An application of global optimization methods to the parametric synthesis of generalized proportional-integral-derivative controller for the flight control problems

Mathematics. Physics. Mechanics


Panteleyev A. V.*, Letova T. А.**, Pomazueva E. A.***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



The solution of the PID-controller optimal parameter search problem for a given set of initial states and the set of input signals is obtained. An algorithm and software is suggested.

The novelty of the approach is to add the term with the second derivative of the error and to calculate the integral component not on the whole time interval, but only on an interval defined by a «memory» of the system as well as to apply the criterion of optimality of the controller parameters that characterize the average cumulative error with respect to the set of possible initial system states and the set of input signals. This problem is solved similar to the problem of unconditional minimization of the multivariable function J(Knp , KD1 , KD2 , KI) using the method of simulated annealing and further refining of the result with the help of adaptive random search method.

An example of solving the problem of finding optimal parameters of the PID controller for the longitudinal aircraft motion is given. A comparative analysis of the impact of the controller parameters on the quality of transition process and appropriate recommendations are made.

The suggested technology of solution of the parametric synthesis problem can be used in solving the engineering problems by constructing PID-controllers.


PID-controller, optimization criterion, initial states set, set of input signals, simulated annealing method


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