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E-raamat: Control and Estimation of Dynamical Nonlinear and Partial Differential Equation Systems: Theory and applications

(Industrial Systems Institute, Unit of Industrial Automation, Greece), (GE Research Center, Niskayuna, NY, USA), (University of Salerno, Department of Management & Innovation Systems, Smart Grids and Smart Cities Laboratory, Italy)
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  • Sari: Control, Robotics and Sensors
  • Ilmumisaeg: 08-Jul-2022
  • Kirjastus: Institution of Engineering and Technology
  • Keel: eng
  • ISBN-13: 9781839534270
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Control and Estimation of Dynamical Nonlinear and Partial Differential Equation Systems: Theory and applicationsSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Control, Robotics and Sensors
  • Ilmumisaeg: 08-Jul-2022
  • Kirjastus: Institution of Engineering and Technology
  • Keel: eng
  • ISBN-13: 9781839534270
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In this comprehensive reference, the authors present new and innovative control and estimation methods based on dynamical nonlinear and partial differential equation systems, which are used in solving control problems such as stability and robustness issues in robotics, mechatronics, and other engineering applications.



Robotic and mechatronic systems, autonomous vehicles, electric power systems and smart grids, as well as manufacturing and industrial production systems can exhibit complex nonlinear dynamics or spatio-temporal dynamics which need to be controlled to ensure good functioning and performance.

In this comprehensive reference, the authors present new and innovative control and estimation methods and techniques based on dynamical nonlinear and partial differential equation systems. Such results can be classified in five main domains for the control of complex nonlinear dynamical systems using respectively methods of approximate (local) linearization, methods of exact (global) linearization, Lyapunov stability approaches, control and estimation of distributed parameter systems and stochastic estimation and fault diagnosis methods.

Control and Estimation of Dynamical Nonlinear and Partial Differential Equation Systems: Theory and applications will be of interest to electrical engineering, physics, computer science, robotics and mechatronics researchers and professionals working on control problems, condition monitoring, estimation and fault diagnosis and isolation problems. It will also be useful to skilled technical personnel working on applications in robotics, energy conversion, transportation and manufacturing.

About the authors xix
Preface xxi
Acknowledgement xxvii
1 Principles of non-linear control
1(62)
1.1 Control based on approximate linearization
1(15)
1.1.1 Overview of the optimal control concept
1(4)
1.1.2 Design of an H-infinity non-linear optimal controller
5(7)
1.1.3 Optimal state estimation with the H-infinity Kalman Filter
12(4)
1.2 Global linearization-based control concepts
16(18)
1.2.1 Foundations of global linearization-based control
16(7)
1.2.2 Elaborating on input-output linearization
23(3)
1.2.3 Input-state linearization
26(5)
1.2.4 Stages in the implementation of input-state linearization
31(1)
1.2.5 Input-output and input-state linearization for MIMO systems
32(1)
1.2.6 Dynamic extension
33(1)
1.3 Global linearization-based control using differential flatness theory
34(20)
1.3.1 The background of differential flatness theory
34(1)
1.3.2 Differential flatness for finite-dimensional systems
35(1)
1.3.3 Equivalence and differential flatness
36(4)
1.3.4 Differential flatness and trajectory planning
40(3)
1.3.5 Differential flatness, feedback control and equivalence
