This book introduces a passivity-based approach which simplifies the controller design task for AC-motors. It presents the application of this novel approach to several classes of AC motors, magnetic levitation systems, microelectromechanical systems (MEMS) and rigid robot manipulators actuated by AC motors.
The novel passivity-based approach exploits the fact that the natural energy exchange existing between the mechanical and the electrical subsystems allows the natural cancellation of several high order terms during the stability analysis. This allows the authors to present some of the simplest controllers proposed in scientific literature, but provided with formal stability proofs. These simple control laws will be of use to practitioners as they are robust with respect to numerical errors and noise amplification, and are provided with tuning guidelines.
Energy-based Control of Electromechanical Systems is intended for both theorists and practitioners. Therefore, the stability proofs are not based on abstract mathematical ideas but Lyapunov stability theory. Several interpretations of the proofs are given along the body of the book using simple energy ideas and the complete proofs are included in appendices. The complete modeling of each motor studied is also presented, allowing for a thorough understanding.
Advances in Industrial Control reports and encourages the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.
Author(s): Victor Manuel Hernández-Guzmán, Ramón Silva-Ortigoza, Jorge Alberto Orrante-Sakanassi
Series: Advances in Industrial Control
Publisher: Springer
Year: 2021
Language: English
Pages: 619
City: Cham
Series Editor’s Foreword
Preface
Acknowledgments
Contents
1 Introduction
2 Mathematical Preliminaries
2.1 Control of Linear Systems
2.2 Mathematical Tools for the Study of Nonlinear Control Systems
2.3 Passivity
2.4 A Novel Passivity-Based Approach for Control of Electromechanical Systems
2.5 The Electromechanical Systems that Are Studied in This Book
3 Permanent Magnet Brushed DC-Motor
3.1 Motor Modeling
3.1.1 A Simple Methodology
3.1.2 A General Methodology
3.2 Standard Control
3.2.1 Case 1
3.2.2 Case 2
3.2.3 Case 3
3.2.4 Case 4
3.2.5 An Improved PI Velocity Controller
3.2.6 An Improved PID Position Controller
3.3 The Standard Control Scheme Revisited
3.4 Open-Loop Energy Exchange
3.4.1 The Velocity Model
3.4.2 The Position Model
3.5 Velocity Control
3.6 Position Control
3.7 Velocity Control Using a DC/DC Buck Power Converter As Power Amplifier
3.7.1 Dynamic Model
3.7.2 Open-Loop Energy Exchange
3.7.3 Control of the DC to DC Buck Converter DC-Motor System
3.7.4 Experimental Results
4 Permanent Magnet Synchronous Motor
4.1 Motor Modeling
4.1.1 The Working Principle
4.1.2 Three-Phase Dynamic Model
4.1.3 Park's Transformation or dq Transformation
4.1.4 The dq Dynamic Model
4.1.5 dq Decomposition of the Stator Magnetic Flux
4.1.6 Standard Field-Oriented Control
4.2 Open-Loop Energy Exchange
4.2.1 The Velocity Model
4.2.2 The Position Model
4.3 Velocity Control
4.3.1 Simulation Results
4.4 Position Control
4.4.1 Simulation Results
4.5 Velocity Ripple Minimization
