Patent GB-1143384-A (GB)
Title: Improvements in or relating to the control of furnaces
Inventor: KODZ WITOLD TADEUSZ
IPC: G05D23/19
Filed: 1965-06-15
Abstract: 1,143,384. Steel furnace control computer. BRITISH IRON & STEEL RESEARCH ASSOCIATION. 15 June, 1966 [15 June, 1965], No. 25242/65. Heading G4G. Theory.-In apparatus for controlling a continuous slab reheat furnace preceding a steel rolling mill, and divided into preheat, tonnage, and soaking zones; it is shown by mathematical analogy that:- where U 1 , U 2 , U 3  are control parameters for preheat, tonnage, and soaking zones. X 1 , X 2  X 3  are slab exit temperatures from the respective zones. T 1 , T 2 , T 3  are minimum zone temperatures determined empirically. Y 1 , Y 2  Y 3  are the respective lengths of the zones. α 1 , α 2 , α 3  are the zonal time constants given by respectively. Z 1 , Z 2 , Z 3  are the mean slab thicknesses within each zone. # is the material density. C 1 , C 2 , C 3  are the specific heats of the zones. a 1 , a 2 , a 3  are the respective zonal heat transfer coefficients derived empirically. V is the slab velocity of movement. M is the fuel consumption rate in heat units. W 1 , W 2 , W 3  are respective zonal tonnage rates. # is furnace efficiency derived empirically and varying with tonnage rates. For most economical operation, equation (4) is minimized using partial derivatives of U 1 , U 2  and U 3  integrated with respect to time within maximum and minimum constants set by measured values of X 1  and X 2 . Operation.-Preheat zone 51 (Fig. 3) receives slabs at zero temperature and heats them to a temperature represented by signal X 1  from pyrometer 54 at exit to tonnage zone 52, which heats the slabs to temperature represented by a signal X 2  from pyrometer 55 at exit to soaking zone 53. The roof temperatures of the preheat, tonage, and soaking zones are preset by servomechanisms controlled by signals U 1 , U 2 , U 3 , and signals V representing slab speed; W 1 , W 2 , W 3  representing tonnage rates and Z 1 , Z 2 , Z 3  representing mean slab thickness for the several zones are conventionally desired. Digital arithmetic unit 56 has a preset control giving a predetermined value to the minimum temperature of the slab leaving zone 51 and yields an output analogue signal representing:- combined in operational amplifier 57, with preheat temperature control signal U 1  to give Operational amplifier 58 receiving signal U 1  and a constant signal U 1  max. representing maximum allowable roof temperature in preheat zone gives a signal representing allowable increase of preheat roof temperature, which is combined in inversion amplifier 59 with the output of 57 and the result is applied to integrating amplifier 60 for combination with the analogue output of digital arithmetic unit 61 receiving digitally the signals W, Z, V, to yield analogue output signal representing so that a signal U 1  is developed after integration representing desired preheat roof temperature. Signal X 1  representing slab exit temperature of zone 51 is applied to digital arithmetic unit 62 also receiving signals V and Z 2  to give analogue signal representing fed to operational amplifier 63 for combination with tonnage zone temperature control signal U 2  and output of digital arithmetic unit 64 receiving signals V and Z 2  with a preset control determining minimum temperatures T 2  of slabs leaving tonnage zone 52. This yields a signal representing and amplifier 63 yields a signal representing A further operational amplifier 65 receives signal U 2  and a constant U 2  max. representing the maximum allowable roof temperature of the tonnage zone, and the difference is combined with the output of 63 and inverted at 66 for application to integrating amplifier 67 for combination with the output of digital arithmetic unit 68 fed with input signals W 2 , Z 2 , V to yield analogue signal representing and the integrating amplifier 67 yields signal U 2  representing the required tonnage zone roof temperature. Signal X 2  representing slab exit temperature of tonnage zone 52 is fed to digital arithmetic unit 69 also receiving signals V and Z 3  to yield analogue output signal representing which is combined in operational amplifier 70 with analogue signal from digital arithmetic unit 71 receiving signals V and Z 3 , and a preset control signal determining the minimum temperature T 3  of slabs leaving the furnace; such signal representing Amplifier 70 also receives signal U 3  representing soaking zone temperature to give output analogue signal representing Operational amplifier 72 receives soaking zone roof temperatures control signal U 3  and a constant signal U 3  max. representing maximum allowable roof temperature, to develop an output signal which represents the difference between actual and allowable roof temperatures. This is combined in amplifier 73 with the signal from amplifier 70 and is fed to integrating operational amplifier 74 where it is combined with the output of digital arithmetic unit 75 receiving digital inputs representing W 3 , Z 3 , V and deriving the analogue signal giving an output analogue signal which represents required soaking zone roof temperature U 3 . Three partial differential equations relating fuel consumption to respective furnace zone temperature for minimum fuel consumption are thus solved within the constants of predetermined minimum slab exit temperatures and maximum allowable roof temperatures. Alternative operation.