43(4)
1.3.6 Flatness-based control and state feedback under the model uncertainties
47(2)
1.3.7 Classification of types of differentially flat systems
49(5)
1.4 Control of PDE dynamical systems
54(9)
1.4.1 Distributed parameter systems and transformation in the canonical form
54(1)
1.4.2 State-space description of a heat diffusion dynamics
54(3)
1.4.3 Differential flatness of the non-linear heat-diffusion PDE
57(2)
1.4.4 Computation of a boundary conditions-based feedback control law
59(2)
1.4.5 Closed loop dynamics
61(2)
2 Control based on approximate linearization for robotic systems
63(222)
2.1 Nonlinear control of the cart and double-pendulum overhead crane
63(15)
2.1.1 Outline
63(2)
2.1.2 Dynamic model of the double-pendulum overhead crane
65(3)
2.1.3 Approximate linearization of the double-pendulum overhead crane
68(5)
2.1.4 Computation of the feedback control gains
73(2)
2.1.5 Simulation tests
75(3)
2.2 Nonlinear control of the underactuated offshore crane
78(17)
2.2.1 Outline
78(5)
2.2.2 Dynamic model of the boom crane
83(4)
2.2.3 Approximate linearization of the dynamic model of boom cranes
87(5)
2.2.4 Computation of the feedback control gains
92(1)
2.2.5 Simulation tests
92(3)
2.3 Nonlinear control of the inertia wheel and pendulum system
95(12)
2.3.1 Outline
95(5)
2.3.2 Dynamic model of the inertia wheel inverted pendulum
100(2)
2.3.3 Approximate linearization of the inertia wheel inverted pendulum
102(1)
2.3.4 Computation of the feedback control gains
102(2)
2.3.5 Simulation tests
104(3)
2.4 Nonlinear control of the torsional oscillator with rotational actuator
107(12)
2.4.1 Outline
107(2)
2.4.2 Dynamic model of the translational oscillator with rotating actuator
109(2)
2.4.3 Approximate linearization of the state-space model
111(2)
2.4.4 Computation of the feedback control gains
113(1)
2.4.5 Simulation tests
114(5)
2.5 Nonlinear control of robotic exoskeletons
119(13)
2.5.1 Outline
119(1)
2.5.2 Dynamic model of the 2-DOF lower-limb exoskeleton
120(5)
2.5.3 Approximate linearization of the exoskeleton's dynamic model
125(3)
2.5.4 Simulation tests
128(4)
2.6 Nonlinear control of brachiation robots
132(23)
2.6.1 Outline
132(2)
2.6.2 Dynamic model of the multi-DOF brachiation robot
134(7)
2.6.3 Approximate linearization of the dynamic model of the brachiation robot
141(8)
2.6.4 Simulation tests
149(6)
2.7 Nonlinear control of power line inspection robots
155(14)
2.7.1 Dynamic model of the power line inspection robot
158(5)
2.7.2 Approximate linearization of the power line inspection robot
163(2)
2.7.3 Simulation tests
165(4)
2.8 Nonlinear control of robots with electrohydraulic actuators
169(11)
2.8.1 Outline
169(1)
2.8.2 Dynamic model of the multi-DOF electrohydraulic manipulator
170(4)
2.8.3 Differential flatness properties of the hydraulic robotic manipulator
174(2)
2.8.4 Approximate linearization of the electro-hydraulic manipulator
176(4)
2.8.5 Simulation tests
180(1)
2.9 Nonlinear control of robots with electropneumatic actuators
180(31)
2.9.1 Outline
180(9)
2.9.2 Dynamic model of a robotic manipulator with electropneumatic actuators
189(6)
2.9.3 Approximate linearization of the robot with electropneumatic actuation
195(10)
2.9.4 Differential flatness of the robot with electropneumatic actuation
205(2)
2.9.5 Simulation tests
207(4)
2.10 Nonlinear control of flexible joint robots
211(21)
2.10.1 Outline
211(6)
2.10.2 Dynamic model of a multi-DOF robotic manipulator with flexible joints
217(6)
2.10.3 Approximate linearization of the model of the flexible-joints robot
223(1)
2.10.4 Jacobian matrices of the linearized model
223(4)
2.10.5 Simulation tests
227(5)
2.11 Nonlinear control of redundant robotic manipulators
232(19)
2.11.1 Outline
232(5)
