.. , Existing and proposed control design of the considered furnace, p.56

M. Overview-on-distributed, , p.62

M. Furnace-zone, , p.68

M. Distributed and .. , 71 5.3.2 Observer design for output feedback, p.72

M. Non-cooperative-distributed, , p.78

M. Serial-cooperative-distributed, , p.82

M. Centralized and B. , , p.84

.. Simulation-results, 86 5.4.2 Control of walking beam reheating furnace . . . . . . . . . . . . . . . . . . . . . . . . 89

.. Industrial-results, , p.91

C. , , p.97

, 6 Slab temperature control 99

.. Problem, 100 6.1.1 Qualitative control objectives and constraints, p.100

. Quantitative and C. Objectives, 103 6.1.2.1 Constraint of zone temperature set-points, p.105

.. , 107 6.2.2 Continuous-time problem, MPC strategy applied to slab temperature control, p.113

.. Discrete-time-problem, , p.114

P. and .. , , p.116

.. Optimization, 120 6.3.1 Simulation-based optimization 121 6.3.2 Direct search methods Pattern search methods, p.127

A. and .. , , p.130

S. Adopted-optimization, , p.132

.. Numerical, , p.135

.. Hot-rolling-of-steel-slabs, , p.14

.. , Hierarchical cascade structure of control system, p.16

.. , Lateral view of a walking beam slab reheating furnace

.. , Top view of a walking-beam slab reheating furnace, p.20

.. , Example of path-time diagram of slabs

.. , Heating curve of a slab with respect to its position, p.22

.. , Instrumented bloom with thermal box before charging into the furnace, p.23

.. , Energy flows in a walking-beam reheating furnace, p.24

.. , Simplified geometry of walking beam reheating furnace, p.31

P. Geometry and .. Of-slab-i, , p.31

.. , Temperature profile of 2n + 1 points inside a slab, p.34

R. Heat-exchange-between-slabs and E. , , p.36

.. , Assumption of local radiation for a slab i residing in zone j, p.37

.. , Overheating of slab due to stops; waste of energy, p.41

.. , Grid-point discretization for one-dimensional heat conduction problem, p.42

.. , Variation of temperature with time for three different schemes, p.44

.. , Radiation exchange between different surfaces, p.44

, Averaged slab temperature from validation experiment of the dynamical furnace model, p.47

.. , Heating trajectory of slab inside reheating furnace, p.57

.. , Hierarchical cascaded structure of reheating furnace, p.57

.. Averaging-technique-of-current-furnace-control, , p.58

.. Mpc-structure-for-walking-beam-reheating-furnace, , p.59

.. Model-predictive-control-principles, , p.61

M. Structure-of-decentralized, , p.62

M. Structure-of-centralized, , p.63

M. Structure-of-distributed, , p.64

.. , Controllable zones of walking-beam reheating furnace, p.65

.. Imposed-space-between-slabs, , p.65

.. Step-signal-of-zone-preheating, , p.66

.. , Step signal of zone heating 1, p.66

.. Input-coupling-of-furnace-zones, , p.68

.. Output-coupling-of-furnace-zones, , p.69

.. Validation, , p.70

O. Structure, , p.72

A. , , p.76

M. Communication-between and .. , , p.77

.. Diagram, , p.83

M. Results-of-non-cooperative-distributed,

M. Results-of-cooperative-distributed, , p.88

. Output and M. Signals-under-centralized, , p.88

I. Number, , p.89

.. Performance, , p.89

.. Input-power-of-furnace-zones, , p.90

Z. and .. , , p.91

, Transient behavior of zone temperature controlled by PID controllers and distributed MPC, p.92

, Overshoot effect of temperature controlled by distributed MPC and PID controllers, p.93

. Histogram and .. Slab-temperature-errors, , p.93

.. , Variations of temperature set-points calculated by level 2, p.94

.. Utilization-of-automatic-mode, , p.94

O. Power-demands, , p.95

C. Specific, , p.96

.. , 31 histogram of specific energy consumption, p.96

.. Oxygen-ratio-inside-the-furnace, , p.97

.. Feedback-in-hierarchical-structure, , p.99

.. , Cascaded closed-loop of the furnace control system with MPC strategy, p.100

, Variation of desired final slab temperatures in an operation of the considered furnace, p.102

S. Variation and L. Width,

.. Constraints-on-slab-temperature-trajectory, , p.105

.. , Constraints on final slab temperature profile, p.106

.. Constraints-on-inhomogeneity-of-slab-temperature, , p.107

, Distinction between S in (? ) and S 1 (? ) for furnace operation during prediction horizon ?, ? + ?t P 108

.. , MPC applied for slab temperature control: a) at time ? , b) at time ? + ?? s, p.110

, Heating of consecutive slabs that have big difference on desired final temperature, p.116

, Variation of weighting coefficient on final slab temperature error according to slab position, p.118

.. , Different stages of heating process, p.118

, Variation of weighting coefficient on temperature gradient according to slab position, p.118

.. , Weighting coefficients according to slab position and time, p.119

.. Architecture-of-the-furnace-control-system, , p.121

.. , Simulation-based calculation of the existing level 2 of the furnace, p.122

.. , Example of search pattern in ? 2 with a given step length parameter ? k, p.124

