Control of Underactuated Mechanical Systems

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

1. Basic principle
2. Periodic reference trajectories generation
3. Control design

4. Application to underactuated mechanical systems
Application 1: The cart-pole inverted pendulum
Application 2: The pendubot
Application 3: The inertia wheel inverted pendulum

5. Conclusion

6. References