Feedforward Optimal Control with Constraints for a Cylindrical Thermoelectric System Actuated by a Peltier Element

Gavrikov, A.; Kostin, G.

Авторы: Gavrikov Alexander, Kostin Georgy
Сборник: Lecture Notes in Mechanical Engineering
Серия: Advanced Problem in Mechanics III
Год издания: 2023
Место издания: Springer
Первая страница: 95
Последняя страница: 107
DOI: 10.1007/978-3-031-37246-9_8
Аннотация: In this work, we consider a cylindrical structure consisting of two heat conducting cylinders with a thermoelectric converter (Peltier element) between them. A control-oriented nonlinear model, which was previously proposed and verified by authors, is used to design an optimal control law that allows us to achieve a steady-state distribution of the temperature in one of the cylinders in much less time than the characteristic time of transient processes. In the first step, the boundary value problem is exactly linearized about temperature distribution by means of feedback linearization. Although the resulting system is nonlinear with respect to a control function, it is possible to construct a finite-dimensional approximation based on analytical solution of corresponding eigenproblems for a constant control signal. After that, an optimal control problem over finite time horizon with constraints is solved numerically using this eigenfunction decomposition. We consider a cost functional that represents a weighted sum of temperature deviation from a steady-state distribution, energy losses, and a penalty for violating the constraints. The finite time interval is split into several parts and on each subinterval the control signal is taken constant. The optimal piecewise constant feedforward control is found partially numerically by applying the gradient descent method and partially analytically by using the eigenfunction expansion. The resulting control is taken as a sum of feedback linearization and feedforward signals. We present numerical results and compare the proposed control law with the optimal feedforward control strategy without constraints.
Добавил в систему: Костин Георгий Викторович

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Feedforward Optimal Control with Constraints for a Cylindrical Thermoelectric System Actuated by a Peltier Elementстатья

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