Stability Analysis of a Closed-loop Thermoforming Reheat Process Using an Affine Quadratic Stability Test

The process of manufacturing plastic parts by heating polymer sheets and forming them on a mold is called thermoforming. The heating stage of the thermoforming process is nonlinear and parameter-varying. The heater temperature set-points are usually determined by trial and error. A control design for this system can improve quality, reduce scrap and allow for temperature zoning. In this paper, the problem of stability analysis for a thermoforming process controlled by a static output feedback controller is addressed. An affine quadratic stability (AQS) test is chosen for this analysis. The AQS test requires a number of linear matrix inequalities (LMIs) to hold in order for the system to be stable. There is only one varying parameter in the thermoforming oven model, and as a result the number of LMIs to be computed is limited to five, which makes the AQS test practical. A parameter-dependent Lyapunov function is developed to prove the stability of the system.