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604 MULTIVARIABLE PROCESSES TABLE 17.2 BLT, Ziegler-Nichols, and empirical controller tuning Wood and Berry Ogunnaike and Ray Empirical Kc 02-0.04 1.2/-0.15/0.6 TI 4&t/2.61 511014 Z-N K 0.96/-0.19 3.24/-0.63J5.66 *I 3.2519.2 7.62/8.36/3.08 BLT L: (dB) +4 +6 F factor 2.55 2.15 KC 0.375/-0.075 1.51/-0.295/2.63 TI 8.29123.6 16.4/18/6.61 If the process transfer functions have greatly differing time constants, the BLT procedure does not work well. It tends to give a response that is too oscillatory. The problem can be handled by breaking up the system into fast and slow sections and applying BLT to each smaller subsection. The BLT procedure discussed above was applied with PI controllers. The method can be extended to include derivative action (PID controllers) by using two detuning factors: F detunes the ZN reset and gain values and F, detunes the ZN derivative value. The optimum value of F, is that which gives the minimum x, 08 WB f;‘l--::” 0 0 ,y* 0 Time. mm FIGURE 17.1 Wood and Berry column: BLT and empirical tuning
DESIGN OF CONTROLLERS FOR MULTIVARIABLE PROCESSES 605 OR 0 ,/-- - - x3 - 25 ~ \ / \ / l-’ I I I I I I 0 20 40 60 Time, min FIGURE 17.2 Ogunnaike and Ray column: BLT and empirical tuning. value of F and still satisfies the + 2N maximum closedloop log modulus criterion (see the paper by Monica, Yu, and Luyben in IEC Research, Vol. 27, 1988, p. 969). 17.6 LOAD REJECTION PERFORMANCE In most chemical processes the principal control problem is load rejection. We want a control system that can keep the controlled variables at or near their setpoints in the face of load disturbances. Thus the closedloop regulator transfer function is the most important. The ideal closedloop relationship between the controlled variable and the load is zero. Of course this can never be achieved, but the smaller the magnitude
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I WILLIAM WIlllAM 1. LUYBEN PROCESS
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The Series Bailey and OUii: Biochem
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PROCESS MODELING, SIMULATION, AND C
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ABOUT THE AUTHOR William L. Luyben
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CONTENTS Preface Xxi 1 1.1 1.2 1.3
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CONTENTS .. . xlu 5.7 Batch Reactor
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CONTENTS xv 10.3 10.4 Performance S
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comwrs xvii 151.3 Transpose of a Ma
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CONTENTS Xix 20.4 Sampled-Data Cont
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. Xxii PREFACE Another significant
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PROCESS MODELING, SIMULATION, AND C
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2 PROCESS MODELING, SIMULATION. AND
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4 PROCESS MODELING, SIMULATION, AND
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6 PROCESS MODELING. SIMULATION, AND
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8 PROCESS MODELING, SIMULATION, AND
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10 PROCESS MODELING, SIMULATION, AN
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12 PROCESS MODELING, SIMULATION, AN
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CHAPTER 2 FUNDAMENTALS 2.1 INTRODUC
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FUNDAMENTALS 17 big, complex system
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FUNDAMENTALS 19 z=o I z + dz z=L FI
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FUNDAMENTALS 21 The minus sign come
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FUNDAMENTALS 23 Molar flow of A lea
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FUNDAMENTALS 25 For liquids the PP
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FUNDAMENTALS 27 Flow of energy (ent
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FUNDAMENTALS 29 The units of this f
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FUNDAMENTALS 31 FIGURE 2.9 Laminar
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FUNDAMENTALS 33 Then Eq. (2.48) bec
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FUNDAMENTALS 35 Wenzel in Chemical
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FUNDAMENTALS .37 This exponential t
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FUNDAMENTALS 39 a direction 0 = 45
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EXAMPLES OF MATHEMATICAL MODELS OF
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EXAMPLES OF MA~EMATICAL MODELS OF C
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EXAMPLES OF MATHEMATICAL MODELS OE
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88 COMPUTER SIMULATION Our discussi
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90 COMPUTER SIMULATION lation packa
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92 COMPUTER SIMULATION For this rea
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94 COMPUTER SIMULATION TABLE 4.1 Ex
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96 COMPUTER SIMULATION Clearly, the
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98 COMPUTER SIMULATION TABLE 4.2 Ex
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I()() COMPUTER SIMULATION Settingfl
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