Dans le paragraphe précédent nous avons donné un aperçu de la machine de coulée continue. Ainsi, le débit sortant du moule à tiges est fixé en fonction de la vitesse de la pompe.
Continuous casting in the steel industry
Introduction
This chapter describes the continuous casting process which is an important stage of the steel production chain, but unfortunately at the origin of many quality problems in the semi-finished product. This is the reason why our thesis work is dedicated to improving the steel flow control loop performances in the continuous casting machine to lower mold level variations responsible for various defects of the semi-finished product.
General aspects of steel
- History
- Composition
- Properties
- Applications
- Steel in figures
It causes damage to the steel, which sometimes likes to return to its natural state in the form of iron oxides. The purpose of this paragraph is to present some figures that indicate the level of the steel industry.
Steel manufacturing
- Ironmaking and steelmaking
- Casting
- Hot rolling and fabrication processes
Adjustment of the chemical composition, addition of alloys and control of carbon, phosphorus, nitrogen, hydrogen and oxygen contents that mainly determine the mechanical properties of the steel. After the steel is refined, it is then continuously cast into different shapes through the casting process shown in Fig.
Continuous casting machine
- Historical development
- Principle and technologies
- Types of products
- Defects from level variations
- Mould level disturbances
- Online measurements and control systems
- Emerging developments
The primary cooling of the steel thereby takes place in the form where approximately 10% of the heat must be extracted. Control of the flow in the mold is achieved by a nozzle and a stop rod or a sliding gate. Again, variations of the form plane appear to be the main cause responsible for these defects.
On the other hand, the turbulent nature of the flow in the meniscus region also increases the level fluctuations.
Instrumentation for mould level control
- Flow control devices
- Mould level sensor
The nozzles have two ports, each of which discharges the molten steel in opposite directions along the large faces of the mold. Furthermore, the control of the flow rate in the mold requires the knowledge of only the average liquid level which is directly measured by various methods including the NKK sensor, radioactive systems and electromagnetic methods. Radioactive sensors (Berthold) [71]: Radioactive sources, such as the Cobalt-60 60Co or the Cesium-137 137Cs, installed outside the mold, emit γ-rays that are attenuated as they pass through the mold level.
Thermocouples: The level difference near the small faces derives from the temperature profile on the copper plates of the mold.
Concluding remarks
Continuous casting process modeling
- Introduction
- Process modeling
- Distributed model (numerical fluid dynamics method)
- Centralized model
- Disturbances
- Introduction
- Clogging/unclogging cycle
- Bulging
- Standing waves
- Chapter summary
In the absence of any disturbance, the flow from the mold Q is determined by the pour speed v (set by the operator) and the mold section S. In the absence of blockage, the flow rate in the mold is determined by the position of the plug independent of the pour speed. Unlike the lock/unlock cycle, inflation occurs at the bottom of the wheel, in the secondary cooling section.
In the absence of bulge, the flow rate out of the mold is calculated from the casting rate.
Estimation and rejection of disturbances
Introduction
This is the main goal of the thesis that will be achieved by using the RMMAC architecture developed in Chapter 5. The first describes step by step the entire procedure that is classically followed to collect data that will be used to determine the unknown to derive values from the factory model. This result will be experimentally validated using the water model in the last part.
Using this experimental tool, we also demonstrate that the values of the gain and the delay occurring in the centralized model change when the casting parameters vary greatly.
Plant model identification
- Data acquisition protocol
- Offline algorithms
Using position autocorrelation as input and cross-correlation between position and flow in the mold as output. Then, the method of least squares can be applied considering this integral as the output and the position integral as the input. Let us denote the input and output of the system, once again, by u(t) and y(t) respectively.
The first is based on the least squares method and will be used in the sequel to identify the dynamics of the water model actuator.
Disturbances estimation
- Clogging/unclogging
- Bulging
- Global estimation
On the left side, the observer inputs are presented, which are mold level and stopper position. In this subsection, it is assumed that the mold level is affected only by the bump. In the first and second cases, the flow from the mold is disturbed by a unique sine wave.
The actual mold flow Qin(t) is then calculated from the difference of QinMAX(t) and dˆclog(t).
Bulging rejection
- Bulging effect compensation principle
- Simulation validation
For this reason, in the sequel we propose another approach based on the prediction of the state vector. To do this, ubulge(t) can be considered as the input to the actuator block, which generates the output. Another point to be tested was the influence of the prediction step on compensation performance.
The time shift between the bulge estimate and its prediction is equal to the time delay of the factory model.
Experiments
- Water model description
- Similarities with real situation
- Mould level control loop
- Water model identification
- Experimental validation of bulging effect cancellation
The gain (L⋅s-1⋅mm-1) and the delay(s) as a function of the flow rate with a clogged nozzle. 3.5.4.2.7 The gain and deceleration as a function of the air flow rate with a clogged nozzle. The gain (L⋅s-1⋅mm-1) and the delay(s) as a function of the air flow rate with a clogged nozzle.
