Stability and robust design using a sector nonlinearity approach for nonlinear manufacturing systems

• It is from design view to achieve stability and robustness under uncertainty.
• A sector-nonlinearity approach is developed to model a nonlinear system.
• A design is developed to ensure stability of a nonlinear system under uncertainty.
• Proposed robust design makes system eigenvalues insensitive to parameter variation.
• A two-loop optimization method is developed for this nonlinear design problem.

Robust design is crucial for the satisfactory performance of manufacturing systems. Robust solutions are difficult to obtain when a system is strongly nonlinear or has large parameter variations. In this work, a novel design approach is proposed to ensure stability and robustness of a nonlinear system under large parameter variations. A sector nonlinearity method is first employed to model a nonlinear system. A stability design is then developed to ensure the stability of this nonlinear system under parameter variations. The influence of parameter variations on the eigenvalues of the system is minimized to maintain the system robustness. The proposed design involves a complex nonlinear optimization that is difficult to solve mathematically. A particle swarm optimization algorithm will be used to formulate a two-loop optimization that can obtain an optimal design solution. A simulation study on the practical system is conducted to demonstrate the effectiveness of the proposed method.