Wind Energy System Control Engineering Design By Mario Garcia Sanz And Constantine H Houpis.pdf - CONTROL ENGINEERING DESIGN Mario Garcia-Sanz \u2022

Wind Energy System Control Engineering Design By Mario Garcia Sanz And Constantine H Houpis.pdf

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Unformatted text preview: CONTROL ENGINEERING DESIGN Mario Garcia-Sanz • Constantine H. Houpis Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business Contents Preface���������������������������������������������������������������������������������������������������������������������������������������������xv Authors����������������������������������������������������������������������������������������������������������������������������������������� xix 1. Introduction..............................................................................................................................1 1.1 Broad Context and Motivation..................................................................................... 1 1.2 Concurrent Engineering: A Road Map for Energy...................................................1 1.3 Quantitative Robust Control........................................................................................5 1.4 Novel CAD Toolbox for QFT Controller Design.......................................................7 1.5 Outline.............................................................................................................................8 Part I Advanced Robust Control Techniques: QFT and Nonlinear Switching 2. Introduction to QFT.............................................................................................................. 15 2.1 Quantitative Feedback Theory................................................................................... 15 2.2 Why Feedback?............................................................................................................. 15 2.3 QFT Overview.............................................................................................................. 17 2.3.1 QFT Design Objective.................................................................................... 17 2.3.2 Parametric Uncertainty: A Basic Explanation............................................ 17 2.3.2.1 Simple Example............................................................................... 17 2.3.2.2 Simple Mathematical Description................................................ 18 2.3.3 Control System Performance Specifications............................................... 18 2.3.4 QFT Design Overview................................................................................... 20 2.3.5 QFT Basics........................................................................................................ 21 2.3.6 QFT Design......................................................................................................22 2.4 Insight into the QFT Technique................................................................................. 24 2.4.1 Open-Loop Plant............................................................................................. 24 2.4.2 Closed-Loop Formulation.............................................................................. 24 2.4.3 Results of Applying the QFT Design Technique........................................ 24 2.4.4 Insight into the Use of the NC in the QFT Technique............................... 24 2.5 Benefits of QFT............................................................................................................. 27 2.6 Summary....................................................................................................................... 28 3. MISO Analog QFT Control System................................................................................... 29 3.1 Introduction.................................................................................................................. 29 3.2 QFT Method (Single-Loop MISO System)................................................................ 29 3.3 Design Procedure Outline.......................................................................................... 31 3.4 Minimum-Phase System Performance Specifications............................................ 32 3.4.1 Tracking Models............................................................................................. 32 3.4.2 Disturbance-Rejection Models...................................................................... 36 3.5 J LTI Plant Models........................................................................................................ 36 vii viii Contents 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 Plant Templates of Pι(s), ℑP( jω i )................................................................................. 37 Nominal Plant.............................................................................................................. 39 U-Contour (Stability Bound)...................................................................................... 39 Tracking Bounds BR(jω) on the NC............................................................................ 41 Disturbance Bounds BD(jωi)........................................................................................ 45 3.10.1 Case 1: (d2(t) = D0u−1(t), d1(t) = 0)..................................................................... 45 3.10.1.1 Control Ratio.................................................................................... 45 3.10.1.2 Disturbance-Response Characteristic.......................................... 46 3.10.1.3 Application....................................................................................... 46 3.10.1.4 Templates.......................................................................................... 47 3.10.1.5 Rotated NC....................................................................................... 49 3.10.1.6 Bounds BD(jωi )................................................................................. 49 3.10.2 Case 2: (d1(t) = Dou−1(t), d2(t) = 0)..................................................................... 50 3.10.2.1 Control Ratio.................................................................................... 50 3.10.2.2 Disturbance Response Characteristics......................................... 50 3.10.2.3 Bounds BD(jωi )................................................................................. 51 Composite Boundary Bo(jωi)....................................................................................... 53 Shaping of Lo(jω)...........................................................................................................54 Guidelines for Shaping Lo(jω)..................................................................................... 