PUBLISHED PAPERS #05.04
| Samir Guliyev, Gasim Gasimov. Controlling the Rod Heating Process Using Feedback on Special Classes of Controls |
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| Abstract. The study proposes a numerical solution to feedback control problems for distributed parameter objects using the rod heating example. The approach involves observing the object’s phase state at specific locations given inaccurate information on the object’s initial state. The heat source’s power serves as a control parameter in the considered problem. The notion of zonality is introduced, and a special class of zonal controls for the control parameter’s values is defined. Zonality in this context means the constancy of the control parameter’s values in each subset of the phase space determined by the set of values of the object’s state measured at the observation points. Unlike the well-known approaches to synthesizing current control values, in which they depend on the value of the object’s state, in the proposed approach, the values of the control parameters change only when the phase state transitions from one set of states to another. To determine the zonal controls, the original feedback control problem is reduced to a parametric optimal control problem that aims to optimize a finite-dimensional vector. Optimality conditions for the zonal control’s values, which include formulas for the gradient of the objective functional with respect to the optimizable parameters, are derived. |
| Keywords: zonal feedback control; distributed parameters object; heat conduction process; parabolic equation; gradient of functional |
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| DOI: https://doi.org/10.30546/MaCoSEP2025.1054 |