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6 Modeling and control of mill discharge pumps in the Aitik copper mine Tomas Vikner June 19, Background 2.1 Process overview After drilling and blasting in the open-pit, large blocks of ore are transported on haul trucks to a crusher, where mechanical force and pressure breaks down the material into copper ore. Copper ore is transported to the concentrator on a conveyor, and this is where valuable minerals are extracted. The concentrator consists partly of a grinding hall and a flotation area. As ore enters the concentrator, grinding is the first stage. Here ore particles are reduced in size by a combination of impact, chipping and abrasion. This is done in large rotating steel cylinders, or grinding mills, which are the main components of the mill circuits. One of the primary mills in the Aitik concentrator can be seen in Figure 1. Figure 1 One of the primary mills (gearless mill drive) in the Aitik grinding hall. Courtesy of ABB and Boliden. During the grinding process, the ore particles are also mixed with water. The mixture of water and the well pulverized ore particles forms a thick and abrasive fluid inside the grinding mills, referred to as slurry. The next stage in concentration is flotation, where water repellant chemicals are added to modify the floatability of minerals in the slurry. This makes it possible to separate the bouyant minerals in various stages, by using a connected line of flotation tanks. Situated at the end of the mill circuit are the discharge pumps. These are centrifugal slurry pumps that operate to transport slurry from mill discharge to the flotation area. 2.2 Mill circuit In the grinding hall there are two identical mill circuits, and each mill circuit has two grinding mills, known as the primary mill and the secondary mill. Ore that enters the concentrator goes 2

7 r s m r t r t q in q out m r t r s q in q out

8 m r = r s + r t m 3 q in q out

9 3 L m P m n m L r L m L e P r P e n r w, V P m L q out q in P r n r q out q out L r L e = L r L m P r P e = P r P m

10 n r P w V n q out L q in 3 3

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13 p ρ v2 + gz = constant, p ρ v g z p/ρ gz 1 2 v2 P f P f = ρgqh a, ρ 3 g 2 q 3 h a z 1 z 2 h a = z 2 z 1 + kq 2, k z 2 z 1 p = ρg(z 2 z 1 ),

14 kq 2 η = P f P s, P s h a q P f = ρgq(z 2 z 1 + kq 2 ), P f = ρgq( z + kq 2 ). z = z 2 z 1 P P = aq z + bq 3, ρ g a b u y y = f(u), τ dy(t) + y(t) = Ku(t), dt K τ 1 τs + 1, s = jw j

15 A(L) dl dt = q in q out, A(L) L q in q out y u u y = K ( 1 e t τ ) u, K τ d(t) r(t) e(t) u(t) y(t) y m (t) n(t) u(t) y m (t) y(t) y m (t) = y(t) + n(t),

16 n(t) r(t) y(t) e(t) = r(t) y m (t), e(t) d(t) y(t) r(t) y r u(t) = K p e(t) + K i t 0 e(t i )dt i + K d de(t) dt + i.c., K p K i K d t i i.c. ( u(t) = K p e(t) + 1 ) t de(t) e(t i )dt i + T d + i.c., T i dt 0 T i T d K p T i T d ( u(t) = K p e(t) + 1 ) t e(t i )dt i + i.c., T i 0

17 u(t) = K p e(t), T i K p T i T d C p y p C s y s M p M s y p y s y m,p y m,s d s d p r p e p r s e s u s y s C p C s P s P p y p y m,s y m,p M s M p y p

18 d s P s P p

19 q out = q in, q out n P q out ρ L

20 m w a q in = (1 + r s ) m ρ o + w a, ρ o r s r s ρ = (1 + r s)m + w a q in, r s

21 3 z

22 P = (a bl)q out + cq 3 out, z = a bl L a b c P q out L 3 P = 10 + aq out + bq 3 out, P = 10 + aq out + bq 2 out.

23 P q out P = 10 + a(n 75),

24 P n ( ) 10 P = n. 75 ( ) 1 (10 ) P = + a(n 75), τs + 1 ( ) ( ) 1 10 P = n, τs τ q out = 1 t q s (P ), (t t m ) t m

25 q s (P ) q out t v = (t t m ) τ t v τ t v 3 n r L m P m r n

26 P sim τ τ τ = P sim P m q out t v t v = L corr L m

27 t v t v L r L e P r P e n r L P P q out q in q in P n r q out q in q out

28 K p T i K p T i L m L m K p T i K p T i K p = 0.14 T i = 2 dnr dt dn r dnr dt = 10 max dt = 5 min dn r dt

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30 L r L e P r P e n r w, V L m P m L r L e n r w, V L m

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34 λ K ipg T dead t r t o λ = t o t r. K ipg = dy dt u, y dy dt u K p T i T i = 2λ + T dead, K p = 2λ + T dead K ipg (λ + T dead ) 2. K ipg T dead K p T i

35 K p T i K p, s T i, s K p, a T i, a K p, m T i, m K p T i K p, a K p, m K p, s K p, m K p, a T i, a T i, m T i, s T i, m T i, a L L K p T i K p T i K p T i

36 K p, a T i, a K p, m T i, m K p, s T i, s α 1 α 2 α 3 α 4 α K p, c T i, c β 1 β 2 β 3 β 4 β

37 L r L e u LC + P r L m A p L m P r P r u LC A p A p,100 K p, a T i, a K p, m T i, m K p, s T i, s A p,100 [%] ζ 2 ζ 3 ζ 4 3 ζ ζ 1 3

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42 3 P r α 1 α 1 P T i K p, a T i, a K p, m T i, m K p, s T i, s γ 1 γ 2 γ 3 γ 4 3 γ

43 α / 3

44 γ 1 γ 3 T i,a T i,m

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47 K p, s T i, s

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51 L m S m P m n m

52 L m n r P r P m L r L 1 L 2 P r,1 P r,2 P r,2

53 L m P r P m