{"product_id":"pid-passivitybased-control-of-nonlinear-systems-with-applications-9781119694168","title":"PID PassivityBased Control of Nonlinear Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eExplore thefoundational and advancedsubjects associated with proportional-integral-derivative controllers fromleading authors in the field\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIn\u003ci\u003ePID Passivity-Based Control of Nonlinear Systems with Applications\u003c\/i\u003e,expert researchers and authors Drs. Romeo Ortega, Jose GuadalupeRomero,Pablo Borja,andAlejandro Donairedelivera comprehensive and detailed discussion of the most crucial and relevant conceptsin the analysis and design ofproportional-integral-derivative controllersusing passivity techniques. The accomplished authors present a formal treatment of the recentresearch in the area and offer readers practical applications of the developed methods to physical systems, including electrical, mechanical, electromechanical, power electronics, and process control.\u003c\/p\u003e \u003cp\u003eThe book offers the material with minimal mathematical background, making it relevant to a wide audience. Familiarity withthe theoretical tools reported in the control systems literature is not necessary\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eAuthor Biographies xv\u003c\/p\u003e \u003cp\u003ePreface xix\u003c\/p\u003e \u003cp\u003eAcknowledgments xxiii\u003c\/p\u003e \u003cp\u003eAcronyms xxv\u003c\/p\u003e \u003cp\u003eNotation xxix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Motivation and Basic Construction of PID Passivity-based Control 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 L2-Stability and Output Regulation to Zero 6\u003c\/p\u003e \u003cp\u003e2.2 Well-Posedness Conditions 9\u003c\/p\u003e \u003cp\u003e2.3 PID-PBC and the Dissipation Obstacle 10\u003c\/p\u003e \u003cp\u003e2.3.1 Passive systems and the dissipation obstacle 11\u003c\/p\u003e \u003cp\u003e2.3.2 Steady-state operation and the dissipation obstacle 12\u003c\/p\u003e \u003cp\u003e2.4 PI-PBC with y0 and Control by Interconnection 14\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Use of Passivity for Analysis and Tuning of PIDs: Two Practical Examples 19\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Tuning of the PI Gains for Control of Induction Motors 21\u003c\/p\u003e \u003cp\u003e3.1.1 Problem formulation 23\u003c\/p\u003e \u003cp\u003e3.1.2 Change of coordinates 27\u003c\/p\u003e \u003cp\u003e3.1.3 Tuning rules and performance intervals 30\u003c\/p\u003e \u003cp\u003e3.1.4 Concluding remarks 35\u003c\/p\u003e \u003cp\u003e3.2 PI-PBC of a Fuel Cell System 36\u003c\/p\u003e \u003cp\u003e3.2.1 Control problem formulation 41\u003c\/p\u003e \u003cp\u003e3.2.2 Limitations of current controllers and the role of passivity 46\u003c\/p\u003e \u003cp\u003e3.2.3 Model linearization and useful properties 48\u003c\/p\u003e \u003cp\u003e3.2.4 Main result 50\u003c\/p\u003e \u003cp\u003e3.2.5 An asymptotically stable PI-PBC 54\u003c\/p\u003e \u003cp\u003e3.2.6 Simulation results 57\u003c\/p\u003e \u003cp\u003e3.2.7 Concluding remarks and future work 58\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 PID-PBC for Nonzero Regulated Output Reference 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 PI-PBC for Global Tracking 63\u003c\/p\u003e \u003cp\u003e4.1.1 PI global tracking problem 63\u003c\/p\u003e \u003cp\u003e4.1.2 Construction of a shifted passive output 65\u003c\/p\u003e \u003cp\u003e4.1.3 A PI global tracking controller 67\u003c\/p\u003e \u003cp\u003e4.2 Conditions for Shifted Passivity of General Nonlinear Systems 68\u003c\/p\u003e \u003cp\u003e4.2.1 Shifted passivity definition 69\u003c\/p\u003e \u003cp\u003e4.2.2 Main results 70\u003c\/p\u003e \u003cp\u003e4.3 Conditions for Shifted Passivity of port-Hamiltonian Systems 73\u003c\/p\u003e \u003cp\u003e4.3.1 Problems formulation 74\u003c\/p\u003e \u003cp\u003e4.3.2 Shifted passivity 75\u003c\/p\u003e \u003cp\u003e4.3.3 Shifted passifiability via output-feedback 77\u003c\/p\u003e \u003cp\u003e4.3.4 Stability of the forced equilibria 78\u003c\/p\u003e \u003cp\u003e4.3.5 Application to quadratic pH systems 79\u003c\/p\u003e \u003cp\u003e4.4 PI-PBC of Power Converters 81\u003c\/p\u003e \u003cp\u003e4.4.1 Model of the power converters 81\u003c\/p\u003e \u003cp\u003e4.4.2 Construction of a shifted passive output 82\u003c\/p\u003e \u003cp\u003e4.4.3 PI stabilization 85\u003c\/p\u003e \u003cp\u003e4.4.4 Application to a quadratic boost converter 86\u003c\/p\u003e \u003cp\u003e4.5 PI-PBC of HVDC Power Systems 89\u003c\/p\u003e \u003cp\u003e4.5.1 Background 89\u003c\/p\u003e \u003cp\u003e4.5.2 Port-Hamiltonian model of the system 91\u003c\/p\u003e \u003cp\u003e4.5.3 Main result 93\u003c\/p\u003e \u003cp\u003e4.5.4 Relation of PI-PBC with Akagi’s PQ method 95\u003c\/p\u003e \u003cp\u003e4.6 PI-PBC of Wind Energy Systems 96\u003c\/p\u003e \u003cp\u003e4.6.1 Background 96\u003c\/p\u003e \u003cp\u003e4.6.2 System model 98\u003c\/p\u003e \u003cp\u003e4.6.3 Control problem formulation 102\u003c\/p\u003e \u003cp\u003e4.6.4 Proposed PI-PBC 104\u003c\/p\u003e \u003cp\u003e4.7 Shifted Passivity of PI-Controlled Permanent Magnet Synchronous Motors 107\u003c\/p\u003e \u003cp\u003e4.7.1 Background 107\u003c\/p\u003e \u003cp\u003e4.7.2 Motor models 108\u003c\/p\u003e \u003cp\u003e4.7.3 Problem formulation 111\u003c\/p\u003e \u003cp\u003e4.7.4 Main result 113\u003c\/p\u003e \u003cp\u003e4.7.5 Conclusions and future research 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Parameterization of All Passive Outputs for port-Hamiltonian Systems 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Parameterization of all Passive Outputs 116\u003c\/p\u003e \u003cp\u003e5.2 Some Particular Cases 118\u003c\/p\u003e \u003cp\u003e5.3 Two Additional Remarks 120\u003c\/p\u003e \u003cp\u003e5.4 Examples 121\u003c\/p\u003e \u003cp\u003e5.4.1 A level control system 121\u003c\/p\u003e \u003cp\u003e5.4.2 A microelectromechanical optical switch 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Lyapunov Stabilization of port-Hamiltonian Systems 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Generation of Lyapunov Functions 127\u003c\/p\u003e \u003cp\u003e6.1.1 Basic PDE 128\u003c\/p\u003e \u003cp\u003e6.1.2 Lyapunov stability analysis 129\u003c\/p\u003e \u003cp\u003e6.2 Explicit Solution of the PDE 131\u003c\/p\u003e \u003cp\u003e6.2.1 The power shaping output 132\u003c\/p\u003e \u003cp\u003e6.2.2 A more general solution 133\u003c\/p\u003e \u003cp\u003e6.2.3 On the use of multipliers 135\u003c\/p\u003e \u003cp\u003e6.3 Derivative Action on Relative Degree Zero Outputs 137\u003c\/p\u003e \u003cp\u003e6.3.1 Preservation of the port-Hamiltonian Structure of I-PBC 138\u003c\/p\u003e \u003cp\u003e6.3.2 Projection of the new passive output 140\u003c\/p\u003e \u003cp\u003e6.3.3 Lyapunov stabilization with the new PID-PBC 141\u003c\/p\u003e \u003cp\u003e6.4 Examples 142\u003c\/p\u003e \u003cp\u003e6.4.1 A microelectromechanical optical switch (continued) 143\u003c\/p\u003e \u003cp\u003e6.4.2 Boost converter 144\u003c\/p\u003e \u003cp\u003e6.4.3 2-dimensional controllable LTI systems 146\u003c\/p\u003e \u003cp\u003e6.4.4 Control by Interconnection vs PI-PBC 148\u003c\/p\u003e \u003cp\u003e6.4.5 The use of the derivative action 150\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Underactuated Mechanical Systems 153\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Historical Review and Chapter Contents 153\u003c\/p\u003e \u003cp\u003e7.1.1 Potential energy shaping of fully actuated systems 154\u003c\/p\u003e \u003cp\u003e7.1.2 Total energy shaping of underactuated systems 156\u003c\/p\u003e \u003cp\u003e7.1.3 Two formulations of PID-PBC 157\u003c\/p\u003e \u003cp\u003e7.2 Shaping the Energy with a PID 158\u003c\/p\u003e \u003cp\u003e7.3 PID-PBC of port-Hamiltonian Systems 161\u003c\/p\u003e \u003cp\u003e7.3.1 Assumptions on the system 161\u003c\/p\u003e \u003cp\u003e7.3.2 A suitable change of coordinates 163\u003c\/p\u003e \u003cp\u003e7.3.3 Generating new passive outputs 165\u003c\/p\u003e \u003cp\u003e7.3.4 Projection of the total storage function 167\u003c\/p\u003e \u003cp\u003e7.3.5 Main stability result 169\u003c\/p\u003e \u003cp\u003e7.4 PID-PBC of Euler-Lagrange Systems 172\u003c\/p\u003e \u003cp\u003e7.4.1 Passive outputs for Euler-Lagrange systems 173\u003c\/p\u003e \u003cp\u003e7.4.2 Passive outputs for Euler-Lagrange systems in Spong’s normal form 175\u003c\/p\u003e \u003cp\u003e7.5 Extensions 176\u003c\/p\u003e \u003cp\u003e7.5.1 Tracking constant speed trajectories 176\u003c\/p\u003e \u003cp\u003e7.5.2 Removing the cancellation of Va(qa) 178\u003c\/p\u003e \u003cp\u003e7.5.3 Enlarging the class of integral actions 179\u003c\/p\u003e \u003cp\u003e7.6 Examples 180\u003c\/p\u003e \u003cp\u003e7.6.1 Tracking for inverted pendulum on a cart 180\u003c\/p\u003e \u003cp\u003e7.6.2 Cart-pendulum on an inclined plane 182\u003c\/p\u003e \u003cp\u003e7.7 PID-PBC of Constrained Euler-Lagrange Systems 190\u003c\/p\u003e \u003cp\u003e7.7.1 System model and problem formulation 191\u003c\/p\u003e \u003cp\u003e7.7.2 Reduced purely differential model 195\u003c\/p\u003e \u003cp\u003e7.7.3 Design of the PID-PBC 196\u003c\/p\u003e \u003cp\u003e7.7.4 Main stability result 199\u003c\/p\u003e \u003cp\u003e7.7.5 Simulation Results 200\u003c\/p\u003e \u003cp\u003e7.7.6 Experimental Results 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Disturbance Rejection in port-Hamiltonian Systems 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Some Remarks On Notation and Assignable Equilibria 209\u003c\/p\u003e \u003cp\u003e8.1.1 Notational simplifications 209\u003c\/p\u003e \u003cp\u003e8.1.2 Assignable equilibria for constant d 210\u003c\/p\u003e \u003cp\u003e8.2 Integral Action on the Passive Output 211\u003c\/p\u003e \u003cp\u003e8.3 Solution Using Coordinate Changes 214\u003c\/p\u003e \u003cp\u003e8.3.1 A feedback equivalence problem 214\u003c\/p\u003e \u003cp\u003e8.3.2 Local solutions of the feedback equivalent problem 217\u003c\/p\u003e \u003cp\u003e8.3.3 Stability of the closed–loop 219\u003c\/p\u003e \u003cp\u003e8.4 Solution Using Nonseparable Energy Functions 221\u003c\/p\u003e \u003cp\u003e8.4.1 Matched and unmatched disturbances 222\u003c\/p\u003e \u003cp\u003e8.4.2 Robust matched disturbance rejection 225\u003c\/p\u003e \u003cp\u003e8.5 Robust Integral Action for Fully Actuated Mechanical Systems 230\u003c\/p\u003e \u003cp\u003e8.6 Robust Integral Action for Underactuated Mechanical Systems 237\u003c\/p\u003e \u003cp\u003e8.6.1 Standard interconnection and damping assignment PBC 239\u003c\/p\u003e \u003cp\u003e8.6.2 Main result 241\u003c\/p\u003e \u003cp\u003e8.7 A New Robust Integral Action for Underactuated Mechanical Systems 244\u003c\/p\u003e \u003cp\u003e8.7.1 System model 244\u003c\/p\u003e \u003cp\u003e8.7.2 Coordinate transformation 245\u003c\/p\u003e \u003cp\u003e8.7.3 Verification of requisites 246\u003c\/p\u003e \u003cp\u003e8.7.4 Robust integral action controller 248\u003c\/p\u003e \u003cp\u003e8.8 Examples 248\u003c\/p\u003e \u003cp\u003e8.8.1 Mechanical systems with constant inertia matrix 249\u003c\/p\u003e \u003cp\u003e8.8.2 Prismatic robot 250\u003c\/p\u003e \u003cp\u003e8.8.3 The Acrobot system 255\u003c\/p\u003e \u003cp\u003e8.8.4 Disk on disk system 260\u003c\/p\u003e \u003cp\u003e8.8.5 Damped vertical take-off and landing aircraft 265\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Passivity and Stability Theory for State-Space Systems 269\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Characterization of Passive Systems 269\u003c\/p\u003e \u003cp\u003eA.2 Passivity Theorem 271\u003c\/p\u003e \u003cp\u003eA.3 Lyapunov Stability of Passive Systems 273\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Two Stability Results and Assignable Equilibria 275\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Two Stability Results 275\u003c\/p\u003e \u003cp\u003eB.2 Assignable Equilibria 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC Some Differential Geometric Results 279\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 Invariant Manifolds 279\u003c\/p\u003e \u003cp\u003eC.2 Gradient Vector Fields 280\u003c\/p\u003e \u003cp\u003eC.3 A Technical Lemma 281\u003c\/p\u003e \u003cp\u003e\u003cb\u003eD Port-Hamiltonian Systems 283\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eD.1 Definition of port-Hamiltonian Systems and Passivity Property 283\u003c\/p\u003e \u003cp\u003eD.2 Physical Examples 284\u003c\/p\u003e \u003cp\u003eD.3 Euler-Lagrange Models 286\u003c\/p\u003e \u003cp\u003eD.4 Port-Hamiltonian Representation of GAS Systems 288\u003c\/p\u003e \u003cp\u003eIndex 309\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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