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On a design of a robust D-stabilizing feedback controller for the matrix second-order systems with interval matrix uncertainty

机译：具有区间矩阵不确定性的矩阵二阶系统鲁棒D稳定反馈控制器的设计

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摘要

It is known that some of the mechanical and/or electrical dynamics can be written in the form called 'Matrix 2nd-order system' or '2nd-order system' in short. On the other hand, pole-assignment is a commonly accepted technique in designing a performance guaranteeing regulator for the ordinal state space first order system. Recently, control design problems combining these two, that is, synthesis of a state feedback controller for the 2nd-order systems achieving closed loop pole-assignment while preserving its special form of dynamics, have been investigated. The proposed regulator is numerically robust,' in the sense that a little perturbation on system matrices would not cause a large shift on the closed loop poles. But this does not suffice as a solution of the robust controller design problem such that matrices contained in the 2nd-order systems are the interval matrices with their lower and upper bounds given. In this paper, robust pole-assignment of the 2nd-order system with interval matrix uncertainties to a circular region in the LHP is discussed. Based on an evaluation of the perturbation in the coefficient space, we have applied the D-stable set expression in the coefficient space that we have obtained recently to determine the feedback gains. It will be shown that the design will finally be reduced to the problem of finding a solution of at most 16 simultaneous inequalities. Also, a numerical example will be given to illustrate the routine of the proposed design procedure.
机译：众所周知，一些机械和/或电气动力学可以简写为“矩阵二阶系统”或“二阶系统”的形式编写。另一方面，极点分配是在设计有序状态空间一阶系统的性能保证调节器时普遍接受的技术。最近，研究了将两者结合的控制设计问题，即研究了用于二阶系统的状态反馈控制器的合成，该控制器在保持其特殊形式的动力学的同时实现了闭环极点分配。所提出的调节器在数值上是稳健的，在某种意义上，对系统矩阵的微扰不会在闭环极点上引起大的偏移。但是，这不足以解决鲁棒的控制器设计问题，例如，包含在二阶系统中的矩阵是区间矩阵，具有上下限。本文讨论了具有区间矩阵不确定性的二阶系统到LHP中圆形区域的鲁棒极点分配。基于对系数空间中摄动的评估，我们在最近获得的系数空间中应用了D稳定集表达式来确定反馈增益。结果表明，设计最终将简化为寻找最多16个同时不等式的解决方案的问题。同样，将给出一个数值示例来说明所提出的设计程序的例程。

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