4.5.1 Mutual Torque
4.5.2 Reluctance Torque
4.5.3 Cogging Torque
4.5.4 Torque Ripple
4.5.5 The Problem to Solve
4.5.6 Stability Analysis
4.5.7 Experimental Results
4.6 A Practical PM Synchronous Motor
4.6.1 Magnetic Field at the Air Gap
4.6.2 Magnetic Flux Linkages
4.6.3 The Motor dq Dynamical Model
4.7 Another Practical PM Synchronous Motor
4.7.1 Magnetic Field at the Air Gap
4.7.2 Magnetic Flux Linkages
4.7.3 The Motor dq Dynamical Model
5 Induction Motor
5.1 Motor Modeling
5.1.1 The Working Principle
5.1.2 Three-Phase Dynamical Model
5.1.3 ab Transformation
5.1.4 The ab Dynamical Model
5.1.5 Park's Transformation or dq Transformation
5.1.6 The dq Dynamical Model
5.1.7 dq Decomposition of the Magnetic Flux
5.1.8 Standard Indirect Field-Oriented Control
5.2 Open-Loop Energy Exchange
5.2.1 The Velocity Model
5.2.2 The Position Model
5.3 Velocity Control
5.3.1 Simulation Results
5.4 Position Control
5.4.1 Simulation Results
5.5 A Practical Induction Motor
5.5.1 Magnetic Field at the Air Gap
5.5.2 The Magnetic Flux Linkages
5.5.3 The Motor Dynamic Model
6 Switched Reluctance Motor
6.1 Motor Modeling
6.1.1 The Working Principle
6.1.2 Magnetic Circuits
6.1.3 SRM Unsaturated Dynamical Model
6.1.4 SRM Saturated Dynamical Model
6.1.5 The Torque Sharing Approach
6.1.6 Standard Control
6.2 Open-Loop Energy Exchange
6.2.1 The Unsaturated Velocity Model
6.2.2 The Saturated and Unsaturated Position Models
6.3 Velocity Control
6.3.1 Simulation Results
6.4 Position Control
6.4.1 Position Control Without Velocity Measurements
6.4.2 Position Control Taking into Account Magnetic Saturation
6.5 A Practical Switched Reluctance Motor
6.5.1 Magnetic Field at the Air Gap
6.5.2 Magnetic Flux Linkages
6.5.3 SRM Dynamical Model
7 Synchronous Reluctance Motor
7.1 Motor Modeling
7.1.1 The Working Principle
7.1.2 dq Dynamical Model
7.1.3 Standard Field-Oriented Control of a SYRM
7.2 Open-Loop Energy Exchange
7.2.1 The Velocity Model
7.2.2 The Position Model
7.3 Velocity Control
7.4 Position Control
8 Bipolar Permanent Magnet Stepper Motor
8.1 Motor Modeling
8.1.1 The Working Principle
8.1.2 Dynamical Model
8.1.3 Standard Control
8.2 Open-Loop Energy Exchange
8.2.1 The Velocity Model
8.2.2 The Position Model
8.3 Velocity Control
8.3.1 Simulation Results
8.4 Position Control
8.4.1 Simulation Results
8.5 A Practical PM Stepper Motor
9 Brushless DC-Motor
9.1 Motor Modeling
9.1.1 Dynamic Model
9.1.2 Standard Control
9.2 Open-Loop Energy Exchange
9.2.1 The Velocity Model
9.2.2 The Position Model
9.3 Velocity Control
9.3.1 Simulation Results
9.4 Position Control
9.4.1 Simulation Results
9.5 A Practical BLDC Motor
9.5.1 Magnetic Field at the Air Gap
9.5.2 Magnetic Flux Linkages
9.5.3 Mathematical Model
10 Magnetic Levitation Systems and Microelectromechanical Systems
10.1 Magnetic Levitation Systems
10.1.1 Mathematical Model
10.1.2 Open-Loop Energy Exchange
10.1.3 Position Control
10.1.4 Simulation Results
10.2 Microelectromechanical Systems
10.2.1 Mathematical Model
10.2.2 Open-Loop Energy Exchange
10.2.3 Position Control
10.2.4 Simulation Study
11 Trajectory Tracking for Robot Manipulators Equipped with PM Synchronous Motors
