The liquid crystal spatial light modulator (LCSLM) is an optical device that can realise non-mechanical beam scanning. However, the traditional integer-order model cannot adequately characterise the dynamic performance of LCSLM beam steering because of the viscoelasticity of liquid crystals. This paper uses the memory characteristics of fractional calculus to construct a fractional constitutive equation for liquid crystals. Combining this equation with the LCSLM beam steering principle, a fractional-order model of the beam steering system is established, and the Legendre wavelet integration operational matrix method is used to estimate the model parameters. In addition, we established a test platform for the dynamic characteristics of LCSLM beam steering system and verified the effectiveness of the established model through experiments. The fitting effects of the integer-order and fractional-order models are compared, and the influence of different model orders on the dynamic performance of beam steering is analysed. Experimental results show that the fractional-order model can accurately describe the dynamic process of beam steering, and this model can be applied to the study of LCSLM-based two-dimensional non-mechanical beam steering control strategies to achieve fast, accurate, and stable beam scanning.
This paper proposes a method of fractional order system (FOS) modelling with Legendre wavelet multi-resolution analysis. The proposed method expands the input and output signals of the system in the form of a Legendre wavelet, and constructs the Legendre wavelet integration operational matrix by use of a block-pulse function. To address the problem of the considerable volume of system identification data and system noise in practical engineering applications, the multi-resolution characteristics of the wavelet are combined to build a wavelet integration operational matrix from the multi-scale space. By continuously discarding the high-frequency information to reduce the length of the identification data, the identification speed of the system is accelerated and the influence of noise on the identification accuracy is reduced. In addition, the least squares method is used to find the optimal order in the identification interval and further accelerate the FOS modelling process. The proposed method rapidly identifies the FOS parameters with high accuracy, and is thus feasible for engineering applications. Its effectiveness is verified by simulation and photoelectric stabilized sighting platform experiment.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.