Design of a Model-Based Observer for Estimation of Steel Strip Tension in Continuous Galvanizing/Annealing Lines

Continuous Galvanizing Lines (CGL) and Continuous Annealing Lines (CAL) are productive manufacturing machines used by steel making companies for the manufacture of thin steel sheet products. In these lines, an annealing furnace is employed to continuously heat and cool a moving steel strip to impart certain mechanical properties to the strip. Although rotational speeds of driven rollers in the furnace are measured, tension measurement is spatially intermittent and located between any two heat transfer sections because of the inability to reliablymeasure tension within each heat transfer section due to harsh conditions.We consider a dynamicmodel of the strip transport behavior consisting of nonlinear governing equations for strip tension and speed. Since strip strain and elastic modulus are functions of the moving strip temperature distribution, the dynamic model contains temperature-dependent parameters. Based on this dynamic model, we design an adaptive nonlinear observer to estimate span tensions within each heating/cooling section. First, we design an observer for estimating strip tension in a single span assuming measurement of tension in adjacent spans using Lyapunov's second method. Then, we extend this to the multiple span case for each heating or cooling section by assuming measurement of tension in the entry and exit spans of the section. In both cases we show stable convergence of the tension observation error to zero and provide conditions on the observer gains. To illustrate the effectiveness of the proposed observer, we present numerical simulation results for a four span case with values for system parameters and reference of transport variables that mimic industrial CGL/CAL.