2.11.2 Kinematic and dynamic model of the redundant manipulator
237(6)
2.11.3 Approximate linearization of the model of the redundant manipulator
243(7)
2.11.4 Simulation tests
250(1)
2.12 Nonlinear control of parallel closed-chain robotic manipulators
251(34)
2.12.1 Outline
251(10)
2.12.2 Dynamic model of the five-link parallel robot
261(6)
2.12.3 Approximate linearization of the five-link parallel robot
267(8)
2.12.4 Simulation tests
275(10)
3 Control based on approximate linearization for autonomous vehicles
285(172)
3.1 Nonlinear control of tracked autonomous vehicles
285(13)
3.1.1 Outline
285(2)
3.1.2 Kinematic model of the tracked mobile robot
287(4)
3.1.3 Approximate linearization of the model of the tracked vehicle
291(2)
3.1.4 Simulation tests
293(5)
3.2 Nonlinear control of the autonomous articulated fire-truck
298(8)
3.2.1 Outline
298(1)
3.2.2 Kinematic model of the autonomous fire-truck robot
299(3)
3.2.3 Approximate linearization of the model of the autonomous fire-truck
302(1)
3.2.4 The nonlinear H-infinity control
303(2)
3.2.5 Simulation tests
305(1)
3.3 Nonlinear control of the truck and N-trailer system
306(20)
3.3.1 Outline
306(6)
3.3.2 Kinematic model of the truck and N trailer robotic system
312(4)
3.3.3 Approximate linearization of the truck and N-trailer robotic system
316(4)
3.3.4 Simulation tests
320(6)
3.4 Nonlinear control of the ball-bot autonomous robot
326(14)
3.4.1 Outline
326(1)
3.4.2 Dynamic model of the ballbot
327(5)
3.4.3 Approximate linearization of the ballbot's state-space model
332(3)
3.4.4 Computation of the feedback control gains
335(1)
3.4.5 Simulation tests
336(4)
3.5 Nonlinear control of the ball-and-plate dynamical system
340(12)
3.5.1 Outline
340(2)
3.5.2 Dynamic model of the ball and plate system
342(3)
3.5.3 Approximate linearization of the model of the ball and plate system
345(5)
3.5.4 Simulation tests
350(2)
3.6 Nonlinear control of 3-DOF unmanned surface vessels
352(22)
3.6.1 Outline
352(7)
3.6.2 Dynamic model of the Unmanned Surface Vessel
359(6)
3.6.3 Approximate linearization of the USV state-space model
365(7)
3.6.4 Simulation tests
372(2)
3.7 Nonlinear control of the 3-DOF autonomous underwater vessel
374(14)
3.7.1 Outline
374(7)
3.7.2 Kinematic and dynamic model of the AUV
381(1)
3.7.3 Differential flatness properties of the AUV's model
382(1)
3.7.4 Approximate linearization of the state-space model of the AUV
383(2)
3.7.5 Simulation tests
385(3)
3.8 Nonlinear control of the vertical take-off and landing aircraft
388(17)
3.8.1 Outline
388(7)
3.8.2 Dynamic model of the vertical take-off and landing aircraft
395(1)
3.8.3 Differential flatness properties of the VTOL aircraft
396(1)
3.8.4 Approximate linearization of the VTOL aircraft dynamic model
397(1)
3.8.5 H-infinity feedback control
397(2)
3.8.6 Simulation tests
399(6)
3.9 Nonlinear control of aerial manipulators
405(16)
3.9.1 Outline
405(1)
3.9.2 Dynamic model of the aerial robotic manipulator
406(7)
3.9.3 Approximate linearization of the model of the aerial robotic manipulator
413(4)
3.9.4 Differential flatness properties of the aerial robotic manipulator
417(1)
3.9.5 Computation of the feedback control gains
418(1)
3.9.6 Simulation tests
419(2)
3.10 Nonlinear control of the 6-DOF autonomous octocopter
421(20)
3.10.1 Outline
421(6)
3.10.2 Dynamic model of the octorotor
427(4)
3.10.3 Approximate linearization of the octorotor's model
431(3)
3.10.4 Simulation tests
434(7)
3.11 Nonlinear control of hypersonic aerial vehicles
441(16)
3.11.1 Outline
441(1)
3.11.2 Dynamic model of the autonomous hypersonic aerial vehicle
442(3)
3.11.3 Differential flatness properties of the hypersonic vehicle
445(3)
3.11.4 Approximate linearization for the dynamic model of the hypersonic vehicle
448(2)
3.11.5 Computation of the feedback control gains
