真三维显示系统的Roesser模型及其性能分析

Roesser Model of True 3D Display System and Its Performance Analysis

文章用多维系统控制理论的思想方法研究光学显示问题,为了对真三维显示系统进行建模,并分析其性能,针对体空间中每个体素点的分布情况,将三维位置坐标和一维时间坐标相结合,建立四维Givone-Roesser(GR)模型对真三维显示系统进行状态空间表示.阐述了真三维显示系统工作过程,对其进行实时性分析,简化了系统矩阵.介绍了定点量化模型,推导出该系统经量化后全局渐近稳定的充分必要条件.实验结果表明,一个尺寸为4*4*4和8*8*8的真三维显示系统中,体素点的状态向量会收敛到0,因此是渐近稳定的.文章提出的Roesser模型表示方法既能简化系统数学表达,又有利于系统分析与设计,便于微控制器的软件实现,实时性与稳定性分析可广泛应用到真三维显示系统分析与设计中,具有极高的应用价值.

This paper studies the optical display problem using the method of multidimensional system control theory.In order to model the true three-dimensional display system and analyze its performance,for the distribution of each voxel point in the body space,a three-dimensional position coordinate and a one-dimensional time coordinate are combined to establish a four-dimensional Roesser model for the state space representation of three-dimensional display system.The working process of the true three-dimensional display system is described,based on which,real-time analysis is performed,and the system matrix is simplified.The fixed-point quantization model is introduced,and the necessary and sufficient conditions for the globally asymptotically stable of the system are derived.Experimental results show that in a true three-dimensional display system of sizes 4*4*4 and 8*8*8,the state vector of the voxel point converges to zero.Therefore,it is asymptotically stable.The Roesser model representation method proposed in this paper not only simplifies the mathematical expression of the system,but also facilitates the system analysis and design,and facilitates the software implementation of the micro controller.The real-time and stability analysis can be widely applied to the analysis and design of true three-dimensional display systems.Therefore,it has a very high application value.