Nonlinear Optimal Control for VSI-fed Three-phase Asynchronous Motors

The use of voltage-source inverter-fed induction (asynchronous) motors is widely met in industry (for instance for actuation in tasks that require high torque and power as well as in transportation systems (for the traction of trains and electric vehicles). In this chapter a nonlinear optimal control method is proposed for voltage source inverter-fed asynchronous (induction) motors (VSI-fed IM). Approximate linearization is performed on the nonlinear dynamic model of VSI-fed induction motors around a temporary operating point which is recomputed at each iteration of the control method. This time-varying operating point is determined by the present value of the VSI-fed IM state vector and by the last sampled value of the system’s control inputs vector. The linearization process is based on Taylor series expansion and on the computation of the system’s Jacobian matrices. Next, an $$H_{\infty }$$ feedback controller is designed for the approximately linearized model of the VSI-fed IM. This control approach provides a solution for the nonlinear optimal control problem of the VSI-fed IM in the case of model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method. Lyapunov analysis is used to prove the global asymptotic stability properties of the control scheme. Moreover, to apply state estimation-based control for this system the $$H_{\infty }$$ Kalman Filter is used as a state observer.