Corresponding author: Nekrasov I. V., Ph.D., Software Solution Consultant, GE Rus Ltd. (General Electric Company, GE Digital), Moscow, Russian Federation, e-mail: ivannekr@mail.ru

Received on November 03, 2015
Accepted on November 17, 2015

In this paper the authors analyze a variety of modern discrete control algorithms from the point of view of their computational complexity. The outcome of their analysis revealed high complexity of the major optimization procedures employed in the discrete algorithms of the optimal control. This uncovered disadvantage concerns implementation of the modern control algorithms in the digital real-time controllers of a limited computational power. The article suggests an approach how to adopt the time-consuming algorithms to the low productivity controllers. This approach is based on the idea to divide the computation process into two stages: the first stage includes preventive offline calculation of the optimal control values for a defined set of points in the system's state space; the second stage involves an online interpolation of the previously calculated control values for the current state of the system (only the second stage is realized in a real-time controller). As a result we observe reduction of the requirements to the controller processing power (assuming that the interpolation procedure is less time-consuming than the investigated optimization methods) accompanied with an insignificant decrease of the transient performance of the system. A practical analysis of the obtained results was conducted for the sample optimal control loop based on the numerical procedure of a random search. The random search procedure belongs to the top computation-consuming algorithms and in most cases is not available for implementation in the real-time controllers. Adaptation of this algorithm to the above-described two-steps computational process simplifies the on-line calculations down to the interpolation operation which can be performed by the modern digital controllers of a modest capacity. The findings of this paper were proved by the results of computer simulation.

Keywords: discrete systems, optimal control, control function, computational complexity, phase space, state space, system state, interpolation, tabular control, interpolative control

For citation:
Nekrasov I. V. Development of a Digital Control Algorithm Based on Interpolation of the Previously Calculated Optimal Solution, Mekhatronika, Avtomatizatsiya, Upravlenie, 2016, vol. 17, no. 3, pp. 158—165.
DOI: 10.17587/mau/17.158-165

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