Details

<p>Author Biographies xv</p> <p>Preface xix</p> <p>Acknowledgments xxiii</p> <p>Acronyms xxv</p> <p>Notation xxix</p> <p><b>1 Introduction 1</b></p> <p><b>2 Motivation and Basic Construction of PID Passivity-based Control 5</b></p> <p>2.1 L2-Stability and Output Regulation to Zero 6</p> <p>2.2 Well-Posedness Conditions 9</p> <p>2.3 PID-PBC and the Dissipation Obstacle 10</p> <p>2.3.1 Passive systems and the dissipation obstacle 11</p> <p>2.3.2 Steady-state operation and the dissipation obstacle 12</p> <p>2.4 PI-PBC with y0 and Control by Interconnection 14</p> <p><b>3 Use of Passivity for Analysis and Tuning of PIDs: Two Practical Examples 19</b></p> <p>3.1 Tuning of the PI Gains for Control of Induction Motors 21</p> <p>3.1.1 Problem formulation 23</p> <p>3.1.2 Change of coordinates 27</p> <p>3.1.3 Tuning rules and performance intervals 30</p> <p>3.1.4 Concluding remarks 35</p> <p>3.2 PI-PBC of a Fuel Cell System 36</p> <p>3.2.1 Control problem formulation 41</p> <p>3.2.2 Limitations of current controllers and the role of passivity 46</p> <p>3.2.3 Model linearization and useful properties 48</p> <p>3.2.4 Main result 50</p> <p>3.2.5 An asymptotically stable PI-PBC 54</p> <p>3.2.6 Simulation results 57</p> <p>3.2.7 Concluding remarks and future work 58</p> <p><b>4 PID-PBC for Nonzero Regulated Output Reference 61</b></p> <p>4.1 PI-PBC for Global Tracking 63</p> <p>4.1.1 PI global tracking problem 63</p> <p>4.1.2 Construction of a shifted passive output 65</p> <p>4.1.3 A PI global tracking controller 67</p> <p>4.2 Conditions for Shifted Passivity of General Nonlinear Systems 68</p> <p>4.2.1 Shifted passivity definition 69</p> <p>4.2.2 Main results 70</p> <p>4.3 Conditions for Shifted Passivity of port-Hamiltonian Systems 73</p> <p>4.3.1 Problems formulation 74</p> <p>4.3.2 Shifted passivity 75</p> <p>4.3.3 Shifted passifiability via output-feedback 77</p> <p>4.3.4 Stability of the forced equilibria 78</p> <p>4.3.5 Application to quadratic pH systems 79</p> <p>4.4 PI-PBC of Power Converters 81</p> <p>4.4.1 Model of the power converters 81</p> <p>4.4.2 Construction of a shifted passive output 82</p> <p>4.4.3 PI stabilization 85</p> <p>4.4.4 Application to a quadratic boost converter 86</p> <p>4.5 PI-PBC of HVDC Power Systems 89</p> <p>4.5.1 Background 89</p> <p>4.5.2 Port-Hamiltonian model of the system 91</p> <p>4.5.3 Main result 93</p> <p>4.5.4 Relation of PI-PBC with Akagi’s PQ method 95</p> <p>4.6 PI-PBC of Wind Energy Systems 96</p> <p>4.6.1 Background 96</p> <p>4.6.2 System model 98</p> <p>4.6.3 Control problem formulation 102</p> <p>4.6.4 Proposed PI-PBC 104</p> <p>4.7 Shifted Passivity of PI-Controlled Permanent Magnet Synchronous Motors 107</p> <p>4.7.1 Background 107</p> <p>4.7.2 Motor models 108</p> <p>4.7.3 Problem formulation 111</p> <p>4.7.4 Main result 113</p> <p>4.7.5 Conclusions and future research 114</p> <p><b>5 Parameterization of All Passive Outputs for port-Hamiltonian Systems 115</b></p> <p>5.1 Parameterization of all Passive Outputs 116</p> <p>5.2 Some Particular Cases 118</p> <p>5.3 Two Additional Remarks 120</p> <p>5.4 Examples 121</p> <p>5.4.1 A level control system 121</p> <p>5.4.2 A microelectromechanical optical switch 123</p> <p><b>6 Lyapunov Stabilization of port-Hamiltonian Systems 125</b></p> <p>6.1 Generation of Lyapunov Functions 127</p> <p>6.1.1 Basic PDE 128</p> <p>6.1.2 Lyapunov stability analysis 129</p> <p>6.2 Explicit Solution of the PDE 131</p> <p>6.2.1 The power shaping output 132</p> <p>6.2.2 A more general solution 133</p> <p>6.2.3 On the use of multipliers 135</p> <p>6.3 Derivative Action on Relative Degree Zero Outputs 137</p> <p>6.3.1 