Numerical Estimation of Bidirectional Plant-Control Design Coupling in Control Co-Design

Abstract Control co-design has been shown to be an effective tool for optimizing engineering systems. One characteristic feature of these problems is the presence of design coupling between the plant and controller, and this coupling is one of the key deciding factors when selecting a solution strategy for the design optimization problem. In this paper, we provide a method to numerically estimate design coupling strength, accounting for bidirectional coupling (plant and control mutually affect each other), and for estimating design coupling when the control design variables are time-varying trajectories. Design coupling strength is one of several factors that can affect what design optimization problem formulation decisions will best meet the needs of the broader engineering design effort. Some guidelines are provided here for how to use design coupling information to help support problem formulation decisions, including identifying the most impactful design variables and design variable relationships. The coupling strength estimation and its use for problem formulation is illustrated with a spacecraft control co-design (CCD) example. In the example, the plant (physical system) and attitude control design of a satellite are optimized, and design coupling strength information is used to identify the most appropriate plant design variable choice out of a small pool of candidates.