450(1)
3.11.6 Simulation tests
451(6)
4 Control based on approximate linearization in energy conversion
457(164)
4.1 Nonlinear control of the VSI-fed three-phase PMSM
457(16)
4.1.1 Outline
457(2)
4.1.2 Dynamic model of the VSI-PMSM system
459(5)
4.1.3 Approximate linearization of the inverter-PMSM dynamics
464(4)
4.1.4 Simulation tests
468(5)
4.2 Nonlinear control of VSI fed six-phase PMSMs
473(31)
4.2.1 Outline
473(3)
4.2.2 Dynamic model of the VSI-fed six-phase PMSM
476(11)
4.2.3 Differential flatness properties of the VSI-fed six-phase PMSM
487(4)
4.2.4 Approximate linearization of the model of the VSI-fed six-phase PMSM
491(4)
4.2.5 Simulation tests
495(9)
4.3 Nonlinear control of DC electric microglias
504(11)
4.3.1 Outline
504(1)
4.3.2 Dynamic model of the DC raicrogrid
505(3)
4.3.3 Approximate linearization of the state-space model of the DC microgrid
508(2)
4.3.4 Computation of the feedback control gains
510(2)
4.3.5 Simulation tests
512(3)
4.4 Nonlinear control of distributed marine-turbine power generation units
515(21)
4.4.1 Outline
515(2)
4.4.2 Dynamic model of the distributed marine turbine power generation units
517(1)
4.4.3 The dynamic model of the distributed power system
517(6)
4.4.4 Differential flatness of the distributed marine power generation units
523(1)
4.4.5 Approximate linearization of the distributed marine power generators
524(3)
4.4.6 Computation of the feedback control gains
527(1)
4.4.7 Simulation tests
528(8)
4.5 Nonlinear control of PMLSGs in wave energy conversion systems
536(10)
4.5.1 Outline
536(1)
4.5.2 Dynamics of the tubular permanent magnet linear synchronous generators
537(4)
4.5.3 Approximate linearization of the model of the tubular PMLSG
541(1)
4.5.4 Computation of the feedback control gains
542(1)
4.5.5 Simulation tests
542(4)
4.6 Nonlinear control of Permanent Magnet Brushless DC motors
546(12)
4.6.1 Outline
546(1)
4.6.2 Dynamic model of the PMBLDC motor
547(6)
4.6.3 Differential flatness of the motor with non-sinusoidal back EMF
553(1)
4.6.4 Computation of the feedback control gains
554(1)
4.6.5 Simulation tests
554(4)
4.7 Nonlinear optimal control of Hybrid Electric Vehicles powertrains
558(19)
4.7.1 Outline
558(1)
4.7.2 Dynamic model of the HEV power supply/traction system
559(4)
4.7.3 Approximate linearization of the model of the HEV's powertrain
563(2)
4.7.4 Differential flatness properties of the HEV's powertrain
565(2)
4.7.5 Computation of the feedback control gains
567(2)
4.7.6 Simulation tests
569(8)
4.8 Nonlinear control of shipboard AC/DC microgrids
577(20)
4.8.1 Outline
577(2)
4.8.2 Dynamic model of the shipboard AC/DC microgrid
579(5)
4.8.3 Computation of the feedback control gains
584(4)
4.8.4 Simulation tests
588(9)
4.9 Nonlinear control of power generation in hybrid AC/DC microgrids
597(24)
4.9.1 Outline
597(2)
4.9.2 Dynamic model of the hybrid distributed microgrid
599(5)
4.9.3 Approximate linearization of the dynamic model of the hybrid microgrid
604(3)
4.9.4 Computation of the feedback control gains
607(2)
4.9.5 Differential flatness properties of the dynamic model of the microgrid
609(6)
4.9.6 Simulation tests
615(6)
5 Control based on approximate linearization for mechatronic systems
621(108)
5.1 Nonlinear control of electrohydraulic actuators
621(11)
5.1.1 Outline
621(2)
5.1.2 Dynamic model of the electrohydraulic actuator
623(3)
5.1.3 Approximate linearization of the electrohydraulic actuator's model
626(3)
5.1.4 Simulation tests
629(3)
5.2 Nonlinear control of electropneumatic actuators
632(16)
5.2.1 Outline
632(2)
5.2.2 Dynamic model of the electropneumatic actuator
634(3)
5.2.3 Approximate linearization of the model of the electropneumatic actuator
637(5)
5.2.4 Differential flatness properties of the electropneumatic actuator
642(3)
