In the magnetically suspended momentum wheel, the orientation of the rotor shaft can be actively changed to generate 2-D torques. An adaptive back-stepping sliding mode control (SMC) method is proposed to precisely control the deflection angles. First, the magnetic torques generated by the magnetic bearings are analyzed. According to the magnetic torques, coupled torques exist and influence the tracking control of the deflection angles. It is difficult to model the coupled torque disturbances because their relationship with translations, deflection angles, currents, and other parameters is complex. By analyzing the dynamics and the magnetic torques, the tracking error dynamic is modeled as a system with unmodeled disturbances and parameter uncertainties. A back-stepping integral sliding mode controller whose sliding surface considers the integrals of the angle error and the tracking error is designed for this system. The switching gain should be relatively large to ensure system stability. This will induce severe chattering, which hinders the precision of the deflection angle. A fuzzy algorithm whose inputs include the sliding value and deflection angle is designed to adaptively tune the switching gain of the sliding mode method. According to the simulation and experimental results, the proposed method improves tracking performances and reduces chattering.

Image-based target tracking methods rely on continuous image acquisition and post-processing, which will result in low tracking efficiency. To realize real-time tracking of fast moving objects, we propose an image-free target tracking scheme based on the discrete cosine transform and single-pixel detection. Our method avoids calculating all the phase values, so the number of samples can be greatly reduced. Furthermore, complementary modulation is applied to reduce the measurement noise, and background subtraction is applied to enhance the contrast. The results of simulations and experiments demonstrate that the proposed scheme can accomplish the tracking task in a complex background with a sampling ratio of less than 0.59% of the Nyquist-Shannon criterion, thereby significantly reducing the measurement time. The tracking speed can reach 208 fps at a spatial resolution of 128 × 128 pixels with a tracking error of no more than one pixel. This technique provides a new idea for real-time tracking of fast-moving targets.