3.5.4.2.8 Gain and delay as a function of sensor position in case of clogged nozzle.
Chapter summary and conclusions
Comparative analysis of non-adaptive control laws
Introduction (specifications)
In particular, its performance is compared with the PID control law introduced in Chapter 3 and considered here as a reference. This comparison is made according to several performance criteria, including the gain margin, the delay margin, the modulus margin, the maximum gain of the bulging rejection transfer function over the bulging frequency range, the maximum level amplitude generated by the plug, and many other factors. Bulging rejection through the transfer function between the flow rate out of the mold and the level.
To get the transfer function of the open loop, multiply TFmodel by the transfer function of the controller as shown in Fig.
State of the art (PID controller)
- Transfer function
- Performances
To get the transfer function of the open loop, one needs to multiply TFmodel by the transfer function of the controller, as shown in Figure 4.2, where ADC is an analog-to-digital converter that converts continuous signals into discrete signals and DAC is a digital- to digital converter. to analog converter that performs the reverse operation. For comparison purposes with other control laws, the Z-transform of the PID control law is converted into the RST form, which is a generic structure for digital control, as illustrated in Figure 4.3, where ADC is an analog-to-digital converter that uses continuous convert signals. to discrete and DAC is a digital-to-analog converter that performs the reverse operation. The stability and robustness of the PID controlled mold level system can be assessed using the diagrams of Fig.
The performance of the PID controller is summarized and compared with the specifications in Table 4.1.
Predictive control laws
- Predictive Functional Control PFC
- Generalized Predictive Control GPC
- Key notions
- Performances comparison
One of the distinguishing features of the PFC design is the structure of the control law. The results indicate that the second version of the PFC control law is comparable in terms of performance to the first. However, the calculation of the control law requires more time and resources due to the presence of the time delay.
Only the first value of the row is actually applied according to the descending horizon principle.
Smith predictor control
- Initial version
- Aström’s modified version
In [13], the authors propose an extension of the original Smith predictor to cancel the steady-state error. In this thesis, Aström's modified Smith predictor is used to reduce the influence of the bulge on the mold level. The next section proposes a design methodology, based on the H∞ framework, for shaping the frequency characteristics of the bulge rejection transfer function.
For the sake of simplicity, we decided to choose only the inflated rejection cycle of Aström's modified Smith predictor, as depicted in Fig.
Internal Model Control IMC
- Principle
- Tuning
To improve the robustness of the IMC structure, a low-pass filter is usually added to minimize the discrepancies between process and model behavior. The regulator C(s) is usually designed as the inverse of the process model in series with a low-pass filter of appropriate order. As a result, a step perturbation variation will generate a non-zero steady state error, which was proved earlier in the case of the original version of the Smith predictor.
In summary, we can say that the initial version of IMC control, which is classically used for stable processes but has serious limitations in others, usually performs poorly in the case of a mold level control problem.
Chapter summary
Robust adaptive control – RMMAC architecture
Introduction
As shown in Chapter 3, the gain G and delay n τn of the plant model vary with machine configuration. Primarily, the word "robust" refers to the controller's ability to meet stated performance specifications in the presence of process model inconsistency. We will also present various representative simulation results to evaluate the usefulness of RMMAC compared to the best non-adaptive control law.
Finally, this chapter concludes with some suggestions and some critical issues related to RMMAC design.
Multiple-model structures
- Multiple-Model Adaptive Estimation MMAE
- Multiple-Model Adaptive Control MMAC
In Kalman filter theory, the residual or novelty is the discrepancy between actual and predicted measurement values. If this is not the case, the identification subsystem should converge to the closest cluster model in the information metric sense. We will give a brief description of the most common structures including the robust multi-model adaptive control RMMAC, which will be described in detail in the fourth section of this chapter.
They are identified using the Baram Proximity Measure BPM to ensure the convergence of the posterior probabilities.
Structured singular value
- Uncertainty representations
- Stability and performance robustness
- Complex-µ synthesis
- Mixed-µ synthesis
Thus, we can evaluate the stability properties of the system by analyzing the frequency characteristics of µ. We now wish to consider the problem of robust performance, which is another feature of the closed-loop system. As in robust performance analysis, the problem can be transformed into a standard µ-analysis problem, as shown in Fig.
By introducing G , the mixed-µ synthesis takes advantage of the presence of real uncertainties in contrast to the complex-µ synthesis which approximates them to complex ones.
RMMAC architecture for a delay uncertainty
- RMMAC benefits
- Control part design
- Identification part design
- Performance evaluation
In [20], the idea is to calculate the upper and lower bounds of the performance parameter achieved using adaptive and non-adaptive control, respectively. The inflated rejection criterion Cperf of GNARC and FNARC as functions of delay are shown in Figs. Comparison of inflated rejection criterion Cperf for GNARC and FNARC under uncertain delay.
The complexity of the RMMAC architecture with respect to the number of models is however decided by the designer.
Chapter summary
Key figures
PIV measurements