Control of Underactuated Mechanical Systems
Stabilisation and Limit Cycle Generation
- 1st Edition - June 2, 2025
- Latest edition
- Authors: Afef Hfaiedh, Ahmed Chemori
- Language: English
Control of Underactuated Mechanical Systems: Stabilization and Limit Cycle Generation clearly explains stabilization and limit cycle generation in underactuated mechanica… Read more
Control of Underactuated Mechanical Systems: Stabilization and Limit Cycle Generation clearly explains stabilization and limit cycle generation in underactuated mechanical systems (UMS),addressing control design challenges and demonstrating concepts through real-time experiments.
The book begins with advancements in UMS, introducing key concepts such as stabilization and limit cycle generation, supported by literature examples. It then focuses on the inertia wheel inverted pendulum, presenting a detailed discussion. The second part tackles stabilization, offering various control solutions validated through numerical simulations and real-time experiments. The final part addresses stable limit cycle generation, detailing three proposed control solutions and their validation through different case studies.
This book is a valuable resource for PhD and Master students, engineers, researchers, and educators. It provides guidance in robotics and automatic control, utilizing a simplified methodology for controlling underactuated mechanical systems.
- Addresses stabilization and stable limit cycle generation in underactuated mechanical systems amid perturbations
- Explores the design, development, and validation of robust control solutions
- Illustrates concepts through case studies
- Validates control solutions with numerical simulations and real-time experiments
Engineers in mechanics, mechatronics, control, and robotics, Researchers and teachers (from academia) in control engineering, mechanics, mechatronics, and robotics, PhD and Master Students, Graduate and undergraduate students from various engineering fields, including, but not limited to, robotics, control engineering, and mechatronics
Part I: General context and case study
I: Introduction and general context of underactuated mechanical systems
1- Introduction
2- Classification of mechanical systems
a) -Fully actuated
b) -Redundant
c) -Underactuated
3- Why research in underactuated mechanical systems?
a) First and second order holonomic constraints
b) Nonlinear dynamics and coupled inputs
c) Non-minimum phase system
d) Uncertainties and parametric variations
4- Stabilization problem
a) Concepts of Stability
b) Basic ideas/definitions
c) Illustrative examples
5- Stable Limit cycle generation problem
a) Definition
b) Stability of limit cycle
c) Illustrative examples of limit cycles:
-Pendulum
-Limit cycle walking
6-Underactuation in broad range of applications
a) Aerospace underactuated systems
b) Flexible systems
c) Locomotive Systems
d) Underactuation in sea vehicles
e) Underactuated mechanical system for education purpose.
7- Literature review about existing control strategies
a) Passivity based control
b) Backstepping control
c) Model predictive control
d) Sliding mode control
e) Intelligent controllers
8- Conclusion
9- References
2: The inertia wheel inverted pendulum case study
1-Introduction
2-System’s detailed description
3-Real-life applications
4-Mathematical modeling of the system
a) Dynamic model
b) Open-loop system
c) Port-Hamiltonian model
d) Linearized model
5- Experimental setup and implementation issues
a) Mechanical part
b) Electrical part
c) Software description
d) Description of the evaluation scenarios
6- Conclusion
7- References
Part II: Control solutions for the stabilisation problem
3: A revisited adaptive sliding mode control scheme
1- Introduction
2- The conventional first-order SMC approach
3- Adaptive sliding mode control for nonlinear systems
4- Proposed adaptive sliding mode control for class I of 2-Dof UMSs
5- Design of sliding mode controller
6- Closed-loop stability analysis
7- Numerical simulation results
8- Real-time experimental results
9- Conclusion
10- References
4: Nonlinear RISE feedback control scheme
1- Introduction
2- Class I of Underactuated mechanical systems
3- RISE controller for SISO systems
4- RISE control for class I
5- Closed-loop stability analysis
6- State estimation with robust Levant differentiator
7- Numerical simulation results
8- Real-time experimental results
9- Conclusion
10- References
5: Model reference adaptive IDA-PBC approach
1- Introduction
2- Standard IDA-PBC controller
3- Model reference adaptive IDA-PBC controller
4- Closed-loop stability analysis
5- Numerical simulation results
6- Real-time experimental results
7- Conclusion
8- References
Part III: Control solutions for stable limit cycle generation problem
6: Partial feedback linearization and optimization
1- Introduction
2- Motivation
a) Partial feedback linearization
b) Reference trajectory generation
c) Proposed control law
d) Illustrative examples
3- Stabilization of the internal dynamics
a) Optimization of reference trajectories
b) Estimation and external disturbance rejection
4- Numerical simulation results
5- Real-time experimental results
6- Conclusion
7- References
7: Nonlinear Model Predictive control
1. Introduction
2. Kangaroo underactuated hopping robot
a) Jump cycle description
b) Kangaroo hopping robot design
c) Robot’s dynamic modelling
3. Control problem formulation
4. Related works
5. Background on Model Predictive Control
6. Proposed running controllers
a) Raibert’s controller
b) NMPC running controller
7. Numerical simulations and results
a) Simulation environment
b) Simulation comparative study
8. Conclusion
9- References
8: Dual Model Free control
1. Introduction
2. background on model-free control
3- Proposed dual model-free control solution
Application 1: The cart-pole inverted pendulum
Application 2: The pendubot
Application 3: The inertia wheel inverted pendulum
5. Conclusion
6. References
I: Introduction and general context of underactuated mechanical systems
1- Introduction
2- Classification of mechanical systems
a) -Fully actuated
b) -Redundant
c) -Underactuated
3- Why research in underactuated mechanical systems?