59 Design of the Prefilter F(s)........................................................................................... 60 Basic Design Procedure for a MISO System............................................................. 62 Design Example 1.........................................................................................................65 Design Example 2......................................................................................................... 75 Template Generation for Unstable Plants................................................................. 75 Summary....................................................................................................................... 79 4. Discrete Quantitative Feedback Technique..................................................................... 81 4.1 Introduction.................................................................................................................. 81 4.2 Bilinear Transformations............................................................................................ 82 4.2.1 w- and w′-Domain Transformations............................................................ 82 4.2.2 s-Plane and w-Plane Relationship................................................................84 4.2.3 s- to z-Plane Transformation: Tustin Transformation................................85 4.3 Non-Minimum-Phase Analog Plant......................................................................... 89 4.3.1 Analog QFT Design Procedure for an n.m.p. Plant.................................... 91 4.4 Discrete MISO Model with Plant Uncertainty........................................................ 93 4.5 QFT w-Domain DIG Design....................................................................................... 95 4.5.1 Closed-Loop System Specifications.............................................................. 96 4.5.2 Plant Templates............................................................................................... 98 4.5.3 Bounds B(jv) on Lo(jv)..................................................................................... 99 4.5.4 Non-Minimum-Phase Lo(w)......................................................................... 100 4.5.5 Synthesizing Lmo(w)....................................................................................... 103 4.5.6 ωs = 120 Is Too Small..................................................................................... 104 4.5.7 Error in the Design....................................................................................... 107 4.5.8 Design of the Prefilter F(w).......................................................................... 110 4.6 Simulation................................................................................................................... 111 4.7 Basic Design Procedure for a MISO S-D Control System.................................... 115 4.8 QFT Technique Applied to the PCT System.......................................................... 118 4.8.1 Introduction to PCT System DIG Technique............................................ 118 4.8.2 Simple PCT Example.................................................................................... 120 Contents ix 4.8.3 S-D Control System Example...................................................................... 121 4.8.4 PCT System of Figure 4.9............................................................................. 123 4.8.5 PCT Design Summary................................................................................. 125 4.9 Applicability of Design Technique to Other Plants.............................................. 125 4.10 Designing L(w) Directly............................................................................................ 126 4.11 Summary..................................................................................................................... 126 4.11.1 Minimum-Phase, Non-Minimum-Phase, and Unstable P(s).................. 126 4.11.2 Digital Controller Implementation............................................................. 126 4.11.3 Conclusions.................................................................................................... 127 5. Diagonal MIMO QFT......................................................................................................... 129 5.1 Introduction................................................................................................................ 129 5.2 Examples and Motivation......................................................................................... 129 5.2.1 MIMO Plant Example................................................................................... 129 5.2.2 Introduction to MIMO Compensation....................................................... 133 5.2.3 MIMO Compensation.................................................................................. 135 5.3 MIMO Systems—Characteristics and Overview.................................................. 137 5.3.1 Loops Coupling and Controller Structure................................................ 137 5.3.1.1 Interaction Analysis...................................................................... 138 5.3.2 Multivariable Poles and Zeros.................................................................... 140 5.3.3 Directionality................................................................................................ 140 5.3.3.1 Gain and Phase.............................................................................. 140 5.3.3.2 Effect of Poles and Zeros.............................................................. 141 5.3.3.3 Disturbance and Noise Signals................................................... 141 5.3.4 Uncertainty.................................................................................................... 141 5.3.5 Stability........................................................................................................... 142 5.4 MIMO QFT Control—Overview............................................................................. 143 5.5 Nonsequential Diagonal MIMO QFT (Method 1)................................................... 146 5.5.1 Effective MISO Equivalents......................................................................... 147 5.5.2 Effective MISO Loops of the MIMO System............................................. 151 5.5.3 Example: The 2 × 2 Plant.............................................................................. 151 5.5.4 Performance Bounds.................................................................................... 