Methods for numerical optimization of regulators has a number of advantages as compared with the analytical methods. The use of modern software, together with well-known and newest methods of forming of the optimization criteria in the form of cost functions provides a set of methods, successfully tested on a number of tasks. These methods, in contrast to analytical ones, allow effectively calculation of robust regulators for objects even in the case of the simultaneous presence in these of non-linear elements, units of lag, discrete elements (such as sampling-and-hold analog storage) and other complicating singularities.

One of the most important tasks of the automatics and robotics is the design of the feedback regulators for the controlling and stabilization systems. This task contends on the two parts: the design of the regulator structure and the numerical calculation or optimization of its parameters. The paper discusses the both tasks and proposes the adequate decisions for the most difficult examples.

This paper proposes a new structure and substantiates the choice of a technique for controller design using fractional integration and fractional differentiation. The method of fractional integration is based on extrapolation using a series of integrating and differentiating links, the time constant of which changes symmetrically from one step to another. The new controller structure does not contain the three traditional links (proportional, integrating, and differentiating) but contains six links, three of which are incomplete integration, incomplete differentiation, and redundant (for example, one and a half) integration. The proposed technique consists of modeling a controller with the indicated six paths and using the numerical optimization method to calculate the coefficients of each such path. Alternative controllers are known PID controllers and PI^λD^µ controllers. Both of these species contain only three tracts. The proposed structure has never been used before, and publications with examples of calculation of such structures were not found in the literature. The effectiveness of the proposed method is confirmed by modeling and examples.

The paper deals with the problem of the design of the regulator for the object having delay link. With all this the parameters of the mathematical model of the object are changing inside some intervals or known with low accuracy, so that it is only known the intervals to which these parameters belong. The states task is supposed to resolve with the helps of the numerical optimization. The result of it is the values of the regulator coefficient, whose structure has been given by the designer in the form of PID-regulator. Searching of the parameter is known as parametric design. The simulation program allows making sure of validity of the result and robust feature of the system which is the product of the regulator design. The optimization is made based on the minimization of the quality criterion in the form of cost function. The robustness has been achieved due to the simultaneous optimization of the several systems with the same regulators and with the different object parameters. The proposed method is illustrated by an example of the design of robust control system with interval-given parameter and with the delay link, which is taken from the close task paper, these results are compared, the advantages of the proposed method has been demonstrated.