5.2.5 Simulation tests
645(3)
5.3 Nonlinear control of hot-steel rolling mills
648(11)
5.3.1 Outline
648(2)
5.3.2 Dynamic model of the hot-steel rolling mill
650(4)
5.3.3 Approximate linearization of the hot-steel rolling mill dynamics
654(1)
5.3.4 Computation of the feedback control gains
655(1)
5.3.5 Simulation tests
656(3)
5.4 Nonlinear control of paper mills
659(15)
5.4.1 Outline
659(2)
5.4.2 Dynamic model of the mechanical pulping process in paper mills
661(5)
5.4.3 Approximate linearization of the state-space model of the pulping process
666(1)
5.4.4 Stabilizing feedback control
667(1)
5.4.5 Simulation tests
668(6)
5.5 Nonlinear control of the injection moulding machine
674(12)
5.5.1 Outline
674(2)
5.5.2 Dynamic model of the injection moulding process
676(5)
5.5.3 Stable feedback control of the injection moulding process
681(2)
5.5.4 Simulation tests
683(3)
5.6 Nonlinear control of the slosh-container system dynamics
686(14)
5.6.1 Outline
686(2)
5.6.2 Dynamic model of the slosh-container system
688(5)
5.6.3 Approximate linearization of the model of the slosh-container system
693(2)
5.6.4 Simulation tests
695(5)
5.7 Nonlinear control of micro-satellites' attitude dynamics
700(13)
5.7.1 Introduction
700(2)
5.7.2 Dynamic model of the micro-satellite attitude system
702(2)
5.7.3 Approximate linearization of the satellite's state-space model
704(5)
5.7.4 Simulation tests
709(4)
5.8 Nonlinear control of the industrial crystallization process
713(16)
5.8.1 Outline
713(5)
5.8.2 Dynamic model of the industrial crystallization process
718(2)
5.8.3 Approximate linearization of the dynamics of the crystallization process
720(3)
5.8.4 Simulation tests
723(6)
6 Control based on global linearisation for industrial and PDE systems
729(168)
6.1 Control of a robotic exoskeleton subject to time-delays
729(15)
6.1.1 Outline
729(2)
6.1.2 Dynamic model of the robotic exoskeleton
731(6)
6.1.3 Estimation of perturbations with the use of a disturbance observer
737(3)
6.1.4 Simulation tests
740(4)
6.2 Adaptive control of synchronous reluctance machines
744(24)
6.2.1 Outline
744(2)
6.2.2 Dynamic model of the synchronous reluctance machines
746(2)
6.2.3 Differential flatness of the synchronous reluctance machine
748(2)
6.2.4 Flatness-based adaptive neurofuzzy control
750(6)
6.2.5 Application of flatness-based adaptive neurofuzzy control to the SRM
756(4)
6.2.6 Lyapunov stability analysis
760(5)
6.2.7 Simulation tests
765(3)
6.3 Control of a mobile robotic manipulator
768(19)
6.3.1 Outline
768(1)
6.3.2 Dynamic model of the mobile manipulator
769(5)
6.3.3 Differential flatness properties of the model of the mobile manipulator
774(1)
6.3.4 Design of a flatness-based controller for the mobile manipulator
775(1)
6.3.5 Design of a flatness-based disturbances estimator
776(3)
6.3.6 Simulation tests
779(8)
6.4 State of charge estimation in EVs with a KF-based disturbance observer
787(8)
6.4.1 Outline
787(1)
6.4.2 Dynamic model of the battery
788(3)
6.4.3 Kalman Filter-based disturbance observer
791(1)
6.4.4 Simulation tests
792(3)
6.5 Control of nonlinear wave PDE dynamics
795(11)
6.5.1 Outline
795(1)
6.5.2 Transformation of the PDE model into a set of nonlinear ODEs
796(2)
6.5.3 Differential flatness of the nonlinear PDE model
798(1)
6.5.4 Computation of a boundary conditions-based feedback control law
799(3)
6.5.5 Closed-loop dynamics
802(1)
6.5.6 Simulation tests
803(3)
6.6 Control of data-flow PDE for bandwidth allocation in internet routes
806(11)
6.6.1 Outline
806(2)
6.6.2 PDE of the internet flow per route
808(2)
6.6.3 Data flow model
810(1)
6.6.4 Differential flatness of the data flow model
811(1)
6.6.5 Flatness-based control for the data-flow model
812(1)
6.6.6 Stability analysis for the data-flow control loop
812(2)
6.6.7 Simulation tests
