An Optimization approach to plant-controller co-design

Improving the behavior of a controlled mechanical device is traditionally accomplished by manipulating the parameters of the control system in isolation. If permitted, a better solution can be achieved by including the physical attributes of the mechanical structure as optimization variables. However, this expansion of the search space increases the importance of properly formulating the optimization problem to avoid undesirable behavior. Some modern (e.g. H∞) methods can be used to simultaneously optimize dynamic performance and robustness, but they require high levels of understanding and do not handle nonlinearities and arbitrary optimization constraints without additional augmentation. This work proposes and applies a method to add robustness to an optimized stabilizing controller and plant combination using constrained performance index optimization of chirp signal tracking. Using a chirp reference helps to improve the generality of the system response and ensures that resonant modes lay outside the useful range of input frequencies. Moreover, applying constraints on physical optimization parameters and their sensitivities helps to limit the solution space of a potentially high-dimensional problem while ensuring that the resultant system is both realizable and robust. An experimental platform for studying the process of toner ink fusion was modeled to demonstrate the effectiveness of the proposed method. For this system, combined optimization resulted in a performance index over 45% better than the result of optimizing the controller alone. Meanwhile, a worst-case robustness floor was maintained on several critical and uncertain system qualities