On the Design of Two-Degree-of-Freedom Multivariable Feedback Control Systems

本研究提出一种设计二自由度（性能和稳定裕度）多变量反馈控制系统的方法。一个二次成本功能是用来衡量这样的性能属性，如跟踪误差，饱和度，和小植物扰动的敏感性。在适当选择的稳定裕度矩阵上用L-无穷范数来度量稳定裕度。将研究性能和稳定裕度之间的折衷机制。这一机制不同于文献中最近描述的机制，并显示出更强大的前景。此外，将研究稳定裕度矩阵的选择。多变量控制系统设计中的另一个重要考虑因素是解耦（每个命令输入仅控制一个输出）。这里提出的结构是非常适合的解耦问题，因为它允许分离的问题，实现理想的稳定裕度的解耦。然而，存在可能使可实现的性能恶化的解耦约束。这项研究的一部分将致力于开发一种设计程序，最大限度地减少这种性能恶化。

This research proposes a methodology for designing two-degree-of-freedom (performance and stability margin) multivariable feedback control systems. A quadratic cost functional is used to measure such performance attributes as tracking error, saturation, and sensitivity to small plant perturbations. Stability margin is measured with an L-infinity norm on an appropriately chosen stability margin matrix. A mechanism for tradeoff between performance and stability margin will be investigated. This mechanism is different from the one recently described in the literature and shows promise of being more powerful. In addition, the choice of the stability margin matrix will be investigated. Another important consideration in the design of multivariable control systems is decoupling (each command input controlling only one output). The structure proposed here is well suited to the decoupling problem since it permits the separation of the problem of decoupling from the problem of realizing a desirable stability margin. There is, however, a decoupling constraint which can deteriorate achievable performance. A portion of this research will be directed towards developing a design procedure which minimizes this performance deterioration.