Andreas Steinboeck

Dynamic Optimization of a Slab Reheating Furnace With Consistent Approximation of Control Variables

A dynamic optimization method is developed for temperature control of steel slabs in a continuous reheating furnace. The work was stimulated by the need for furnace control concepts that are computationally undemanding, robust, accurate, and capable of non-steady-state operating scenarios, where the properties and the temperature goals of slabs may vary significantly. The proposed hierarchical control structure is based on a continuous-time switched nonlinear model and uses the furnace zone temperatures as intermediate control variables. Consistent approximation is applied to obtain a parametric optimization problem that can be efficiently solved with the quasi-Newton method. Constraints on system states and control variables are considered by penalty terms in the cost function and saturation functions, respectively. The optimization method plans temperature trajectories for both the furnace and the slabs, which may be useful for open-loop control and feedforward branches of two-degrees-of-freedom control structures. The capabilities of the method are demonstrated in an example problem.

A fast simulation method for 1D heat conduction

Abstract: A flexible solution method for the initial-boundary value problem of the temperature field in a one-dimensional domain of a solid with significantly nonlinear material parameters and radiation boundary conditions is proposed. A transformation of the temperature values allows the isolation of the nonlinear material characteristics into a single coefficient of the heat conduction equation. The Galerkin method is utilized for spatial discretization of the problem and integration of the time domain is done by constraining the boundary heat fluxes to piecewise linear, discontinuous signals. The radiative heat exchange is computed with the help of the Stefan-Boltzmann law, such that the ambient temperatures serve as system inputs. The feasibility and accuracy of the proposed method are demonstrated by means of an example of heat treatment of a steel slab, where numerical results are compared to the finite difference method.

Automatic gauge control under laterally asymmetric rolling conditions combined with feedforward

The most common and well proven control strategy for thickness control in industrial rolling mills is the automatic gauge controller (AGC). However, it is still unclear how to use AGC for the control of asymmetries in lateral direction. How should the controller react to different thickness estimations at both sides of the mill. Such laterally asymmetric rolling conditions may originate from strip track-off, asymmetric friction in the mill stand, or a wedge-shaped entry profile of the strip thickness. In this paper, two different versions of AGC are compared and a feedforward approach is developed for lateral asymmetries of the entry thickness profile. Simulation studies based on a validated mill stand model demonstrate the benefit of combining AGC with a feedforward controller to compensate for asymmetries.

Automatic Gauge Control under Laterally Asymmetric Rolling Conditions Combined with Feedforward

The most common and well proven control strategy for thickness control in industrial rolling mills is the automatic gauge controller (AGC). However, it is still unclear how to use AGC for the control of asymmetries in lateral direction. How should the controller react to different thickness estimations at both sides of the mill? Such laterally asymmetric rolling conditions may originate from strip track-off, asymmetric friction in the mill stand, or a wedge-shaped entry profile of the strip thickness. In this paper, three control approaches are discussed. Two different setups of AGC are compared and a feedforward (FF) approach is developed for lateral asymmetries of the entry thickness profile. Simulation studies based on a validated mill stand model demonstrate the benefit of combining AGC with a feedforward controller to compensate for asymmetries.

Control of Strip Tension in a Rolling Mill Based on Loopers and Impedance Control

Abstract A mathematical model of a strip-looper system of a hot strip tandem rolling mill is developed using Hamiltons principle and the Galerkin weighted residual method. Several nonlinearities are considered and the effects of bending and dynamic forces on the accuracy of the model are studied. Based on the model, an estimator for the strip tension is proposed. Finally, an impedance controller for the strip tension and the looper position is designed. It can be used in the whole operating range of the system, which is also demonstrated in a simulation scenario.

Feedback Tracking Control of Continuous Reheating Furnaces

Abstract A Lyapunov-based MIMO state feedback controller is developed for slab temperatures in a continuous, fuel-fired reheating furnace. Following an early lumping approach, the computationally simple tracking controller is designed for a nonlinear, switched dynamic model that captures both conductive and radiative heat transfer. The controller modifies reference trajectories of furnace temperatures and is part of a cascade control scheme. Given some nonrestrictive conditions, exponential stability is ensured, even under non-steady state operating conditions. The capabilities of the controller are demonstrated by means of an example problem.

Modelling and experimental validation of the deflection of a leveller for hot heavy plates

In order to successfully automate levelling processes, in particular for heavy plates, the deflection of the leveller has to be compensated based on a deflection model. In this work, a detailed mathematical deflection model of a hot leveller with bending mechanism and its experimental validation are presented. The roll intermesh profiles are calculated based on the deflection of the work rolls that are elastically supported by support rolls, frames, posts and adjustment screws. The deflection model is suited to compensate the effect of deflection on the roll intermesh and the plate flatness as well as to assess the loads of critical parts, for example the support rolls. A new experimental design to measure the deflection of a leveller is presented and successfully applied for model validation. The work roll deflection is measured directly by means of displacement sensors that are inserted in cut-outs of test plates. These test plates are modelled as linear elastic stripes. For normal load levels, the relative accuracy (repeatability) of the roll intermesh prediction of the model is better than 0.08 mm.

An integrated thermal model of hot rolling

During the heavy plate rolling process, different production steps, i.e., roll passes, descaling passes, and air cooling periods, influence the temperature evolution of the plate. All these relevant aspects are covered by a one-dimensional thermal model proposed in this paper. Experiments were conducted in a rolling mill under realistic rolling conditions to parametrise and validate the model. Using pyrometer measurements, a simple model adaption strategy is developed, which can cope with uncertainties in the initial temperature profile. The model provides accurate predictions of the temperature evolution of the plate during the whole rolling process from the plate’s exit of the furnace to the last pass. Thus, it can be used for scheduling the production process. Based on the model, an observer can be designed.

Model-Based Condition Monitoring of an Electro-Hydraulic Valve

In many hydraulic systems, it is difficult for human operators to detect faults or to monitor the condition of valves. Based on dynamical models of an electro-hydraulic servo valve and a hydraulic positioning unit, we develop a parametric fault detection and condition monitoring system for the valve. Our approach exploits the nexus between the spool position, the geometric orifice area, the flow conditions at wearing control edges, and the velocity of the controlled cylinder. The effective orifice area of each control edge is estimated based on measurement data and described by aggregate wear parameters. Their development is monitored during the service life of the valve, which allows consistent tracking of the condition of the valve. The method is suitable for permanent in situ condition monitoring. Flow measurements are not required. Computer simulations and measurement results from an industrial plant demonstrate the feasibility of the method.

Energy-Efficient Control of Continuous Reheating Furnaces

Abstract Several control strategies for reducing the energy consumption of continuous reheating furnaces are reviewed. The energy flows and the efficiencies occurring in such furnaces are analyzed. Moreover, the nexus between energy savings and emission reduction is discussed. A case study of an industrial slab reheating furnace shows how the implementation of a nonlinear model predictive controller for the slab temperatures has reduced the primary energy consumption by 9.6%.