Maximal input limits for independent SISO control in modal space under consideration of actuator constraints

Modal decoupling is a common approach in engineering to analyze the dynamic behavior of mechanical systems and simplify the controller design. By bringing the system dynamics into diagonal form, one obtains SISO systems for which independent feedback strategies can be implemented. Furthermore, there exist control laws that utilize the available control inputs up to their limits, e.g. optimization-based controllers. While these limits can be applied easily in original space, a still open question is which bounds are feasible in modal space, as one property of the (linear) decoupling transformation is that the actuator constraints become coupled. In this paper, we address the problem of finding the largest possible input limits in modal space that allow independent SISO control and meet the real actuator saturations at the same time. We identify how the controller structure influences the search for the modal constraints and find the limits via optimization. The methods are developed for the general n-DOF case and applied to 2-, 3-, and 7-DOF examples in simulation.