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

Cover
Contents
About the authors
Preface
Acknowledgement
1 Principles of non-linear control
Abstract
1.1 Control based on approximate linearization
1.1.1 Overview of the optimal control concept
1.1.2 Design of an H-infinity non-linear optimal controller
1.1.3 Optimal state estimation with the H-infinity Kalman Filter
1.2 Global linearization-based control concepts
1.2.1 Foundations of global linearization-based control
1.2.2 Elaborating on input–output linearization
1.2.3 Input-state linearization
1.2.4 Stages in the implementation of input-state linearization
1.2.5 Input–output and input-state linearization for MIMO systems
1.2.6 Dynamic extension
1.3 Global linearization-based control using differential flatness theory
1.3.1 The background of differential flatness theory
1.3.2 Differential flatness for finite-dimensional systems
1.3.3 Equivalence and differential flatness
1.3.4 Differential flatness and trajectory planning
1.3.5 Differential flatness, feedback control and equivalence
1.3.6 Flatness-based control and state feedback under the model uncertainties
1.3.7 Classification of types of differentially flat systems
1.4 Control of PDE dynamical systems
1.4.1 Distributed parameter systems and transformation in the canonical form
1.4.2 State-space description of a heat diffusion dynamics
1.4.3 Differential flatness of the non-linear heat-diffusion PDE
1.4.4 Computation of a boundary conditions-based feedback control law
1.4.5 Closed loop dynamics
2 Control based on approximate linearization for robotic systems
Abstract
2.1 Nonlinear control of the cart and double-pendulum overhead crane
2.1.1 Outline
2.1.2 Dynamic model of the double-pendulum overhead crane
2.1.3 Approximate linearization of the double-pendulum overhead crane
2.1.4 Computation of the feedback control gains
2.1.5 Simulation tests
2.2 Nonlinear control of the underactuated offshore crane
2.2.1 Outline
2.2.2 Dynamic model of the boom crane
2.2.3 Approximate linearization of the dynamic model of boom cranes
2.2.4 Computation of the feedback control gains
2.2.5 Simulation tests
2.3 Nonlinear control of the inertia wheel and pendulum system
2.3.1 Outline
2.3.2 Dynamic model of the inertia wheel inverted pendulum
2.3.3 Approximate linearization of the inertia wheel inverted pendulum
2.3.4 Computation of the feedback control gains
2.3.5 Simulation tests
2.4 Nonlinear control of the torsional oscillator with rotational actuator
2.4.1 Outline
2.4.2 Dynamic model of the translational oscillator with rotating actuator
2.4.3 Approximate linearization of the state-space model
2.4.4 Computation of the feedback control gains
2.4.5 Simulation tests
2.5 Nonlinear control of robotic exoskeletons
2.5.1 Outline
2.5.2 Dynamic model of the 2-DOF lower-limb exoskeleton
2.5.3 Approximate linearization of the exoskeleton’s dynamic model
2.5.4 Simulation tests
2.6 Nonlinear control of brachiation robots
2.6.1 Outline
2.6.2 Dynamic model of the multi-DOF brachiation robot
2.6.3 Approximate linearization of the dynamic model of the brachiation robot
2.6.4 Simulation tests
2.7 Nonlinear control of power line inspection robots
2.7.1 Dynamic model of the power line inspection robot
2.7.2 Approximate linearization of the power line inspection robot
2.7.3 Simulation tests
2.8 Nonlinear control of robots with electrohydraulic actuators
2.8.1 Outline
2.8.2 Dynamic model of the multi-DOF electrohydraulic manipulator
2.8.3 Differential flatness properties of the hydraulic robotic manipulator
2.8.4 Approximate linearization of the electro-hydraulic manipulator
2.8.5 Simulation tests
2.9 Nonlinear control of robots with electropneumatic actuators
2.9.1 Outline
2.9.2 Dynamic model of a robotic manipulator with electropneumatic actuators
2.9.3 Approximate linearization of the robot with electropneumatic actuation
2.9.4 Differential flatness of the robot with electropneumatic actuation
2.9.5 Simulation tests
2.10 Nonlinear control of flexible joint robots
2.10.1 Outline