Preservation of the port-Hamiltonian Structure of I-PBC 138</p> <p>6.3.2 Projection of the new passive output 140</p> <p>6.3.3 Lyapunov stabilization with the new PID-PBC 141</p> <p>6.4 Examples 142</p> <p>6.4.1 A microelectromechanical optical switch (continued) 143</p> <p>6.4.2 Boost converter 144</p> <p>6.4.3 2-dimensional controllable LTI systems 146</p> <p>6.4.4 Control by Interconnection vs PI-PBC 148</p> <p>6.4.5 The use of the derivative action 150</p> <p><b>7 Underactuated Mechanical Systems 153</b></p> <p>7.1 Historical Review and Chapter Contents 153</p> <p>7.1.1 Potential energy shaping of fully actuated systems 154</p> <p>7.1.2 Total energy shaping of underactuated systems 156</p> <p>7.1.3 Two formulations of PID-PBC 157</p> <p>7.2 Shaping the Energy with a PID 158</p> <p>7.3 PID-PBC of port-Hamiltonian Systems 161</p> <p>7.3.1 Assumptions on the system 161</p> <p>7.3.2 A suitable change of coordinates 163</p> <p>7.3.3 Generating new passive outputs 165</p> <p>7.3.4 Projection of the total storage function 167</p> <p>7.3.5 Main stability result 169</p> <p>7.4 PID-PBC of Euler-Lagrange Systems 172</p> <p>7.4.1 Passive outputs for Euler-Lagrange systems 173</p> <p>7.4.2 Passive outputs for Euler-Lagrange systems in Spong’s normal form 175</p> <p>7.5 Extensions 176</p> <p>7.5.1 Tracking constant speed trajectories 176</p> <p>7.5.2 Removing the cancellation of Va(qa) 178</p> <p>7.5.3 Enlarging the class of integral actions 179</p> <p>7.6 Examples 180</p> <p>7.6.1 Tracking for inverted pendulum on a cart 180</p> <p>7.6.2 Cart-pendulum on an inclined plane 182</p> <p>7.7 PID-PBC of Constrained Euler-Lagrange Systems 190</p> <p>7.7.1 System model and problem formulation 191</p> <p>7.7.2 Reduced purely differential model 195</p> <p>7.7.3 Design of the PID-PBC 196</p> <p>7.7.4 Main stability result 199</p> <p>7.7.5 Simulation Results 200</p> <p>7.7.6 Experimental Results 202</p> <p><b>8 Disturbance Rejection in port-Hamiltonian Systems 207</b></p> <p>8.1 Some Remarks On Notation and Assignable Equilibria 209</p> <p>8.1.1 Notational simplifications 209</p> <p>8.1.2 Assignable equilibria for constant d 210</p> <p>8.2 Integral Action on the Passive Output 211</p> <p>8.3 Solution Using Coordinate Changes 214</p> <p>8.3.1 A feedback equivalence problem 214</p> <p>8.3.2 Local solutions of the feedback equivalent problem 217</p> <p>8.3.3 Stability of the closed–loop 219</p> <p>8.4 Solution Using Nonseparable Energy Functions 221</p> <p>8.4.1 Matched and unmatched disturbances 222</p> <p>8.4.2 Robust matched disturbance rejection 225</p> <p>8.5 Robust Integral Action for Fully Actuated Mechanical Systems 230</p> <p>8.6 Robust Integral Action for Underactuated Mechanical Systems 237</p> <p>8.6.1 Standard interconnection and damping assignment PBC 239</p> <p>8.6.2 Main result 241</p> <p>8.7 A New Robust Integral Action for Underactuated Mechanical Systems 244</p> <p>8.7.1 System model 244</p> <p>8.7.2 Coordinate transformation 245</p> <p>8.7.3 Verification of requisites 246</p> <p>8.7.4 Robust integral action controller 248</p> <p>8.8 Examples 248</p> <p>8.8.1 Mechanical systems with constant inertia matrix 249</p> <p>8.8.2 Prismatic robot 250</p> <p>8.8.3 The Acrobot system 255</p> <p>8.8.4 Disk on disk system 260</p> <p>8.8.5 Damped vertical take-off and landing aircraft 265</p> <p><b>A Passivity and Stability Theory for State-Space Systems 269</b></p> <p>A.1 Characterization of Passive Systems 269</p> <p>A.2 Passivity Theorem 271</p> <p>A.3 Lyapunov Stability of Passive Systems 273</p> <p><b>B Two Stability Results and Assignable Equilibria 275</b></p> <p>B.1 Two Stability Results 275</p> <p>B.2 Assignable Equilibria 276</p> <p><b>C Some Differential Geometric Results 279</b></p> <p>C.1 Invariant Manifolds 279</p> <p>C.2 Gradient Vector Fields 280</p> <p>C.3 A Technical Lemma 281</p> <p><b>D Port-Hamiltonian Systems 283</b></p> <p>D.1 Definition of port-Hamiltonian Systems and Passivity Property 283</p> <p>D.2 Physical Examples 284</p> <p>D.3 Euler-Lagrange Models 286</p> <p>D.4 Port-Hamiltonian Representation of GAS Systems 288</p> <p>Index 309</p>

