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

选取中性系统和滞后系统作为集总参数部分和分布参数部分的特殊系统，研究了它们的LQ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来构造的，状态反馈由无限维Riccati方程的解来确定。该方程求解困难，状态反馈难以实现。在这项研究中，我们开发了一种方法来构造一个LQ调节器具有规定的指数稳定性使用无记忆反馈确定的LMTs的解决方案。这个解可以用数字计算机很容易地计算出来。无记忆反馈不需要存储内部变量和实时积分运算，易于实现。从这些意义上讲，拟议的监管机构易于设计和实施。在有限维情况下，LQ稳压器具有许多理想的特性。在本研究中，对上述中性系统调节器的特性进行了研究，发现它具有至少50%的增益减小公差和至少60度的相位裕度，并且对参数变化不敏感。此外，还证明了中性系统的保成本控制是可以构建的。

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.