2.10.2 Dynamic model of a multi-DOF robotic manipulator with flexible joints
2.10.3 Approximate linearization of the model of the flexible-joints robot 2.10.4 Jacobian matrices of the linearized model
2.10.5 Simulation tests
2.11 Nonlinear control of redundant robotic manipulators
2.11.1 Outline
2.11.2 Kinematic and dynamic model of the redundant manipulator
2.11.3 Approximate linearization of the model of the redundant manipulator
2.11.4 Simulation tests
2.12 Nonlinear control of parallel closed-chain robotic manipulators
2.12.1 Outline
2.12.2 Dynamic model of the five-link parallel robot
2.12.3 Approximate linearization of the five-link parallel robot
2.12.4 Simulation tests
3 Control based on approximate linearization for autonomous vehicles
Abstract
3.1 Nonlinear control of tracked autonomous vehicles
3.1.1 Outline
3.1.2 Kinematic model of the tracked mobile robot
3.1.3 Approximate linearization of the model of the tracked vehicle
3.1.4 Simulation tests
3.2 Nonlinear control of the autonomous articulated fire-truck
3.2.1 Outline
3.2.2 Kinematic model of the autonomous fire-truck robot
3.2.3 Approximate linearization of the model of the autonomous fire-truck
3.2.4 The nonlinear H-infinity control
3.2.5 Simulation tests
3.3 Nonlinear control of the truck and N-trailer system
3.3.1 Outline
3.3.2 Kinematic model of the truck and N trailer robotic system
3.3.3 Approximate linearization of the truck and N-trailer robotic system
3.3.4 Simulation tests
3.4 Nonlinear control of the ball-bot autonomous robot
3.4.1 Outline
3.4.2 Dynamic model of the ballbot
3.4.3 Approximate linearization of the ballbot’s state-space model
3.4.4 Computation of the feedback control gains
3.4.5 Simulation tests
3.5 Nonlinear control of the ball-and-plate dynamical system
3.5.1 Outline
3.5.2 Dynamic model of the ball and plate system
3.5.3 Approximate linearization of the model of the ball and plate system
3.5.4 Simulation tests
3.6 Nonlinear control of 3-DOF unmanned surface vessels
3.6.1 Outline
3.6.2 Dynamic model of the Unmanned Surface Vessel
3.6.3 Approximate linearization of the USV state-space model
3.6.4 Simulation tests
3.7 Nonlinear control of the 3-DOF autonomous underwater vessel
3.7.1 Outline
3.7.2 Kinematic and dynamic model of the AUV
3.7.3 Differential flatness properties of the AUV’s model
3.7.4 Approximate linearization of the state-space model of the AUV
3.7.5 Simulation tests
3.8 Nonlinear control of the vertical take-off and landing aircraft
3.8.1 Outline
3.8.2 Dynamic model of the vertical take-off and landing aircraft
3.8.3 Differential flatness properties of the VTOL aircraft
3.8.4 Approximate linearization of the VTOL aircraft dynamic model
3.8.5 H-infinity feedback control
3.8.6 Simulation tests
3.9 Nonlinear control of aerial manipulators
3.9.1 Outline
3.9.2 Dynamic model of the aerial robotic manipulator
3.9.3 Approximate linearization of the model of the aerial robotic manipulator
3.9.4 Differential flatness properties of the aerial robotic manipulator
3.9.5 Computation of the feedback control gains
3.9.6 Simulation tests
3.10 Nonlinear control of the 6-DOF autonomous octocopter
3.10.1 Outline
3.10.2 Dynamic model of the octorotor
3.10.3 Approximate linearization of the octorotor’s model
3.10.4 Simulation tests
3.11 Nonlinear control of hypersonic aerial vehicles
3.11.1 Outline
3.11.2 Dynamic model of the autonomous hypersonic aerial vehicle
3.11.3 Differential flatness properties of the hypersonic vehicle
3.11.4 Approximate linearization for the dynamic model of the hypersonic vehicle
3.11.5 Computation of the feedback control gains
3.11.6 Simulation tests
4 Control based on approximate linearization in energy conversion
Abstract
4.1 Nonlinear control of the VSI-fed three-phase PMSM
4.1.1 Outline
4.1.2 Dynamic model of the VSI-PMSM system
4.1.3 Approximate linearization of the inverter-PMSM dynamics
4.1.4 Simulation tests
4.2 Nonlinear control of VSI fed six-phase PMSMs
4.2.1 Outline
4.2.2 Dynamic model of the VSI-fed six-phase PMSM
