What is it about?
The paper discusses an optimal control problem for the energy optimal control for an induction motor drive. The optimal control problem with linear state dynamics for the rotor speed and non-quadratic objective function given by a weighted sum of various quantities. The optimal control problem is solved using the Hamilton-Jacobi-Bellman equation.
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Why is it important?
An original technique leading to determine the optimal rotor flux is put forward. The method uses a reduced model of the IM in a turning (d,q) reference frame. The proposed optimum-energy method is based on the optimal control theory focus on minimizing a cost function subjected dynamic stress of the flux and of the rotation speed. The task is to find an optimal rotor flux that provides a minimum energy consumption along a given load torque and velocity. The main contrinutions are as follows: The functional considered in the Optimal Control Problem (OCP) is a weighting sum of stored energy, copper-losses and mechanical power and subjected to the above mentioned dynamic equation which is novelty. The OCP leads to the Hamilton- Jacobi- Bellman equation. The resolution of this equation was our main contribution in this paper and it presented at the first time!. The resolution utilized sub-optimal conditions and leading to an analytical solution noted: Φ ̂_r^opt (t) In order to adapt the proposed sub-optimal solution Φ ̂_r^opt (t) to the real optimal Φ_r^opt (t) when the IM is operating in torque transients, Φ ̂_r^opt (t) approaches the transient-regime solution in the inifinite horizon by using the lemma of Grönwall when is applied to the Duhamel theorem. Dealing with the time-varying expression of Φ ̂_r^opt (t) we succeed to perform our theoretical contribution. Simulation results and experimental results ar conducted for abrupt input speed profile and a random desired torque evolving smoothly at least its first derivative is non zero.
Perspectives
The minimum-energy solution presented in an analytical form and is dedicated to optimizing a transient regime characterized by a random load torque, but it evolves smoothly or by a step input of the motor speed. The field oriented control using this analytical solution has imposed itself by a remarkable reduction in the IM energy consumption. The perspective is to use a polynomial or exponential function to approche to the load torque behaviour usually registered in closed-cycle industrial applications for IM drives.
Riadh Abdelati
University of Monastir
Read the Original
This page is a summary of: Loss minimization of induction machines during torque transients, Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering, June 2019, SAGE Publications,
DOI: 10.1177/0959651819856966.
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