Relations among Open-loop Control Ability, Control Strategy Space and Closed-loop Performance for Linear Discrte-time Systems

TL;DR

This paper systematically studies the relationship between open-loop control ability, control strategy space, and closed-loop performance in linear discrete-time systems, emphasizing normalization and optimization for practical engineering applications.

Contribution

It introduces a normalized framework for comparing control abilities and proves theorems linking open-loop control, control strategy space, and closed-loop performance.

Findings

Normalization of variables aids in comparing control abilities.

Theorems establish the importance of optimizing control ability.

Simulation confirms the effectiveness of normalization and comparison methods.

Abstract

In this article, the definition on the control ability, and the relation between the open-loop control ability and the closed-loop performance are studied systematically for the linear dynamical systems. Firstly, to define and compare rationally the state control ability between the different controlled plants or one controlled plant with the different system parameters, the normalization of the input variables, the state variables, the system mdeols are discussed. With the help of the normalization, the state control ability with the time attribute can be difined under the unit input constraint (input amplitude limited). And then, two theorems on the relations among the open-loop control ability, the control strategy space (i.e., the solution space of the input variables for control problems), and the closed-loop performance with the time attribute are purposed and proven. Based on that, the conclusion that it is very necessary to optimize the control ability for the practical engineering problems can be got. Finally, the simulation experiments show us the normalizing the variables and system models, and comparing the contol ability between the different controlled palnts.