4.2.3 Differential flatness properties of the VSI-fed six-phase PMSM
4.2.4 Approximate linearization of the model of the VSI-fed six-phase PMSM
4.2.5 Simulation tests
4.3 Nonlinear control of DC electric microgrids
4.3.1 Outline
4.3.2 Dynamic model of the DC microgrid
4.3.3 Approximate linearization of the state-space model of the DC microgrid
4.3.4 Computation of the feedback control gains
4.3.5 Simulation tests
4.4 Nonlinear control of distributed marine-turbine power generation units
4.4.1 Outline
4.4.2 Dynamic model of the distributed marine turbine power generation units
4.4.3 The dynamic model of the distributed power system
4.4.4 Differential flatness of the distributed marine power generation units
4.4.5 Approximate linearization of the distributed marine power generators
4.4.6 Computation of the feedback control gains
4.4.7 Simulation tests
4.5 Nonlinear control of PMLSGs in wave energy conversion systems
4.5.1 Outline
4.5.2 Dynamics of the tubular permanent magnet linear synchronous generators
4.5.3 Approximate linearization of the model of the tubular PMLSG
4.5.4 Computation of the feedback control gains
4.5.5 Simulation tests
4.6 Nonlinear control of Permanent Magnet Brushless DC motors
4.6.1 Outline
4.6.2 Dynamic model of the PMBLDC motor
4.6.3 Differential flatness of the motor with non-sinusoidal back EMF
4.6.4 Computation of the feedback control gains
4.6.5 Simulation tests
4.7 Nonlinear optimal control of Hybrid ElectricVehicles powertrains
4.7.1 Outline
4.7.2 Dynamic model of the HEV power supply/traction system
4.7.3 Approximate linearization of the model of the HEV’s powertrain
4.7.4 Differential flatness properties of the HEV’s powertrain
4.7.5 Computation of the feedback control gains
4.7.6 Simulation tests
4.8 Nonlinear control of shipboardAC/DC microgrids
4.8.1 Outline
4.8.2 Dynamic model of the shipboard AC/DC microgrid
4.8.3 Computation of the feedback control gains
4.8.4 Simulation tests
4.9 Nonlinear control of power generation in hybridAC/DC microgrids
4.9.1 Outline
4.9.2 Dynamic model of the hybrid distributed microgrid
4.9.3 Approximate linearization of the dynamic model of the hybrid microgrid
4.9.4 Computation of the feedback control gains
4.9.5 Differential flatness properties of the dynamic model of the microgrid
4.9.6 Simulation tests
5 Control based on approximate linearization for mechatronic systems
Abstract
5.1 Nonlinear control of electrohydraulic actuators
5.1.1 Outline
5.1.2 Dynamic model of the electrohydraulic actuator
5.1.3 Approximate linearization of the electrohydraulic actuator’s model
5.1.4 Simulation tests
5.2 Nonlinear control of electropneumatic actuators
5.2.1 Outline
5.2.2 Dynamic model of the electropneumatic actuator
5.2.3 Approximate linearization of the model of the electropneumatic actuator
5.2.4 Differential flatness properties of the electropneumatic actuator
5.2.5 Simulation tests
5.3 Nonlinear control of hot-steel rolling mills
5.3.1 Outline
5.3.2 Dynamic model of the hot-steel rolling mill
5.3.3 Approximate linearization of the hot-steel rolling mill dynamics
5.3.4 Computation of the feedback control gains
5.3.5 Simulation tests
5.4 Nonlinear control of paper mills
5.4.1 Outline
5.4.2 Dynamic model of the mechanical pulping process in paper mills
5.4.3 Approximate linearization of the state-space model of the pulping process
5.4.4 Stabilizing feedback control
5.4.5 Simulation tests
5.5 Nonlinear control of the injection moulding machine
5.5.1 Outline
5.5.2 Dynamic model of the injection moulding process
5.5.3 Stable feedback control of the injection moulding process
5.5.4 Simulation tests
5.6 Nonlinear control of the slosh-container system dynamics
5.6.1 Outline
5.6.2 Dynamic model of the slosh-container system
5.6.3 Approximate linearization of the model of the slosh-container system
5.6.4 Simulation tests
5.7 Nonlinear control of micro-satellites’ attitude dynamics
5.7.1 Introduction
5.7.2 Dynamic model of the micro-satellite attitude system
5.7.3 Approximate linearization of the satellite’s state-space model
