Combined embodiment design and control optimization: Effects of cross -disciplinary coupling.

Abstract

This dissertation examines systems, such as spacecraft, robots and motors, that are engineering systems that involve a physical object and its desired dynamic response. Separate optimization of the physical object, its embodiment, and the response, its control, can determine the system, however separate optimizations do not allow for explorations of the tradeoffs between improving the embodiment or improving the control. System optimization is the natural solution: Create a model of the system and attempt to optimize the entire system at once. The concept is simple; however, the practice of system optimization has many challenges: collecting the component models into a single system model, modeling the coupling between the components properly, optimizing the large scale system that results, and interpreting the optimal solutions. In the literature these systems are often optimized using ad hoc strategies. The traditional strategy of optimizing the design then optimizing the control is called a Single Pass Strategy. Since the Single Pass Strategy requires that one set of coupling quantities be fixed, an improvement is to modify those parameters via an Iterative Strategy, repetitively designing and controlling until the coupling quantities agree. A Decoupled System Strategy optimizes the entire design and control system while fixing one set of coupling parameters. An All At Once (AAO) Strategy optimizes the system, making all of the coupling quantities into variables. A Bilevel Strategy optimizes the system assuming that the optimal system will have optimal controller gains. These strategies are examined and compared throughout this dissertation. Since optimization is a decision making process, we would like to make the correct decisions. The issue is whether those strategies are capable of finding the true optimum of the system. Along the way to answering that question, a consistent terminology for embodiment design and control systems is created. Coupling between the two disciplines is identified as the key to the ability of the solution strategy to find an a true optimum. Then, we find that, though the ad hoc strategies work for their particular system models, they do not find the true optimum for the general combined systems. The AAO Strategy does find the true optimum, but it can be difficult to solve. A new strategy, termed the Partition Strategy, is developed that decomposes the AAO Strategy into separate embodiment design and control problems with a master problem that links the two subproblems, making the problem easier to solve. The Partition Strategy finds the true system optimum of embodiment design and control systems. The comparison of the solutions strategies in this dissertation is made using three models. First, a direct current motor is modeled as an embodiment design and control system. The embodiment design determines the rotor dimensions and winding characteristics; control design determines the input voltage or current (depending on the type of motor) needed to control the rotational response of the rotor. Second, an elementary example, a mathematical construct, is used to explore issues that were found in the solution of the motor example. Finally, a general model of the combined optimal embodiment design and control problem is created.