Research Initiation: Analysis and Computer-Aided Design of Multi-rate Digital Control Systems

本项目的目标是为多速率数字控制系统构建一种全面的计算机辅助设计方法，该方法在以下五点中的一个或多个方面与现有方案不同：1)有效性-如果存在满足所需规范的控制器，将确保找到满足要求的控制器。2)自然性--使用智能控制规范语言编译器，设计者可以直接参考传递函数、信号峰值、噪声功率、阶跃响应等。3)灵活性--设计者可以表达对信号峰值、噪声功率、传递函数的频域行为、脉冲响应的时域行为、建立时间、过冲等的约束或优化。4)通用性--它将严格地处理异步系统。5)易操纵性-利用可用的计算能力，设计大型系统将成为可能。所设计的控制器将具有合理的实施顺序。这将通过将普通的单速率“Q-设计”扩展到多速率控制系统，开发和编码用于将异步系统与同步系统近似的分析、严格的方法以及用于多速率控制器的模型降阶的方法来实现。多速率数字控制系统在工业和军事上的广泛应用，以及当前设计方法的不足，意味着本研究应该在实际控制界产生重大影响。

The objective of this project is to construct a comprehensive computer-aided design methodology for multi-rate digital control systems that differs from existing schemes in one or more of five points: 1) Effectiveness - It will be guaranteed to find a controller that meets the desired specifications if one exists. 2) Naturalness - The use of an intelligent control specification language compiler will allow designers to refer directly to transfer functions, signal peaks, noises powers, step responses, etc. 3) Flexibility - The designer will be allowed to express constraints or optimize on signal peaks, noise powers, frequency domain behavior of transfer functions, time domain behavior of pulse responses, settling times, overshoots, and more. 4) Generality - It will handle asynchronous systems, rigorously. 5) Tractability - Design of large systems will be possible with available computing power. Designed controllers will be of reasonable order for implementation. This will be accomplished by extending ordinary, single-rate "Q-Design" to multi-rate control systems, developing and coding analytical, rigorous methods for approximating asynchronous systems with synchronous ones and methods for model reduction of multi-rate controllers. The widespread industrial and military use of multi-rate digital control systems and the shortcomings of current design methodologies means this research should have significant impact in the practicing control community.