Model reduction, sensor/actuator selection and control system redesign for large flexible structures

Jae Hoon Kim, Purdue University

Abstract

The purpose of this thesis is to investigate some practical methods for designing a control system for large flexible structures, and to pave a way to integrate all the established ingredients. The methods of interest comprise the three parts of this thesis; (1) model reduction in both the system and component level, (2) selection of actuators and sensors, and (3) optimal redesign of both the structure and the controller. For system model reduction, we consider the dynamics of finite bandwidth inputs. When the input dynamics are added to the plant to be reduced by the component cost analysis, the method is called Weighted Component Cost Analysis (WCCA). Analytical expressions of component costs will be derived for both continuous and discrete time cases when a mechanical system is described by modal data. For component model reduction, the component cost analysis and the canonical correlation analysis are combined into a new method, which reduces the model of each component in a large scale multibody system, while taking into account the interactions with the rest of the system. A specified number of actuators are selected from a given set of admissible actuators. The selected set of actuators is likely to use minimum control energy while the required output variance constraints are guaranteed to be satisfied. The actuator selection procedure is an iterative algorithm composed of an output variance constrained control and an input variance constrained control algorithm. In the covariance control theory, there are two conditions for a specified covariance to be assignable to the closed-loop system by some stabilizing controller. Sensors and actuators are selected so as to reduce the two assignability conditions to standard Lyapunov and Riccati equations. By solving the Lyapunov and Riccati equations, we may get an assignable closed-loop covariance. The minimum numbers of actuators and sensors needed to assign a covariance to the closed-loop system will be given. For a class of mechanical systems with a given initial controller, the best combination of structure redesign and active dynamic controller will be derived by minimizing active control power. The theory falls into two classes, characterized by two different side constraints in the optimization problem. The first problem requires matching the entire closed-loop system matrix before and after the redesign while the second requires only matching the state covariance matrix. The first problem is a standard convex quadratic program. Although the second problem is a general nonlinear program, we provide an efficient algorithm which makes use of the quadratic program and the freedom in the covariance control theory. Even though mass is not penalized in our optimization, the minimization of control power would cause mass to be reduced in the redesign.

Degree

Ph.D.

Advisors

Skelton, Purdue University.

Subject Area

Aerospace materials|Mechanical engineering

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