Discrete-Time Modeling and Control of Induction Motors by Means of Variational Integrators and Sliding Modes—Part I: Mathematical Modeling

This paper deals with the discrete-time modeling of induction motors (IMs) by means of a variational integrator. A Lagrangian is first formulated for the IM, where the corresponding discrete Lagrangian is derived based on the one-point quadrature rule integration method (in this case, the variational integrator is known as symplectic Euler). Then, a discrete action principle is applied, which guarantees the optimum path in a discrete-time setting. The forcing and dissipation are added by using the discrete Lagrange d´Alembert principle. Finally, discrete-time update rules are obtained for IMs. Then, theoretic properties such as relative degree and steady state are studied for the continuous-time symplectic Euler and explicit Euler models. Simulations are carried out for different sampling periods, where results are compared with a discrete-time model obtained with the classical explicit Euler method. It is put in evidence that the symplectic Euler model approximates better the IM dynamics than the model obtained with the classical Euler method.