5.7.4 Simulation tests
5.8 Nonlinear control of the industrial crystallization process
5.8.1 Outline
5.8.2 Dynamic model of the industrial crystallization process
5.8.3 Approximate linearization of the dynamics of the crystallization process
5.8.4 Simulation tests
6 Control based on global linearisation for industrial and PDE systems
Abstract
6.1 Control of a robotic exoskeleton subject to time-delays
6.1.1 Outline
6.1.2 Dynamic model of the robotic exoskeleton
6.1.3 Estimation of perturbations with the use of a disturbance observer
6.1.4 Simulation tests
6.2 Adaptive control of synchronous reluctance machines
6.2.1 Outline
6.2.2 Dynamic model of the synchronous reluctance machines
6.2.3 Differential flatness of the synchronous reluctance machine
6.2.4 Flatness-based adaptive neurofuzzy control
6.2.5 Application of flatness-based adaptive neurofuzzy control to the SRM
6.2.6 Lyapunov stability analysis
6.2.7 Simulation tests
6.3 Control of a mobile robotic manipulator
6.3.1 Outline
6.3.2 Dynamic model of the mobile manipulator
6.3.3 Differential flatness properties of the model of the mobile manipulator
6.3.4 Design of a flatness-based controller for the mobile manipulator
6.3.5 Design of a flatness-based disturbances estimator
6.3.6 Simulation tests
6.4 State of charge estimation in EVs with a KF-based disturbance observer
6.4.1 Outline
6.4.2 Dynamic model of the battery
6.4.3 Kalman Filter-based disturbance observer
6.4.4 Simulation tests
6.5 Control of nonlinear wave PDE dynamics
6.5.1 Outline
6.5.2 Transformation of the PDE model into a set of nonlinear ODEs
6.5.3 Differential flatness of the nonlinear PDE model
6.5.4 Computation of a boundary conditions-based feedback control law
6.5.5 Closed-loop dynamics
6.5.6 Simulation tests
6.6 Control of data-flow PDE for bandwidth allocation in internet routes
6.6.1 Outline
6.6.2 PDE of the internet flow per route
6.6.3 Data flow model
6.6.4 Differential flatness of the data flow model
6.6.5 Flatness-based control for the data-flow model
6.6.6 Stability analysis for the data-flow control loop
6.6.7 Simulation tests
6.7 Diffusion PDE control of data flow in communication networks
6.7.1 Outline
6.7.2 Model of diffusion describing data flow in the communication network
6.7.3 Transformation of the Fokker-Planck PDE into a set of nonlinear ODEs
6.7.4 Differential flatness of the Fokker–Planck PDE model
6.7.5 Computation of a boundary conditions-based feedback control law
6.7.6 Closed-loop dynamics
6.7.7 Simulation tests
6.8 Control of the diffusion PDE in Li-ion batteries
6.8.1 Outline
6.8.2 Diffusion PDE in Li-ion batteries
6.8.3 Modeling in state-space form of the of the Li-ions diffusion PDE
6.8.4 Differential flatness of the battery’s PDE diffusion model
6.8.5 Computation of a boundary conditions-based feedback control law
6.8.6 Closed-loop dynamics
6.8.7 State estimation for the PDE diffusion model
6.8.8 Simulation tests
6.9 Control of the diffusion PDE in financial assets’ management
6.9.1 Outline
6.9.2 Dynamic model of stock-loans valuation
6.9.3 Transformation of the stock-loan PDE into a set of nonlinear ODEs
6.9.4 Differential flatness of the stock-loan PDE model
6.9.5 Computation of a boundary conditions-based feedback control law
6.9.6 Closed-loop dynamics
6.9.7 Simulation tests
6.10 Estimation of PDE dynamics of the highway traffic
6.10.1 Outline
6.10.2 Traffic modeling with the use of PDEs
6.10.3 Estimation of the Payne–Whitham model using Extended Kalman Filter
6.10.4 Estimation of Payne–Whitham PDE with the derivative-free KF
6.10.5 Derivative-free nonlinear Kalman Filter for the Payne–Whitham PDE
6.10.6 Simulation tests
6.11 Estimation of the PDE dynamics of a cable-suspended bridge
6.11.1 Outline
6.11.2 Dynamic model of the suspended-bridge and vehicle interaction
6.11.3 Kalman Filtering for state-estimation in the bridge and vehicle system
6.11.4 Statistical fault diagnosis using the Kalman Filter
6.11.5 Simulation tests
Epilogue
Glossary
References
Index
Back Cover