On the method of interconnection and damping assignment passivity-based control for the stabilization of mechanical systems
TLDR
In this article, the use of quadratic gyroscopic forces is proposed in place of the skew-symmetric interconnection submatrix in the conventional form of IDA-PBC, which is shown to have some redundancy for systems with the number of degrees of freedom greater than two.Abstract:
Interconnection and damping assignment passivity-based control (IDA-PBC) is an excellent method to stabilize mechanical systems in the Hamiltonian formalism. In this paper, several improvements are made on the IDA-PBC method. The skew-symmetric interconnection submatrix in the conventional form of IDA-PBC is shown to have some redundancy for systems with the number of degrees of freedom greater than two, containing unnecessary components that do not contribute to the dynamics. To completely remove this redundancy, the use of quadratic gyroscopic forces is proposed in place of the skew-symmetric interconnection submatrix. Reduction of the number of matching partial differential equations in IDA-PBC and simplification of the structure of the matching partial differential equations are achieved by eliminating the gyroscopic force from the matching partial differential equations. In addition, easily verifiable criteria are provided for Lyapunov/exponential stabilizability by IDA-PBC for all linear controlled Hamiltonian systems with arbitrary degrees of underactuation and for all nonlinear controlled Hamiltonian systems with one degree of underactuation. A general design procedure for IDA-PBC is given and illustrated with examples. The duality of the new IDA-PBC method to the method of controlled Lagrangians is discussed. This paper renders the IDA-PBC method as powerful as the controlled Lagrangian method.read more
Citations
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Journal ArticleDOI
Simultaneous interconnection and damping assignment passivity-based control of mechanical systems using dissipative forces
TL;DR: Two modifications to the standard IDA-PBC method are presented, it is proposed to avoid the splitting of the control action into energy-shaping and damping injection terms, but instead to carry them out simultaneously and to consider the inclusion of dissipative forces.
Book ChapterDOI
Passivity-Based Control of Mechanical Systems
TL;DR: In this article, the authors briefly recall the history of PBC of mechanical systems and summarize its main recent developments, including an explicit formula for one of the free tuning gains that simplifies the computations, addition of PID controllers to robustify and make constructive the PBC design and to track ramp references.
Journal ArticleDOI
On the matching equations of energy shaping controllers for mechanical systems
TL;DR: This paper proves that the claim that considering a more general form for the target dynamic forces that relax the skew-symmetry condition further reduces the number of KE PDEs is wrong.
Journal ArticleDOI
Designing of robust adaptive passivity-based controller based on reinforcement learning for nonlinear port-Hamiltonian model with disturbance
TL;DR: Reinforcement learning (RL) designs the PBC parameters via solving PDE online through the utilisation of adaptive control technique to make the nonlinear closed-loop system robust against the disturbance and model uncertainty.
Journal ArticleDOI
Function Approximation Based Control for Non-Square Systems
TL;DR: In this article, a generic control method for non-square systems where the number of system inputs is not equal to that of the states is proposed, and the non-squares system to be controlled is first restructured in...
References
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Book
Introduction to Smooth Manifolds
TL;DR: In this paper, a review of topology, linear algebra, algebraic geometry, and differential equations is presented, along with an overview of the de Rham Theorem and its application in calculus.
Journal ArticleDOI
Interconnection and damping assignment passivity-based control: a survey
TL;DR: The fundamental theory, main new results and practical applications of this control system design approach are reviewed as well as to discuss the current open problems and future directions.
Journal ArticleDOI
Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem
TL;DR: In this article, a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians was developed, which involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagranian.
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Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping
TL;DR: The method of controlled Lagrangians is extended to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems and extends the method to include a class of mechanical system without symmetry such as the inverted pendulum on a cart that travels along an incline.
Journal ArticleDOI
Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one
TL;DR: The problem of (asymptotic) stabilization of mechanical systems with underactuation degree one is considered and a state-feedback design is derived applying the interconnection and damping assignment passivity-based control methodology that endows the closed-loop system with a Hamiltonian structure with desired potential and kinetic energy functions.