The paper considers the problem of an optimal system controlling the motion of a plant consisting of two masses connected by a non-linear spring. Examples of such plants include motorcars with trailers or dumb barges pulled by ships. The irregular motion of elements in such plants negatively impacts energy consumption. Additionally, for safety reasons, the speed of motion must be limited.As a quality criterion, we use the energy of the error signals. Until now, the two-mass problem (benchmark problem) has been considered only for linear cases.
The novelty of our work is the generalization of this problem (using the describing function method) for non-linear cases. H∞ control theory (robust control) is adapted for the first time to handle non-linear plants. The high effectiveness of the optimal controller has been confirmed by computer simulation in MATLAB.
OPTIMAL CONTROL OF PLANTS CONSISTING OF TWO MASSES CONNECTED BY A NON-LINEAR SPRING
The paper considers a control system that optimizes the motion of a plant consisting of two elements with significant masses connected by a non-linear spring.
Such plants include, for example, cars with trailers or water barges pulled by ships. Irregularities in the motion of such plant elements cause large energy losses in the drive and, due to safety concerns, necessitate speed limitations, which increases transport duration. The quality criterion is energy consumption defined by the error signal. To find the optimal controller, harmonic linearization of the system was performed, and for the linearized equation, optimization methods based on Banach space H∞ and H (robust control) methods were applied. The high effectiveness of the controller determined by the described method was confirmed by computer simulation. An additional effect of the applied control is ensuring system stability. (…)
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Source: Logistyka Magazine