Position control of a permanent magnet stepper motor by MISO backstepping in semi-strict feedback form

In this paper, we present a recursive application of multiple-input single-output (MISO) backstepping for the position tracking of permanent magnet stepper motors (PMSMs) in the form of semi-strict feedback. This backstepping method does not use direct-quadrature (DQ) transformation but it turns out that the MISO backstepping is equivalent to field oriented control (FOC). In the dynamics of a PMSM, the quadrature current can be regarded as the input to the mechanical dynamics of PMSM for realization of FOC. In the proposed controller, however, virtual velocity is designed to track the desired position while the desired current vector is designed to track the virtual velocity. Since the proposed controller requires full state information, assuming position and currents measurement available, a new reduced order observer with a state augmentation for load torque is developed. The global exponentially of tracking error is guaranteed by using a composite Lyapunov function. In addition, we show that the estimator and controller gains can be independently tuned due to principle of separation. Simulation results validate the effectiveness of the proposed method.