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Process Dynamics and Control, Subject Code:7CH03, Department of Chemical Engineering, Anuradha Engineering College, , Chikhli, Friday, September 8, 2017, 1, Prepared by M.A.Quazi
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Lecture 2, Contents:, , Block Diagram Algebra, , Regular Control problem for Negative Feed Back System., , Regular Control problem for Positive Feed Back System., Friday, September 8, 2017, 2, Prepared by M.A.Quazi
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Objectives, To get familiar with Block Diagram Reduction for Regulator Control., Friday, September 8, 2017, 3, Prepared by M.A.Quazi
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Representation of Block diagram for Negative Feed Back system, Friday, September 8, 2017, Prepared by M.A.Quazi, 4, Consider,, , , , , , GC is the transfer function of Controller, GV is the transfer function of Control Value, GP is the transfer function of Process., H is the transfer function of measuring element., GC, H, R, GP, GV, +, _, P, U, +, +, B, e, M, C
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Regulator Control Mechanism Problem of Negative Feed Back System., Friday, September 8, 2017, Prepared by M.A.Quazi, 5, Aim is to determine the overall transfer function relating the control variable with load variable for constant value of set point., From the block diagram we can write the transfer function of each element of system as,, , , , , Substituting value of P from equation 1 in equation 2 we have,, GC, P, e, GV, P, M, GCGV, M, e
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Regulator Control Mechanism Problem of Negative Feed Back System. (Part 2), Friday, September 8, 2017, Prepared by M.A.Quazi, 6, Since Set point R is Constant therefore dR/dt = 0, that is e = - B., The block Reduce to,, , , , , Again we can write Transfer function for process as,, GCGV, H, GP, _, B, e =, C, GP, M+U, C, U, +, +, M
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Regulator Control Mechanism Problem of Negative Feed Back System. (Part 3), Friday, September 8, 2017, Prepared by M.A.Quazi, 7, For transfer function of measuring element we can write,, , , Evaluating equation 3, 4 and 5 gives,, , , , , Therefore equation 7 can be written in terms of C and U as ,, H, B, C
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Regulator Control Mechanism Problem of Negative Feed Back System. (Part 4), Friday, September 8, 2017, Prepared by M.A.Quazi, 8, Therefore Overall Transfer function for Regulator Control Negative Feed back system is,, , , Therefore we can write for Regulator Control Negative Feed back system as,, U
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Regulator Control Mechanism Problem of Negative Feed Back System. (Part 5), Friday, September 8, 2017, Prepared by M.A.Quazi, 9, Therefore overall Block diagram reduction for Negative feed back Regular control system is,, C, U
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Representation of Block diagram for Positive Feed Back system, Friday, September 8, 2017, Prepared by M.A.Quazi, 10, Consider,, , , , , , GC is the transfer function of Controller, GV is the transfer function of Control Value, GP is the transfer function of Process., H is the transfer function of measuring element., GC, H, R, GP, GV, +, +, P, U, +, +, B, e, M, C
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Regulator Control Mechanism Problem of Positive Feed Back System., Friday, September 8, 2017, Prepared by M.A.Quazi, 11, Aim is to determine the overall transfer function relating the control variable with load variable for constant value of set point., From the block diagram we can write the transfer function of each element of system as,, , , , , Substituting value of P from equation 1 in equation 2 we have,, GC, P, e, GV, P, M, GCGV, M, e
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Regulator Control Mechanism Problem of Positive Feed Back System. (Part 2), Friday, September 8, 2017, Prepared by M.A.Quazi, 12, Since Set point R is Constant therefore dR/dt = 0, that is e = B., The block Reduce to,, , , , , Again we can write Transfer function for process as,, GCGV, H, GP, +, B, e =, C, GP, M+U, C, U, +, +, M
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Regulator Control Mechanism Problem of Positive Feed Back System. (Part 3), Friday, September 8, 2017, Prepared by M.A.Quazi, 13, For transfer function of measuring element we can write,, , , Evaluating equation 3, 4 and 5 gives,, , , , , Therefore equation 7 can be written in terms of C and U as ,, H, B, C
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Regulator Control Mechanism Problem of Positive Feed Back System. (Part 4), Friday, September 8, 2017, Prepared by M.A.Quazi, 14, Therefore Overall Transfer function for Regulator Control Positive Feed back system is,, , , Therefore we can write for Regulator Control Positive Feed back system as,, U, U
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Regulator Control Mechanism Problem of Positive Feed Back System. (Part 5), Friday, September 8, 2017, Prepared by M.A.Quazi, 15, Therefore overall Block diagram reduction for Positive feed back Regular control system is,, C, U
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Problem (1) on Block Diagram Reduction., Friday, September 8, 2017, Prepared by M.A.Quazi, 16, Obtain C/R and C/U for the block diagram shown in figure,, , , , , , , Solution: , Step 1: Represent Input and output deviation variable of given elements by alphabets as shown, 1, s, +, +, +, +, _, _, R, U, C
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Problem (1) on Block Diagram Reduction., Friday, September 8, 2017, Prepared by M.A.Quazi, 17, Step 2: Consider the inner loop first if present,, For here which input variable is X and the output variable is Y., 1, s, +, +, +, +, _, _, R, U, C, X, Y, A, B, D, E
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Problem (1) on Block Diagram Reduction., Friday, September 8, 2017, Prepared by M.A.Quazi, 18, Here Inner Loop is Negative feed back system., Therefore from Negative feed back system transfer function of inner loop is given by,, , , , , That is,, X, Y
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Problem (1) on Block Diagram Reduction., Friday, September 8, 2017, Prepared by M.A.Quazi, 19, Block Diagram Reduce to,, , , , , , , Step 3: Obtain the overall transfer function for Servo Control relating C(s)/R(s) at constant Load variable U(s)., As Load variable U(s) is constant therefore dU/dt =U= 0., s, +, +, +, _, R, U, C, X, Y, E
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Problem (1) on Block Diagram Reduction., Friday, September 8, 2017, Prepared by M.A.Quazi, 20, Block Diagram Reduce to,, Outer loop is also Negative feed back system., Negative feed back system transfer function for overall inner and outer in terms of C(s)/R(s) is given by,, +, _, R, C, X, Y, E, Ans. 1
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Problem (1) on Block Diagram Reduction., Friday, September 8, 2017, Prepared by M.A.Quazi, 21, Therefore block diagram for C(s)/R(s) at U = 0 reduce to,, , , , , Step 4: Similarly obtain transfer C(s)/U(s) , For Regulator Control overall transfer function is related by C(s)/U(s) at constant Set point R(s)., As Set point R(s) is constant therefore dR/dt = R = 0., Reducing inner loop and setting R = 0, we have,, R, C
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Problem (1) on Block Diagram Reduction., Friday, September 8, 2017, Prepared by M.A.Quazi, 22, Block Diagram Reduce as,, , , , , , For above negative feed back system in terms of C(s)/U(s) as,, s, +, +, _, U, C, X =, Y, E, Ans. 2
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Problem (1) on Block Diagram Reduction., Friday, September 8, 2017, Prepared by M.A.Quazi, 23, Therefore block diagram for C(s)/U(s) at R = 0 reduce to,, U, C
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HW, Friday, September 8, 2017, Prepared by M.A.Quazi, 24, Obtain Transfer function for Servo Control Mechanism for Positive Feedback System?
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Friday, September 8, 2017, Prepared by M.A.Quazi, 25, Discussion