3. , , p.127

.. , Reflection of worst vertex on the centroid of the opposite face in ? 2 and ? 3, p.128

.. , ) fail to replace best vertex x k and the edges adjacent to x k is reduced to continue the algorithm, Reflections, issue.1 2 5, p.128

, Reflection, expansion, and contraction moves of Nedlder-Mead simplex method, p.129

.. , Reducing of the simplex when reflection, expansion, contraction moves fail to replace the best vertex x k, p.129

.. , Rosenbock's method in problem of dimension 2, p.131

P. , , p.131

.. , Simulation-based optimization of the MPC strategy, p.132

.. , Software-based simulation environment, p.135

S. Thickness, , p.136

L. Width, , p.136

.. , Residence time of slabs 1 to 399, p.137

.. , Residence time of slabs 400 to 783, p.138

.. , Position-time diagram of slabs 179 to 189, p.138

.. , Position-time diagram of slabs 506 to 606, p.139

.. , Desired final temperature of slabs 1 to 399, p.140

.. , Desired final temperature of slabs 400 to 783, p.140

S. Averaged-final, , p.141

C. Power-of-the-furnace and .. , , p.142

.. , Temperature set-point of soaking zone calculated by MPC controller compared to that of the existing controller, p.143

.. , Temperature set-point of zone heating 2 calculated by MPC controller compared to that of the existing controller, p.143

.. , Temperature set-point of zone heating 1 calculated by MPC controller compared to that of the existing controller, p.144

.. , Temperature set-point of zone preheating calculated by MPC controller compared to that of the existing controller, p.144

.. , Final temperature of slabs 1 to 202, p.145

.. , Final temperature of slabs 203 to 404, p.146

.. , Final temperature of slabs 405 to 606, p.147

.. , Final temperature of slabs 607 to 783, p.148

, Histogram of error of final slab temperature: MPC controller; Existing controller, p.148

.. Final-temperature-gradient-of-slabs, , p.149

.. , Histogram of final slab temperature gradients, p.149

=. Temperature-trajectory-of-slab-j and .. , , p.150

9. , , p.151

=. Temperature-trajectory-of-slab-j and .. , , p.151

.. , , p.152

=. Temperature-trajectory-of-slab-j and .. , , p.152

4. , , p.153

=. Temperature-trajectory-of-slab-j and .. , , p.154

6. , , p.154

=. Temperature-trajectory-of-slab-j and .. , , p.155

6. , , p.155

=. Temperature-trajectory-of-slab-j and .. , , p.156

6. , , p.156

.. , Average temperature trajectory of 900 slabs, p.157

.. , Average temperature gradient of 900 slabs, p.157

.. Fuel-consumption-of-controllable-zones, , p.158

F. , Total fuel consumption of the, p.158

.. Predefined-scheduling-table-of-slabs, , p.163

.. , Simulation diagram of scheduling optimization, p.170

M. Implementation-diagram-of and .. , , p.171

.. , Discharging time interval of events j = 1 to j = 450, p.171

.. , Discharging time interval of events j = 451 to j = 900, p.172

.. , Average final temperature of slabs j = 1 to j = 450, p.172

.. , Average final temperature of slabs j = 451 to j = 900, p.173

. Histogram and .. Slab-temperature-error, , p.173

.. Final-slab-temperature-gradient, , p.174

.. Histogram-of-final-temperature-gradient, , p.174

.. , Furnace throughput rate measured at discharging events j = 1 to j = 450, p.175

.. , Furnace throughput rate measured at discharging events j = 451 to j = 923, p.175

.. , Average temperature of slab number 570, p.176

.. , Average temperature gradient of slab number 570, p.177

O. Reheating-time, , p.177

P. Continuous, , p.179

.. , Temperature trajectory of the strip through different zones, p.180

P. Continuous-galvanizing, , p.181

P. Temperature-control-of-furnace-with and .. , , p.182

.. Hot-blast-stoves-with-blast-furnace, , p.183

.. , Internal structure of hot blast stoves, p.184

.. , blast air, waste gas) and the solid (refractory layers) at different levels of a hot blast stove, p.185

S. Hot, , p.185

?. and .. , 1 Trial points of coordinate search in ? 2 for a given step length 196 B.2 All possible trial steps for coordinate search in ? 2 ;? : f (x i k ) ? f (x k )

.. , List of Tables 3.1 System of equations for radiative heat transfer inside reheating furnace, p.45

M. Classification-of-distributed and .. , , p.91

-. , 104 6.2 Constraints of slab temperature profile, Constraints on zone temperature set, p.107

. Correspondence and D. Continuous, , p.115

, Difference between steady-state model used in furnace observer and set-point optimizer, p.122

. Average and .. Power-of-the-furnace, , p.142

.. Average-zone-temperature-set-points, , p.145

.. , Deviation of final slab temperature from the desired value, p.147

.. Inhomogeneity, , p.158

, Final slab temperature and temperature gradient with MPC strategy and the existing controller, p.174

. Production-rate and .. Energy-consumption-indicators, , p.176

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