a) First and second order holonomic constraints
b) Nonlinear dynamics and coupled inputs
c) Non-minimum phase system
d) Uncertainties and parametric variations
4- Stabilization problem
a) Concepts of Stability
b) Basic ideas/definitions
c) Illustrative examples
5- Stable Limit cycle generation problem
a) Definition
b) Stability of limit cycle
c) Illustrative examples of limit cycles:
-Pendulum
-Limit cycle walking
6-Underactuation in broad range of applications
a) Aerospace underactuated systems
b) Flexible systems
c) Locomotive Systems
d) Underactuation in sea vehicles
e) Underactuated mechanical system for education purpose.
7- Literature review about existing control strategies
a) Passivity based control
b) Backstepping control
c) Model predictive control
d) Sliding mode control
e) Intelligent controllers
8- Conclusion
9- References
2: The inertia wheel inverted pendulum case study
1-Introduction
2-System’s detailed description
3-Real-life applications
4-Mathematical modeling of the system
a) Dynamic model
b) Open-loop system
c) Port-Hamiltonian model
d) Linearized model
5- Experimental setup and implementation issues
a) Mechanical part
b) Electrical part
c) Software description
d) Description of the evaluation scenarios
6- Conclusion
7- References
Part II: Control solutions for the stabilisation problem
3: A revisited adaptive sliding mode control scheme
1- Introduction
2- The conventional first-order SMC approach
3- Adaptive sliding mode control for nonlinear systems
4- Proposed adaptive sliding mode control for class I of 2-Dof UMSs
5- Design of sliding mode controller
6- Closed-loop stability analysis
7- Numerical simulation results
8- Real-time experimental results
9- Conclusion
10- References
4: Nonlinear RISE feedback control scheme
1- Introduction
2- Class I of Underactuated mechanical systems
3- RISE controller for SISO systems
4- RISE control for class I
5- Closed-loop stability analysis
6- State estimation with robust Levant differentiator
7- Numerical simulation results
8- Real-time experimental results
9- Conclusion
10- References
5: Model reference adaptive IDA-PBC approach
1- Introduction
2- Standard IDA-PBC controller
3- Model reference adaptive IDA-PBC controller
4- Closed-loop stability analysis
5- Numerical simulation results
6- Real-time experimental results
7- Conclusion
8- References
Part III: Control solutions for stable limit cycle generation problem
6: Partial feedback linearization and optimization
1- Introduction
2- Motivation
a) Partial feedback linearization
b) Reference trajectory generation
c) Proposed control law
d) Illustrative examples
3- Stabilization of the internal dynamics
a) Optimization of reference trajectories
b) Estimation and external disturbance rejection
4- Numerical simulation results
5- Real-time experimental results
6- Conclusion
7- References
7: Nonlinear Model Predictive control
1. Introduction
2. Kangaroo underactuated hopping robot
a) Jump cycle description
b) Kangaroo hopping robot design
c) Robot’s dynamic modelling
3. Control problem formulation
4. Related works
5. Background on Model Predictive Control
6. Proposed running controllers
a) Raibert’s controller
b) NMPC running controller
7. Numerical simulations and results
a) Simulation environment
b) Simulation comparative study
8. Conclusion
9- References
8: Dual Model Free control
1. Introduction
2. background on model-free control
3- Proposed dual model-free control solution
- Basic principle
- Periodic reference trajectories generation
- Control design
Application 1: The cart-pole inverted pendulum
Application 2: The pendubot
Application 3: The inertia wheel inverted pendulum
5. Conclusion
6. References
- Edition: 1
- Latest edition
- Published: June 2, 2025
- Language: English
AH
Afef Hfaiedh
Afef Hfaiedh received her Master’s degree in Automatic Control, Robotics, and Signal Processing in 2015 and her Ph.D. in Automatic Control in 2021. She is a postdoctoral researcher at RISC-LAB and a part-time professor at the University of Tunis El Manar, specializing in nonlinear control applications in robotics and underactuated mechanical systems.
Affiliations and expertise
University of Tunis El Manar, National Engineering School of Tunis, LR16ES07, RISC Lab, Tunis, Tunisia.AC
Ahmed Chemori
Ahmed Chemori earned his M.Sc. and Ph.D. in Automatic Control from the Grenoble Institute of
Technology in 2001 and 2005, respectively. He has worked as a research and teaching assistant and is currently a senior research scientist at LIRMM, University of Montpellier, focusing on nonlinear control and its applications in robotics.
Affiliations and expertise
LIRMM, University of Montpellier, CNRS, Montpellier, France.Read Control of Underactuated Mechanical Systems on ScienceDirect