Over the last few decades, mechatronic design has revolutionized the design of motion systems. Its concurrent engineering design approach, which integrates mechanical, electrical and various other aspects of a product, is now widely accepted in industry and often based on the following two-step approach:

First, a multi-physics model is created, that is, a model in which the mechanical, electrical, hydraulic, and other physical aspects of the considered mechatronic system are incorporated.
Second, numerical optimization techniques are used to find a better design. That is, the designer defines an objective (cost, weight, energy consumption, etc) and constraints (elastic stresses below some upper bound, lifetime greater than some upper bound, etc), and then pushes a button that starts up some numerical optimization routine. This routine automatically adjusts the available design parameters until a solution is found that minimizes or maximizes the objective and satisfies the constraints.

This two-step approach was, until a few years ago, deemed too complicated and therefore only suited for the academic research environment. Nowadays, however, it has been brought within reach of the industrial designer through the advent of new and highly user-friendly software products that, at first sight, reduce multi-physics modeling to appropriately connecting basic building blocs and numerical optimization (or, as it is also called, mathematical programming) to a push on the button.

Although this workflow has resulted in significantly better industrial products and shorter design cycles, its major shortcoming is that it cannot guarantee that the ’best’ or ’globally optimal’ product be found. That is, the software often yields a reasonably good design, but one never knows if better designs might exist and how much better these designs are than the one actually obtained. Obviously, a company able to quickly find globally optimal designs has a major competitive advantage with respect to its competitors.

The question thus arises if it is possible to quickly find globally optimal designs at all. The answer is yes. If one can formulate a mechatronic design problem such that it is equivalent to a convex optimization problem, it is guaranteed that the global optimum be found fast and reliably using dedicated algorithms.

Formulating design problems as convex optimization problems, however, requires that the current two-step approach be integrated to a single-step approach. That is, the system modeling and simulation as well as the choice of optimization objective and constraints needs to be done such that a convex optimization problem results. This design approach is termed mechatronic programming. While mechatronic design integrates the various modeling and simulation aspects of a product, mechatronic programming considers modeling, simulation and optimization as concurrent aspects of the same challenge: obtaining convex optimization problems. Hence its name, which merges mechatronic design with mathematical programming.

Mechatronic programming