable and integrating processes.
Furthermore, the tuning formulas contain a single adjustable parameter that enables a designer to address the tradeoff between performance and robustness.
PID controllers are widely used in industries and so many tuning rules have been proposed over the past 50 years that users are often lost in the jungle of tuning formulas.
From the reported Pareto optimal front of the GP-based optimal rule extraction technique, a trade-off can be made between the complexity of the tuning formulae and the control performance.
One algorithm determines the optimal time delay in the reference model by solving an optimization problem, whereas the other algorithm avoids the nonlinear optimization by using a simple approximation for the time delay term, enabling derivation of analytical PID tuning formulas.
But by using scanning electron microscopes and computers, GreatPoint's experts were able to rapidly assess the effectiveness of different catalysts and fine-tune the formula.
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