Equivalent control law design for Micro Motor

  The output torque of reaction flywheel is implemented by controlling the rotational speed of the BLDCM. The BLDCM adopts 3-phase full bridge topology with a buck converter. In order to achieve 4-quadrant operation for the BLDCM, the rotational speed is changed by regulating the duty ratio for the buck converter’s switching diodes VT7 and VT8. In the buck converter, the duty ratio belongs to control limited situation. Therefore, the design of the buck converter controller focuses on selection of the sliding surface and derivation of the sliding mode control law for u1, u2, u3, and u4 at different quadrants. The sliding surface is important to the control precision of the reaction flywheel. The sliding surface
must make sure that all the measurable states are included in the sliding surface, and the actual rotational speed can track the rotational speed command with first-order transition dynamic.

  By searching a dominating set, the SMC of reaction flywheel utilizes the states discrepancy of the buck converter to
reach the sliding surface as quickly as possible during the continuous conduction mode, which satisfies the asymptotic stability criteria with preferable dynamics performance.However, the control input is 0 or 1, which is confined strictly.
Therefore, most SMC designs concentrate on the selection of sliding surfaces. In this section, we deduce detailedly the analytical equivalent control laws at electromotion, energy consumption braking, and reverse connection braking stages by selecting different sliding surfaces, respectively.

  In general, we should choose sliding surfaces and appropriate coefficients to guarantee the sliding mode stability and
favorable dynamic performance based on the anticipant control object. According to the state averaging models, the
sliding surfaces are selected as s1(x), s2(x), and s3(x) at electromotion, energy consumption braking, and reverse connection braking stages, respectively.