Tuning Rules for a Class of Passivity-Based Controllers for Mechanical Systems

In this paper, we propose several rules to tune the gains for a class of passivity-based controllers for nonlinear mechanical systems. Such tuning rules prescribe a desired local transient response behavior to the closed-loop system. To establish the tuning rules, we implement a PID passivity-based controller. Then, we linearize the closed-loop system, and we transform the matrix of the resulting system into a class of saddle point matrices to analyze the influence of the control gains, in terms of the oscillations and the rise time, on the transient response of the closed-loop system. Hence, the resulting controllers stabilize the plant and simultaneously address the performance of the closed-loop system. Moreover, our analysis provides a clear insight into how the kinetic energy, the potential energy, and the damping of the mechanical system are related to its transient response, endowing in this way the tuning rules with a physical interpretation. Additionally, we corroborate the analytical results through the practical implementation of a controller that stabilizes a two degrees-of-freedom (DoF) planar manipulator, where the control gains are tuned following the proposed rules.Comment: Final submission for journal: IEEE Control Systems Letter

Automated Generation of Explicit Port-Hamiltonian Models from Multi-Bond Graphs

Port-Hamiltonian system theory is a well-known framework for the control of complex physical systems. The majority of port-Hamiltonian control design methods base on an \emph{explicit} input-state-output port-Hamiltonian model for the system under consideration. However in the literature, little effort has been made towards a systematic, automatable derivation of such explicit models. In this paper, we present a constructive, formally rigorous method for an explicit port-Hamiltonian formulation of multi-bond graphs. Two conditions, one necessary and one sufficient, for the existence of an explicit port-Hamiltonian formulation of a multi-bond graph are given. We summarise our approach in a fully automated algorithm of which we provide an exemplary implementation along with this publication. The theoretical and practical results are illustrated through an academic example

Passivity-Based Plug-and-Play Voltage and Frequency Control in Islanded Inverter-Based AC Microgrids

In this paper, we propose a decentralized scalable, plug-and-play control of voltage-source inverters (VSIs) in islanded, inverter-based AC microgrids at primary level. Particularly in islanded mode without inertia from conventional generators in the main grid, voltage and frequency stabilization must be performed exclusively by these VSIs. In contrast to existing approaches, we propose a systematic procedure that does not require the proposition of a Lyapunov function as well as avoids computationally expensive and possibly infeasible numerical optimization. It follows passivity techniques, namely interconnection and damping assignment passivity-based control (IDA-PBC) on the basis of port-Hamiltonian systems (PHSs) theory. By employing the Hamiltonian naturally obtained from the PHS approach as Lyapunov function and analyzing load dynamics, we prove microgrid-wide asymptotic voltage and frequency stability. A simulation validating our theoretical results concludes our work

Tuning of Passivity-Based Controllers for Mechanical Systems

This article describes several approaches for tuning the parameters of a class of passivity-based controllers for standard nonlinear mechanical systems. In particular, we are interested in tuning controllers that preserve the mechanical system structure in the closed loop. To this end, first, we provide tuning rules for stabilization, i.e., the rate of convergence (exponential stability) and stability margin (input-to-state stability). Then, we provide guidelines to remove the overshoot. In addition, we propose a methodology to tune the gyroscopic-related parameters. We also provide remarks on the damping phenomenon to facilitate the practical implementation of our approaches. We conclude this article with experimental results obtained from applying our tuning rules to a fully actuated and an underactuated mechanical system

Control of an Underactuated Three-Link Passive-Active- Active Manipulator Based on Three Stages and Stability Analysis

This paper presents a novel three-stage control strategy for the motion control of an underactuated three-link passive-active-active (PAA) manipulator. First, a nonlinear control law is designed to make the angle and angular velocity of the third link convergent to zero. Then, a swing-up control law is designed to increase the system energy and control the posture of the second link. Finally, an integrated method with linear control and nonlinear control is introduced to stabilize the manipulator at the straight-up position. The stability of the control system is guaranteed by Lyapunov theory and LaSalle's invariance principle. Compared to other approaches, the proposed strategy innovatively introduces a preparatory stage to drive the third link to stretch-out toward the second link in a natural way, which makes the swing-up control easy and quick. Besides, the intergraded method ensures the manipulator moving into the balancing stage smoothly and easily. The effectiveness and efficiency of the control strategy are demonstrated by numerical simulations

Modeling and analysis of non-isothermal chemical reaction networks:A port-Hamiltonian and contact geometry approach

In dit proefschrift worden verschillende benaderingen gebruikt voor de meetkundige modellering en analyse van chemische reactienetwerken met varierende temperatuur. deze benaderingen kunnen in twee klassen worden verdeeld: de ene gebaseerd op poort-Hamiltonse systeemtheorie, en de ander gebaseerd op de theorie van contactsystemen. De eerste aanpak is de irreversibele poort-Hamiltonse formulering op basis van de interne energie. Beginnend met een overzicht van de wiskundige structuur van chemische reactienetwerken in het niet-isothermische geval wordt een irreversibele poort-Hamiltonse formulering van niet-isothermische reactienetwerken gegeven. Daarna volgt een thermodynamische analyse, inclusief de voorwaarden voor het bestaan van een thermodynamisch evenwicht en de asymptotische stabiliteit van de verzameling van thermodynamische evenwichtspunten. De tweede benadering betreft de quasi poort-Hamiltonse modellering met behulp van de totale entropie. In dit poort-Hamiltonse systeem wordt niet alleen de energiebalans maar ook de entropiebal- ansvergelijking gebruikt. Ook de thermodynamische analyse wordt in dit kader uitgevoerd, in het bijzonder de karakterisatie van evenwichtspunten en hun asymptotische stabiliteit.Gebaseerd op deze nieuwe quasi poort-Hamiltonse formulering wordt verder de interconnectie van chemische reactienetwerken bestudeerd. Tenslotte wordt de regeling van contactsystemen door middel van structuurbe-houdende terugkoppeling bestudeerd. Een aantal regelontwerpen die hierop gebaseerd zijn worden bestudeerd. Een lokale stabiliteitsanalyse wordt uitgevoerd om de structuurbehoudende terugkoppeling te bepalen, op basis van evenwichtsvoorwaarden en de Jacobimatrix van het teruggekoppelde systeem. Verder worden voorwaarden voor lokale en gedeeltelijke stabiliteit ten opzichte van de gesloten-lus invariant Legendre deelvarieteit gegeven, alsmede de gesloten-lus contact Hamiltonfunctie