<p><b>ROMEO ORTEGA,</b> PhD, is a full-time professor and researcher at the Mexico Autonomous Institute of Technology, Mexico. He is a Fellow Member of the IEEE since 1999. He has served as chairman on several IFAC and IEEE committees and participated in various editorial boards of international journals.</p> <p><b>JOSÉ GUADALUPE ROMERO</b>, PhD, is a full-time professor and researcher at the Mexico Autonomous Institute of Technology, Mexico. His research interests are focused on nonlinear and adaptive control, stability analysis, and the state estimation problem. <p><b>PABLO BORJA,</b> PhD, is a Postdoctoral researcher at the University of Groningen, Netherlands. His research interests encompass nonlinear systems, passivity-based control, and model reduction. <p><b>ALEJANDRO DONAIRE,</B> PhD, is a full-time academic at the University of Newcastle, Australia. His research interests include nonlinear systems, passivity, and control theory.

<p><b>Explore the foundational and advanced subjects associated with ­proportional-integral-derivative controllers from leading authors in the field</b></p> <p>In <i>PID Passivity-Based Control of Nonlinear Systems with Applications,</i> expert researchers and authors Drs. Romeo Ortega, Jose Guadalupe Romero, Pablo Borja, and Alejandro Donaire deliver a comprehensive and detailed discussion of the most crucial and relevant concepts in the analysis and design of proportional-integral-­derivative controllers using passivity techniques. The accomplished authors present a formal treatment of the recent research in the area and offer readers practical applications of the developed methods to physical systems, including electrical, mechanical, electromechanical, power electronics, and process control. <p>The book offers the material with minimal mathematical background, making it relevant to a wide audience. Familiarity with the theoretical tools reported in the control systems literature is not necessary to understand the concepts contained within. You’ll learn about a wide range of concepts, including disturbance rejection via PID control, PID control of mechanical systems, and Lyapunov stability of PID controllers. <p>Readers will also benefit from the inclusion of: <ul><li> A thorough introduction to a class of physical systems described in the port-Hamiltonian form and a presentation of the systematic procedures to design PID-PBC for them</li> <li>An exploration of the applications to electrical, electromechanical, and process control systems of Lyapunov stability of PID controllers</li> <li>Practical discussions of the regulation and tracking of bilinear systems via PID control and their application to power electronics and thermal process control</li> <li>A concise treatment of the characterization of passive outputs, incremental models, and Port Hamiltonian and Euler-Lagrange systems</li></ul> <p>Perfect for senior undergraduate and graduate students studying control systems, PID <i>Passivity-Based Control</i> will also earn a place in the libraries of engineers who practice in this area and seek a one-stop and fully updated reference on the subject.

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