Certification of linear closed-loop controllers using the ν-gap metric and the generalized stability margin

In almost all mechatronic devices, safety is a fundamental requirement. Unpredicted system behavior resultant from control instability may potentially damage objects or even harm human users. To certify that the system will remain stable under predefined conditions is not only desirable but mandatory for systems like jet engines and wearable robots (e.g., robotic prosthesis and exoskeleton robots). The certification of control algorithms is already a standard procedure in some engineering fields, such as aviation. In robotics, however, a certification procedure is not yet traditionally incorporated in the control design. To fill this gap is an essential step towards making robots, especially those that closely interact with human beings, largely available on the market and endorsed by the public in general. This paper uses the ν -gap metric and the generalized stability margin to assess the stability of a closed-loop linear system, accounting for differences between plants. A novel iterative certification procedure based on these two techniques is proposed, combined with optimization techniques to reduce conservatism. The procedure is demonstrated on a real 1-DoF hydraulically actuated platform.