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Large scale control

Large scale control. Hierarchical and pratial control The evaporation process in sugar production. Partial control. controlling a subset of the outputs y for which there is a control objective y 1 - (temporary) uncontrolled outputs, can be controlled at some higher level.

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Large scale control

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  1. Large scale control Hierarchical and pratial control The evaporation process in sugar production

  2. Partial control • controlling a subset of the outputs y for which there is a control objective • y1- (temporary) uncontrolled outputs, can be controlled at some higher level. • y2 – (locally) measured and controlled output • The inputs u is diveded • u2 –inputs used for controlling y2 • u1 – remaining inputs which may be used for controlling y1

  3. Applications of partial control • Sequential control of decentralized controllers • Sequential design of convensional cascade control • True partial control • Indirect partial control

  4. Transfer function for y1 and y2 y= Gu y1= G11u1 +G12u2+Gd1d y2 = G21u1 + G22u2+Gd2d Feedback control u2 = K2(r2-y2) =>u2 and y2 can be eliminated y1=(G11-G12K2(I+G22K2)-1u1+ (Gd1-G21K2(I+G22K2)-1Gd2)d+ (G12K2(I+G22K2)-1r2

  5. Control objectives for y2 Fast control of y2 => y2 =r2 By substitution Pu is the effect of u1 on y2 Pd is the partial disturbance gain Pr is reference gain

  6. Hierarchical decomposition by sequential design First implement a local lower level control or an inner loop for controlling the output y2 Objectives: Simpel or on-line tuning of lower-layer controllers Longer sampling intervals for hiegher layers Simpel models for design of higher-layer control systems To stabilize lower layers such that manual control is possible

  7. Selecting u2 and y2 • The lower layer must quickly implement the setpoints computed by the higher layers • control of y2 using u2 schould provide local disturbance rejection • control of y2 using u2 schouldnot impose unnecessary control limitations on the remaining control problem

  8. Distilation column u=[L V D B VT]T L = reflux V = boilup D= destilate B=bottom flow VT = overhead vapour y= [yd xb MD MB p]T yD = top composition xB= bottom composition MD=condenser holdup MB = reboiler holdup p= pressure 5 X 5 control problem

  9. Stabilizing the distilation column Locally measured and controlled outputs are loops for level and pressure, they interacts weakly y2=[MD MB p]T The levels(tanks) has an inlet and two outlets ther are several possible inputs. One can be: u2 = [D B VT]T Three SISO loops can be designed

  10. Composition control Teporary uncontrolled inputs y1= [yD xB ]T u1=[L V ]T YD can be controlled using L XB can be controlled using V The choise of u2 made u1 usefull for controlling y1

  11. ”True” Partial control y1 is left uncontrolled when control of y2 indirectly gives acceptable control of y1. y1 must be left uncontrolled if the effects of all disturbances on y1 are less than 1 in magnitude for all frequencies. y1 must be left uncontrolled if the effects of all reference changes in the controlled outputs (y2) on y1, are less than 1 in magnitude for all frequencies.

  12. y= Gu y1= G11u1 +G12u2+Gd1d y2 = G21u1 + G22u2+Gd2d The effect of a disturbance dk on an uncontrolled output yi is Select the unused input uj such that j’th row in G-1Gd has small elements = keep the input constant if its desired change is small. Select the uncontrolled output yi an unused uj such that the ji’th element in G-1 is large = Keep an output uncontrolled if it is insentive to changes in the unused input with the other outputs controlled.

  13. Simpel distilation column 2 X 2 control problem u=[L V ]T L = reflux V = boilup y= [yd xb]T yD = top composition xB= bottom composition Disturbances d=[F zF] F= feed flowrate zF=feed composition

  14. Control problems in the destilation proces • Difficult to control the two outputs idenpendently due to strong interactions • y1 is left uncontrolled • To improve performance of y1 (yD composition), u1 (reflux L)is adjusted by a feedforward from the disturbance – not from y1 measurements.

  15. Distillation matrices Eksample: At steady state we have The row elements in G-1Gd are similar i magnitude as are the elements in G-1 => The values of Pd are quite similar In cases the elements in Pd is much smaller than i Gd => control of one output reduces the effect of the distrubance of the uncontrolled output.

  16. Effect of disturbance d1 on output y1 Control y2 using u2 with y1 uncontrolled and worst disturbance d1 Curve 1:open loop disturbance gain Curve 2: partial disturbance gain Low frequency gains > 1

  17. Reduction of disturbance effect on y1 using feed forward Measure d1 (F) and adjust u1 (L) as a ratio controller curve 3 Unsecure measurements (20%) reduce the effect curve 4 The static FF reacts to fast – a filter is introduced Curve 5 Reduction of the disturbance at all frequences

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