A segmented model based internal model control scheme of electromagnetic micro-mirror systems

Abstract

In this paper, a segmented internal model control (SIMC) scheme based on the segmented combination model of the electromagnetic micro-mirror system (EMMS) is established. Notice that highly underdamped oscillation and rate-dependent hysteresis exist in the EMMS, so it is a complex nonlinear dynamic system. In order to control the deflection angle of the EMMS using the internal model control strategy, it is necessary to establish the inverse model of the EMMS. Therefore, a new model structure that is convenient for inversion is proposed in this paper to describe the characteristics of the EMMS with underdamped and rate-dependent hysteresis. In the proposed scheme, the model is a combination of a group of weighted sub-models based on the segmentation of the system's operating frequency. The weight of each segmented sub-model is not a constant but a new type of function which is also called the smoothing factor. Its function is to smooth the switching between sub-models, thereby reducing the dynamic error caused by model switching. In addition, the particle swarm optimization (PSO) algorithm is used to determine the optimal frequency segmentation points, which helps to obtain the optimal model for describing the system characteristics. Based on the proposed segmented combination model, the corresponding segmented internal model control with two-degree-of-freedom filters is proposed, and the corresponding filters in the internal model control are designed based on the small gain theorem. Finally, the proposed control strategy is applied to the control of the deflection angle of the electromagnetic micro-mirror to verify the proposed control method. Moreover, the non-smooth internal model control strategy is also used for comparison in the experiments.