Physical programming for computational control

A new approach to design optimization, physical programming, has recently been developed. Physical programming allows the designer to express design preferences explicitly for each design metric of interest, e.g., settling time or control effort, in a flexible and physically meaningful manner. This flexibility allows the designer to introduce a quantitative degree of desirability into the problem formulation by using the categories highly desirable, desirable, tolerable, undesirable, highly undesirable, and unacceptable and by defining numerical ranges that fit in these categories for each design metric. In this study we demonstrate the use of physical programming for controller synthesis by solving a benchmark control problem. We implement a physical-programming-based problem solution, where a preference function is developed for each design metric. These metrics include nominal and worst-case settling time, nominal and worst-case control effort, worst-case noise amplification, and robust stability. We design controllers of three different orders and compare these against published controller solutions of the same order for the benchmark problem. Physical programming control synthesis methods are used to design high-performing and robust controllers with remarkable ease, and the controllers compare quite favorably with published solutions.