11.1 Dynamical Model of Robot Manipulators Equipped with PM Synchronous Motors
11.2 Main Result
11.3 Simulation and Experimental Results
11.3.1 Simulation Study
11.3.2 Experimental Results
12 PID Control of Robot Manipulators Equipped with SRMs
12.1 Dynamical Model
12.2 The Torque Sharing Approach
12.3 Main Result
12.3.1 The Rationale Behind Controller in Proposition 12.1
12.3.2 Sketch of Proof of Proposition 12.1
12.3.3 Closed-Loop Dynamics
12.3.4 A Positive Definite and Decrescent Function
12.3.5 Time Derivative of V(y)
12.3.6 Proof of Proposition 12.1
12.4 Simulation Study
Appendix A Energy Functions
A.1 Velocity Control
A.2 Position Control
A.3 Velocity Control with Saturated Integral of Velocity
A.4 PID position Control with Saturated Proportional and Integral Actions
A.5 Velocity Sensorless Regulator for Switched Reluctance Motors
A.6 Trajectory Tracking in Robots Equipped with PM Synchronous Motors
A.6.1 Positive Definiteness and Radially Unboundedness
A.6.2 Expression for Along the Trajectories of the Closed-Loop System
A.6.3 Entries of Matrix Q Introduced in (11.17摥映數爠eflinkRBTtrack:eq:10011.1711)
Appendix B Proofs of Propositions for Brushed DC-Motors
B.1 Proof of Proposition 3.3摥映數爠eflinkPropDCvelStandard3.33
B.2 Proof of Proposition 3.5摥映數爠eflinkPropDCposStandard3.53
B.3 Proof of Proposition 3.8摥映數爠eflinkmain1DCbuck3.83
Appendix C Proofs of Propositions for PM Synchronous Motors
C.1 Proof of Proposition 4.5摥映數爠eflinkpropPMSynMvel14.54
C.2 Proof of Proposition 4.12摥映數爠eflinkPIDpmsmGobalmain14.124
C.3 Proof of Proposition 4.18摥映數爠eflinkpropPMsynMpos14.184
Appendix D Proofs of Propositions for Induction Motors
D.1 Proof of Proposition 5.10摥映數爠eflinkmain1IMspsSsifoc5.105
D.1.1 Stability of the (tildeψdq,tildeId) Subsystem Dynamics
D.1.2 Additional Stability Properties of the (tildeψdq,tildeId) Subsystem Dynamics
D.1.3 Boundedness of the State and Global Convergence to the Origin in the Complete Closed-Loop System
D.2 Proof of Proposition 5.20摥映數爠eflinkmain1IMspsSsifocPos5.205
Appendix E Proofs of Propositions for Switched Reluctance Motors
E.1 A Function to Replace sqrtvertτ*vert, forallvertτ*vertleqT*
E.2 Proof of Proposition 6.1摥映數爠eflinkSRMctrlspsprop16.16
E.3 Proof of Proposition 6.16摥映數爠eflinkposSRMCTRLspspropSat6.166
E.3.1 Closed-Loop Dynamics
E.3.2 A Positive Definite and Decrescent Function
E.3.3 Time Derivative of V(y)
E.3.4 Proof of Proposition 6.16摥映數爠eflinkposSRMCTRLspspropSat6.166
Appendix F Proofs for BLDC Motors
F.1 Proof of Proposition 9.1摥映數爠eflinkposmain1BLDC9.19
F.1.1 Closed-Loop Dynamics
F.1.2 A Positive Definite and Decrescent Function
F.1.3 Time Derivative of V(y)
F.1.4 Proof of Proposition 9.1摥映數爠eflinkposmain1BLDC9.19
F.2 Proof of Proposition 9.7摥映數爠eflinkpropBLDCpend9.79
F.2.1 Closed-Loop Dynamics
F.2.2 A Positive Definite and Decrescent Function
F.2.3 Time Derivative of V(y)
F.2.4 Proof of Proposition 9.7摥映數爠eflinkpropBLDCpend9.79
Appendix G Derivation of Some Expressions for the Proofs in Chap.10摥映數爠eflinkMagLev1010
G.1 Proof of Proposition 10.1摥映數爠eflinkpropMagLevMain10.110
G.2 Proof of Proposition 10.7摥映數爠eflinkpropMEMSMain10.710
Appendix References
Index
