
ThBR 
Sala
degli Affreschi 
ControlÂ of Lagrangian and
HamiltonianÂ Systems (II) 
Regular Session 

14:0014:20, Paper ThBR.1 

FiniteGain L2 Stability of PID Set Position Control with AntiWindup Compensation for EulerLagrange Systems with Actuator Saturation 
Kanamori, Mitsuru 
Maizuru National Coll. of Tech. 
Keywords: Passivitybased control, Robotics, Nonlinear control
Abstract: Finitegain L2 stabilization is achieved locally for the system using PID set position controller with the proposed static antiwindup compensation for EulerLagrange systems with actuator saturation andÂ external disturbances. On a closedloop nonlinear system with feedback and input saturation, L2 stability of the EulerLagrange systems is guaranteed based on passivity for antiwindup compensation. The control performance against the external disturbance added to saturate input is
verified by numerical simulations and experiments on a twolink robot arm.


14:2014:40, Paper ThBR.2 

On a Generalized PortHamiltonian Representation for the Control of Damped Underactuated Mechanical Systems 
Kotyczka, Paul 
Tech. Univ. M\FCnchen 
Delgado Londo\F1o, Sergio 
Tech. Univ. of Munich, Inst. of AutomaticControl 
Keywords: Passivitybased control, PortHamiltonian systems, Modeling
Abstract: A wellknown problem in controller design for underactuated mechanical systems using the Interconnection and Damping Assignment (IDAPBC) technique is friction in unactuated degrees of freedom. For certain equilibria the definiteness requirements on the virtual energy of the portHamiltonian (pH) target system and the closedloop dissipation matrix can not be satisfied simultaneously. In this contribution a modification of the pH target system is proposed, where particularly the total energy function is augmented by a cross term between coordinates and momenta. The approach stems from the fact that, although IDAPBC may fail, unstable equilibria of underactuated mechanical systems are stabilized by linear state feedback, if the linearization is stabilizable. Then the solution of a Lyapunov equation for the linearized closedloop system is not block diagonal, which gives rise to the proposed structure of the energy.


14:4015:00, Paper ThBR.3 

Coordination of MultiAgent Systems Via EnergyShaping: Networking Improves Robustness 
Nuno, Emmanuel 
Univ. of Guadalajara 
Ortega, Romeo 
Supelec 
Jayawardhana, Bayu 
Univ. of Groningen 
Basanez, Luis 
Univ. Pol. de Catalunya 
Keywords: Passivitybased control, Nonlinear control, Robotics
Abstract: In this paper the problem of robust coordination of multiagent systems via energyshaping is studied. The agents are nonidentical, Euler–Lagrange systems with uncertain parameters. The control objective is to drive all agents states to the same constant equilibriumwhich is achieved shaping their potential energy function. It is assumed that, if the parameters are known, this task can be accomplished with a decentralized strategy. In the face of parameter uncertainty, the assigned equilibrium is shifted away from its desired value. It is shown that adding information exchange between the agents to this decentralized control policy improves the performance. More precisely, it is proven that if the communication graph is connected and balanced, the equilibrium of the networked controller is always closer (in a suitable metric) to the desired one. If the the potential energy functions are quadratic, the result holds for all interconnection gains, else, it is true for sufficiently large gains. The decentralized controller is the well–known energy–shaping proportional plus derivative controller, extensively used in applications. An additional advantage of networking is that the control objective is achieved injecting lower gains into the loop.

15:0015:20, Paper ThBR.4 

On the Modeling, Linearization and Energy Shaping Control of Mechanical Systems 
Sarras, Ioannis 
CNRS 
Ortega, Romeo 
Supelec 
van der Schaft, Arjan J. 
Univ. of Groningen 
Keywords: PortHamiltonian systems, Passivitybased control, Modeling
Abstract: In this work some recent results on the linearization and passivitybased control of mechanical systems are reviewed from a unified perspective. This is established by adopting a generalization of the Poisson bracket formalism to more general structures than smooth functions. In this manner, the corresponding geometric structures as well as their respective energy terms are all expressed by simple, identifiable terms. More precisely, the objective consists in illustrating that the proposed framework captures the essential terms involved in the conditions of the literature, reveals the connection between theÂ results in linearization and stabilization, and reduces the cumbersome calculations. In this direction, the generalized Poisson bracket is shown to be an effective tool that leads to (i) the refinement of wellknown results on interconnection and damping assignment passivitybased control (IDAPBC), (ii) the derivation of a new set of simplified conditions for partial linearization via a change of coordinates, and (iii) the identification of certain relationships connecting the Hamiltonian with the EulerLagrange description.


15:2015:40, Paper ThBR.5 

CasimirBased Control Beyond the Dissipation Obstacle 
Koopman, Johan 
Delft Univ. of Tech. 
Jeltsema, Dimitri 
Delft Univ. of Tech. 
Keywords: Passivitybased control, PortHamiltonian systems, Nonlinear control
Abstract: A prevailing trend in the stabilization of portHamiltonian systems is the assumption that the plant and the controller are both passive. In the standard approach of control by interconnection based on the generation of Casimir functions, this assumption leads to the dissipation obstacle, which essentially means that dissipation is admissible only on the coordinates of the closedloop Hamiltonian that do not require shaping and thus severely restricts the scope of applications. In this contribution, we show that we can easily go beyond the dissipation obstacle by allowing the controller to have a negative semidefinite resistive structure, while guaranteeing stability of both the closedloop and the controller.


15:4016:00, Paper ThBR.6 

Memristive PortHamiltonian Control: PathDependent Damping Injection in Control of Mechanical
Systems 
DoriaCerezo, Arnau 
Tech. Univ. of Catalonia (UPC) 
van der Heijden, Laurens 
Faculty of Math. & Natural Sciences, Univ.
ofGroningen 
Scherpen, Jacquelien M.A. 
Univ. of Groningen 
Keywords: Passivitybased control, PortHamiltonian systems, Hamiltonian dynamics
Abstract: This paper presents the use of the memristor as a new element for designing passivitybased controllers. From the portHamiltonian description of the electrical circuits with memristors, a target dynamics is assigned to the matching equation proposed by the methodology known as Interconnection and Damping AssignmentPassivitybased Control. The inclusion of the memristor element extends the closed loop dynamics and it results in an extra term in the control algorithm that can be seen as a statemodulated gain. Two mechanical examples, in the form of a position control systems are included to show possible applications.
