Optimization of controlled motion systems using robustness response surfaces

Abstract

The absolute and relative stability are critical aspects of designing Controlled Motion Systems (CMS). The maximum attainable CMS performance depends highly on the design of the structural part and the actuator and sensor configuration, as mechanical vibrations can endanger stability. This thesis presents a method for designing CMS's using optimal design. The set of vibration modes that violates the stability criterion might change during the optimization process, which is undesired from an optimization point of view. An aspect of this method is to ensure stability by imposing a constraint regarding the stability of each vibration mode individually. The stability constraint proposed in this thesis aids in well-performing optimization that converges to feasible designs. This thesis presents a new way of modeling the open-loop response. It uses a standard PID controller often used in industry, and the structural model is a function of the poles and zeros of the system instead of the conventional modal parameters. Only three parameters are required to evaluate the robustness of a single mode. A robustness response surface was obtained via simulations and modeled using NURBS. The robustness response surface is used to evaluate the proposed robustness constraint. The surface model is suited for gradient-based optimization methods. The proposed method was tested on a relatively simple model of a motion system. The optimizer converged to unconventional solutions that outperformed designs obtained using engineering principles.