A nonlinear optimal control approach for PM Linear Synchronous Motors

Permanent Magnet Linear Synchronous Motors are of wide use in industry in applications where actuation through rotational motors and a gears-based transmission system can be costly and prone to failures. In this article, a nonlinear optimal (H-infinity) control method is proposed for Permanent Magnet Linear Synchronous Motors (PMLSM). The dynamic model of the Permanent Magnet Linear Synchronous Motor undergoes approximate linearization around a temporary operating point (equilibrium) which is recomputed at each iteration of the control method. The linearization procedure is based on first-order Taylor-series expansion and on the computation of the Jacobian matrices of the motor's model. For the approximately linearized model of the motor an H-infinity feedback controller is designed. This controller stands for the solution of the motor's optimal control problem under model uncertainty and external disturbances. The computation of the controller's feedback gain requires the solution of an algebraic Riccati equation, which is performed again at each time-step of the control algorithm. The stability properties of the control scheme are proven trough Lyapunov analysis. First, it is confirmed that the controller satisfies the H-infinity tracking performance criterion which ascertains its robustness. Moreover, it is proven that the control loop is globally asymptotically stable. Finally, to implement sensorless control of the motor the H-infinity Kalman Filter is used as a robust state estimator.