814(3)
6.7 Diffusion PDE control of data flow in communication networks
817(13)
6.7.1 Outline
817(2)
6.7.2 Model of diffusion describing data flow in the communication network
819(1)
6.7.3 Transformation of the Fokker-Planck PDE into a set of nonlinear ODEs
820(1)
6.7.4 Differential flatness of the Fokker-Planck PDE model
821(2)
6.7.5 Computation of a boundary conditions-based feedback control law
823(2)
6.7.6 Closed-loop dynamics
825(2)
6.7.7 Simulation tests
827(3)
6.8 Control of the diffusion PDE in Li-ion batteries
830(15)
6.8.1 Outline
830(1)
6.8.2 Diffusion PDE in Li-ion batteries
830(4)
6.8.3 Modeling in state-space form of the of the Li-ions diffusion PDE
834(1)
6.8.4 Differential flatness of the battery's PDE diffusion model
835(2)
6.8.5 Computation of a boundary conditions-based feedback control law
837(1)
6.8.6 Closed-loop dynamics
838(2)
6.8.7 State estimation for the PDE diffusion model
840(3)
6.8.8 Simulation tests
843(2)
6.9 Control of the diffusion PDE in financial assets' management
845(17)
6.9.1 Outline
845(2)
6.9.2 Dynamic model of stock-loans valuation
847(2)
6.9.3 Transformation of the stock-loan PDE into a set of nonlinear ODEs
849(4)
6.9.4 Differential flatness of the stock-loan PDE model
853(2)
6.9.5 Computation of a boundary conditions-based feedback control law
855(2)
6.9.6 Closed-loop dynamics
857(2)
6.9.7 Simulation tests
859(3)
6.10 Estimation of PDE dynamics of the highway traffic
862(16)
6.10.1 Outline
862(1)
6.10.2 Traffic modeling with the use of PDEs
863(2)
6.10.3 Estimation of the Payne--Whitham model using Extended Kalman Filter
865(4)
6.10.4 Estimation of Payne-Whitham PDE with the derivative-free KF
869(2)
6.10.5 Derivative-free nonlinear Kalman Filter for the Payne-Whitham PDE
871(4)
6.10.6 Simulation tests
875(3)
6.11 Estimation of the PDE dynamics of a cable-suspended bridge
878(19)
6.11.1 Outline
878(2)
6.11.2 Dynamic model of the suspended-bridge and vehicle interaction
880(6)
6.11.3 Kalman Filtering for state-estimation in the bridge and vehicle system
886(4)
6.11.4 Statistical fault diagnosis using the Kalman Filter
890(3)
6.11.5 Simulation tests
893(4)
Epilogue 897(2)
Glossary 899(2)
References 901(100)
Index 1001
Gerasimos Rigatos is research director at the Industrial Systems Institute, Greece. He has led research cooperation projects in the areas of nonlinear control, nonlinear filtering and control of distributed parameter systems. His results have appeared in eight research monographs and more than 120 journal articles. He has held visiting professor positions at several academic institutes and is a senior member of the IEEE and a member and CEng of the IET.



Masoud Abbaszadeh is a principal research engineer at GE Research Center, Niskayuna, NY, USA. He has also held an adjunct professor position at Rensselaer Polytechnic Institute, NY, USA. His research interests include estimation and detection theory, robust and nonlinear control, and machine learning with applications in diagnostics, cyber-physical resilience and autonomous systems. He serves as an associate editor of IEEE Transactions on Control Systems Technology, and a member of IEEE CSS Conference Editorial Board.



Pierluigi Siano is a professor and scientific director of the Smart Grids and Smart Cities Laboratory with the Department of Management & Innovation Systems, University of Salerno, Italy. He is also a distinguished visiting professor in the Department of Electrical & Electronic Engineering Science, University of Johannesburg. His research activities are centered on demand response, energy management, the integration of distributed energy resources in smart grids, electricity markets and planning and management of power systems.
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