-Slab velocity is adjustable to maintain the variables U 1 , U 2 , U 3  at a steady level to minimise fuel consumption per ton throughout, and more conveniently the pushing rate or interval between slab movements is controllable, by a computer programme (Fig. 4) in which each programme is initiated by completion of a pushing cycle (step 80) after which the programme advances to step 81 at which the current variables of slab thickness in the furnace zones Z 1 , Z 2 , mean slab width W, slab length l, and pushing rate r in seconds since last push are derived from the hot mill control computer. At step 82 the corresponding variables Z 1 <SP>1</SP>, Z 2 <SP>1</SP>, w<SP>1</SP>, l<SP>1</SP>, r<SP>1</SP> for the preceding programme cycle are derived from the programme store, and the two sets of values are compared. For no change the programme is terminated at step 84 but for a change of the variables the stored values are updated to the current values (step 85). At step 86 the pushing rate r 1  is compared with the optimum pushing rate and if correct the furnace zone temperatures U 1 <SP>1</SP>, U 2 <SP>1</SP> are set at step 87 to optimum values U 1  opt. and U 2  opt. If the pushing rate r<SP>1</SP> is not optimum, the values of U 1 , U 2  for the actual pushing rate are derived from a tabular store and at step 89 the zone temperatures are set to the new values U 1 <SP>1</SP> and U 2 <SP>1</SP> obtained. On completion of either preceding step the new value of r opt. is determined for the values of U 1 <SP>1</SP>, U 2 <SP>1</SP> from a tabular store at step 90, and the furnace temperature controllers are adjusted to the new required temperature values, which are printed out. The new predicted optimum values U 1  opt., U 2  opt., r opt. are inserted in the appropriate stores to replace the current values at step 92 and the new value of r opt. is displayed to the pusher operator (step 93). No programme cycle will be restarted (step 94) until the pusher operator reacts to the instruction (step 80), and if the next push is initiated after an interval r differing from r opt. the cycle will proceed according to step 88. Analog system for modified computation of Fig. 4.-In Figs. 5, 6 the signals U 1 , U 2 , U 3  controlling the temperatures of the preheat, tonnage and soaking zones 51, 52, 53 are inverted at 59, 65, 73 and applied to operational amplifiers 57, 63, 70, 100 for combination with signals derived from digital arithmetic units 56, 64, 71, 99. Unit 56 develops analog signal representing from input signals r, W, Z 1 , where A is a reference temperature for the preheat zone and B is a factor representing the rate of change of zone temperature with rate of zonal advance of material. Unit 64 develops analog signal representing from input signals r, W, Z 2  where C is a first reference temperature for the tonnage zone and D is a factor representing the rate of change of zone temperature with rate of zonal advance of material. ' Unit 99 develops analog signal representing from input signals r 1 , W 1 , Z 2  where G is a second reference temperature for the tonnage zone and H is a factor representing the rate of change of zone temperature with rate of zonal advance of material. Unit 71 develops analog signal representing where E is a reference temperature for the soaking zone and F is a factor representing the rate of change of zonal temperature with rate of zonal advance of material. The signals -U 1 , U 2 , -U 3  are also applied to operational amplifiers 58, 64, 72 for continuation with fixed signals U 1  max., U 2  max., U 3  max. representing the maximum allowable zonal furnace roof temperatures, and the resultant signals are combined with those from operational amplifiers 57, 63, 70, 100 to amplifiers 60, 67, 74 also receiving the partial differential coefficient signals from arithmetic units 61, 68, 75 to develop the zonal temperature control signals U 1 , U 2 , U 3 . The arithmetic units 61, 68, 75 receive signals representing the distance K through which material is moved at average intervals of r seconds, the width L z  and mean thickness Z z  of material, the specific heat C z , the mean temperature X z  of material leaving the zone and the density #, a differential coefficient representing rate of variation of heat H L  dissipated in the furnace chamber with change of zone temperature U z  and a heat utilization coefficient # characteristic of the furnace; and produce analogue signals representing for a furnace zone. The partial differential signal for preheat zone from arithmetic unit 61 is comb