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

本研究提出了一种设计二自由度（性能和稳定裕度）多变量反馈控制系统的方法。二次代价函数用于测量跟踪误差、饱和度和对小植物扰动的灵敏度等性能属性。在适当选择的稳定裕度矩阵上用l无穷范数测量稳定裕度。将研究性能和稳定裕度之间的权衡机制。这种机制不同于最近在文献中描述的机制，并显示出更强大的前景。此外，还研究了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是解耦（每个命令输入只控制一个输出）。这里提出的结构很适合解耦问题，因为它允许解耦问题与实现理想稳定裕度的问题分离。然而，存在解耦约束，这可能会降低可实现的性能。这项研究的一部分将用于开发一种设计程序，以最大限度地减少这种性能下降。

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.