153 5.5.5 Constraints on the Plant Matrix................................................................. 158 5.6 Sequential Diagonal MIMO QFT (Method 2).......................................................... 161 5.7 Basically Noninteracting Loops............................................................................... 165 5.8 MIMO QFT with External (Input) Disturbances................................................... 166 5.9 Summary..................................................................................................................... 171 6. Non-Diagonal MIMO QFT................................................................................................ 173 6.1 Introduction................................................................................................................ 173 6.2 Non-Diagonal MIMO QFT: A Coupling Minimization Technique (Method 3)........174 6.2.1 Tracking.......................................................................................................... 175 6.2.2 Disturbance Rejection at Plant Input......................................................... 177 6.2.3 Disturbance Rejection at Plant Output...................................................... 178 6.3 Coupling Elements..................................................................................................... 179 6.4 Optimum Non-Diagonal Compensator.................................................................. 181 6.4.1 Tracking.......................................................................................................... 182 6.4.2 Disturbance Rejection at Plant Input......................................................... 182 6.4.3 Disturbance Rejection at Plant Output...................................................... 182 x Contents 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 Coupling Effects......................................................................................................... 182 6.5.1 Tracking.......................................................................................................... 182 6.5.2 Disturbance Rejection at Plant Input......................................................... 183 6.5.3 Disturbance Rejection at Plant Output...................................................... 183 Quality Function of the Designed Compensator.................................................. 183 Design Methodology................................................................................................. 184 6.7.1 Methodology................................................................................................. 184 Some Practical Issues................................................................................................. 187 Non-Diagonal MIMO QFT: A Generalized Technique (Method 4)...................... 187 Reformulation............................................................................................................. 188 6.10.1 Case 1: Reference Tracking and Disturbance Rejection at Plant Output.............................................................................................. 189 6.10.1.1 Methodology.................................................................................. 189 6.10.2 Case 2: Disturbance Rejection at Plant Input............................................ 193 6.10.3 Stability Conditions and Final Implementation....................................... 194 6.10.3.1 Stability Conditions...................................................................... 194 6.10.3.2 Final Implementation................................................................... 194 Translating Matrix Performance Specifications.................................................... 195 6.11.1 Case n × n....................................................................................................... 195 6.11.1.1 Tracking.......................................................................................... 195 6.11.1.2 Disturbance Rejection at Plant Output...................................... 195 6.11.1.3 Disturbance Rejection at Plant Input.......................................... 196 6.11.1.4 Noise Attenuation......................................................................... 196 6.11.1.5 General Expression....................................................................... 196 6.11.2 Case 2 × 2....................................................................................................... 201 6.11.2.1 Tracking.......................................................................................... 201 6.11.2.2 Disturbance Rejection at Plant Output...................................... 202 6.11.2.3 Disturbance Rejection at Plant Input.......................................... 203 6.11.2.4 Noise Attenuation......................................................................... 204 Comparison of Methods 3 and 4............................................................................... 205 Summary..................................................................................................................... 205 7. QFT for Distributed Parameter Systems........................................................................ 207 7.1 Introduction................................................................................................................ 207 7.2 Background................................................................................................................. 207 7.3 Generalized DPS Control System Structure.......................................................... 208 7.4 Extension of Quantitative Feedback Theory to DPS............................................. 211 7.4.1 Classical QFT for Lumped Systems........................................................... 211 7.4.2 QFT for Distributed Parameter Systems................................................... 213 7.5 Modeling Approaches for PDE................................................................................ 215 7.6 Examples..................................................................................................................... 216 7.6.1 Bernoulli–Euler Beam.................................................................................. 216 7.6.1.1 Definition........................................................................................ 216 7.6.1.2 Modeling........................................................................................ 217 7.6.1.3 Control Specifications................................................................... 217 7.6.1.4 C...
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