Abstract: Based on the study of the tridiagonal matrix and the block tridiagonal matrix calculation, a new algorithm of diagonal decoupling is proposed for a typical class of multi-variable coupled tridiagonal industrial systems. The key of the algorithm is to construct two compensation matrices, the former series compensation matrix L（s） and after series compensation matrix R（s）. Thus the multi-variable coupled system is transferred to a diagonal system and decoupling purposes are achieved. Considering zero components may exist on sub-diagonal, two construction algorithms of L（s） and R（s） are discussed. The simulation not only confirms the validity of the method, but obtains the L（s） and R（s） have the feature of many same components, which will greatly reduce the workload in industry.

Key words: tridiagonal, decoupling control, compensation matrix

摘要： 针对一类典型的多变量耦合三对角工业系统，在研究（块）三对角矩阵计算的基础上，提出了一种新的三对角解耦算法。该算法关键在于构造两补偿矩阵，即前串联补偿阵L（s）和后串联补偿阵R（s），从而使耦合三对角工业系统变为对角系统，实现解耦。考虑到三对角工业系统次对角线上可能存有零传递函数分量，在此讨论了两种L（s）和R（s）的构造算法。经仿真不仅证实了方法的有效性，而且得出了构造的L（s）和R（s）具有多分量相等的特点，这将大大减轻其在工业实现方面的工作量。

关键词: 三对角, 解耦控制, 补偿阵