State-space modelling approach for control and observer design in property-controlled reverse flow forming

Flexible, metal forming processes such as flow forming are exposed to many disturbances that affect geometry and material properties during forming and reduce the reproducibility of those processes. In this context, closed-loop property control is a feasible solution for process improvement. To include advanced controllers and observers in closed-loop property control concepts, mathematical models in terms of state-space models are advantageous. However, especially in case of flow forming these models are not spread due to the complex process kinematics, nonlinearity of the process and spatial dimensions of the workpiece. This makes mathematic state-space modelling challenging. Thus, a model has to be newly developed. This paper therefore presents a novel discrete-time state-space model for flow forming. The model treats the workpiece geometry as discrete and represents the complex process kinematics in the form of a local sampling of the roller trajectory. It can be shown that the model is valid and that the resulting system dynamics especially results the from the displacement between roller and sensor which is considered in the model. Thus, the result of this paper is a valid state-space model that can be prospectively used in a model-based state observer for flow forming. This state observer could later extent a closed-loop property control to enable more complex property structures than before.