We have designed a nonlinear H ₂ controller for permanent magnet stepper motors. The proposed method consists of a new torque modulation scheme, a passive nonlinear observer, and a nonlinear H ₂ controller. The nonlinear torque modulation is incorporated to generate desired torque. The H ₂ controller and a passive nonlinear observer are independently designed. The use of the passive nonlinear observer allows operation based on only angular position without requiring an additional sensor. The nonlinear H ₂ controller is developed to improve transient response in the position control. Tracking performance is evaluated in the view point of a linear system. The control gains are linearly scheduled by using interpolation parameters based on a linear matrix inequality approach. A stability of the passive nonlinear observer is proven by using a passivity theorem. The proposed method improves transient response in position tracking and allows evaluation of performance criteria. The performance of the proposed method was validated by means of experimental comparison with a previous method.

This paper proposes a robust nonlinear position control for permanent magnet (PM) stepper motors. We develop new single-input single-output (SISO) model that consists of position, velocity, and acceleration using a commutation scheme to lump a system function and a external disturbance into a disturbance. An augmented observer (AOB) is designed to estimate the position, velocity, acceleration, and disturbance. Because the disturbance refers to external disturbance, acceleration dynamics, and parameter uncertainties, it is difficult to accurately estimate disturbance without the high observer gain. It may result in the degradation of the position tracking performance. The nonlinear controller is then developed using backstepping to suppress the position tracking error using the input-to-state stability (ISS) property. The key innovation of the proposed method is the design of the nonlinear gain to suppress the position tracking error according to the disturbance estimation error. Thus the use of the high observer gain to accurately estimate the disturbance can be avoided. The proposed control algorithm was experimentally verified using the PM stepper motor control system and can be easily implemented in real-time using position measurements only.

In this paper, we propose a nonlinear position control using only position feedback to guarantee the tolerances for position tracking errors and yaw. In the proposed method, both mechanical and electrical dynamics are considered. The proposed method consists of the nonlinear position controller and nonlinear observer. The nonlinear position controller is designed by a backstepping procedure using the barrier Lyapunov function to satisfy the constraints of position error and yaw. The nonlinear observer is developed to estimate full state using only position feedback. The stability of the closed-loop system is proven using Lyapunov and input-to-state stabilities. Consequently, the proposed method satisfies the constraints of position error and yaw using only position feedback for the planar motor.

This paper presents gain scheduling H ₂ controller for speed control of permanent magnet synchronous motors (PMSMs) in the sense of linear parameter varying (LPV) synthesis. First, the nonlinear dynamics of a PMSM is transformed to a LPV system which has state-dependent varying parameters. The proposed method is composed of torque modulation, commutation scheme and H ₂ controller based on parameter-dependent system. The stability of closed-loop system is proven by Lyapunov theorem. The proposed method has not only fast velocity tracking performance but also reduced energy consumption. Finally, the effectiveness of the proposed method was validated with experimental results.