Synthesis and Properties of LQ Regulators for systems of Lumped-Parameter Part and Distributed-Parameter Part

选取中立型系统和时滞系统作为集中参数部分和分布参数部分的特殊系统，研究了它们的线性二次型调节器的合成和性质。一般情况下，时滞系统的LQ调节器是用状态反馈构造的，状态反馈由无穷维黎卡提方程的解来确定。该方程求解困难，状态反馈难以在实际对象中实现。在这项研究中，提出了一种利用LMT的解确定的无记忆反馈来构造具有指定指数稳定性的LQ调节器的方法。该解可以用数字计算机很容易地计算出来。无记忆反馈不需要记忆内变量和实时积分运算，易于实现。从这个意义上说，拟议的监管机构易于设计和实施。在有限维情形下，LQ调节器具有许多理想的性质。本研究对上述中性点系统调节器的性能进行了研究，发现其具有至少50%的增益抑制容限和至少60度的相位裕度，并且对参数变化不敏感。此外，还证明了中立型系统的保成本控制是可以构造的。

As particular classes of systems of a lumped-parameter part and a distributed-parameter part, neutral systems and retarded systems were chosen, and synthesis and properties of LQ regulators for them were investigated. Generally, LQ regulators for systems with time-delay was constructed with the state feedback, which was determined with a solution of an infinite dimensional Riccati equation. It was difficult to solve the equation and the state feedback was difficult to implement to the real plants. In this research, a method was developed to construct an LQ regulator with prescribed exponential stability using a memoryless feedback determined with a solution of LMTs. The solution could be calculated easily by a digital computer. The memoryless feedback did not require the memory of the internal variables and the real-time integral operation, so it was easy to implement. In these senses, the proposed regulator was easy to design and easy to implement. In the finite dimensional case, LQ regulators have many desirable properties. In this research, properties of above mentioned regulator of neutral systems were investigated, and some facts were found, such that, it had at least 50 percent of gain reduction tolerance and at least 60 degree of phase margin, and it had insensitivity against the parameter variation. Additionally, it was shown that the guaranteed cost control of neutral systems could be constructed.