792 research outputs found
Integral control of port-Hamiltonian systems: non-passive outputs without coordinate transformation
In this paper we present a method for the addition of integral action to
non-passive outputs of a class of port-Hamiltonian systems. The proposed
integral controller is a dynamic extension, constructed from the open loop
system, such that the closed loop preserves the port-Hamiltonian form. It is
shown that the controller is able to reject the effects of both matched and
unmatched disturbances, preserving the regulation of the non-passive outputs.
Previous solutions to this problem have relied on a change of coordinates
whereas the presented solution is developed using the original state vector
and, therefore, retains its physical interpretation. In addition, the resulting
closed loop dynamics have a natural interpretation as a Control by
Interconnection scheme.Comment: 8 pages, 2 figure
Well-posedness and Stability for Interconnection Structures of Port-Hamiltonian Type
We consider networks of infinite-dimensional port-Hamiltonian systems
on one-dimensional spatial domains. These subsystems of
port-Hamiltonian type are interconnected via boundary control and observation
and are allowed to be of distinct port-Hamiltonian orders .
Wellposedness and stability results for port-Hamiltonian systems of fixed order
are thereby generalised to networks of such. The abstract
theory is applied to some particular model examples.Comment: Submitted to: Control Theory of Infinite-Dimensional System. Workshop
on Control Theory of Infinite-Dimensional Systems, Hagen, January 2018.
Operator Theory: Advances and Applications. (32 pages, 5 figures
Matching in the method of controlled Lagrangians and IDA-passivity based control
This paper reviews the method of controlled Lagrangians and the interconnection and damping assignment passivity based control (IDA-PBC)method. Both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an Euler-Lagrange system, respectively Hamiltonian system, by searching for a stabilizing structure preserving feedback law. The conditions under which two Euler-Lagrange or Hamiltonian systems are equivalent under feedback are called the matching conditions (consisting of a set of nonlinear PDEs). Both methods are applied to the general class of underactuated mechanical systems and it is shown that the IDA-PBC method contains the controlled Lagrangians method as a special case by choosing an appropriate closed-loop interconnection structure. Moreover, explicit conditions are derived under which the closed-loop Hamiltonian system is integrable, leading to the introduction of gyroscopic terms. The -method as introduced in recent papers for the controlled Lagrangians method transforms the matching conditions into a set of linear PDEs. In this paper the method is extended, transforming the matching conditions obtained in the IDA-PBC method into a set of quasi-linear and linear PDEs.\u
Putting energy back in control
A control system design technique using the principle of energy balancing was analyzed. Passivity-based control (PBC) techniques were used to analyze complex systems by decomposing them into simpler sub systems, which upon interconnection and total energy addition were helpful in determining the overall system behavior. An attempt to identify physical obstacles that hampered the use of PBC in applications other than mechanical systems was carried out. The technique was applicable to systems which were stabilized with passive controllers
Modeling and Control of High-Voltage Direct-Current Transmission Systems: From Theory to Practice and Back
The problem of modeling and control of multi-terminal high-voltage
direct-current transmission systems is addressed in this paper, which contains
five main contributions. First, to propose a unified, physically motivated,
modeling framework - based on port-Hamiltonian representations - of the various
network topologies used in this application. Second, to prove that the system
can be globally asymptotically stabilized with a decentralized PI control, that
exploits its passivity properties. Close connections between the proposed PI
and the popular Akagi's PQ instantaneous power method are also established.
Third, to reveal the transient performance limitations of the proposed
controller that, interestingly, is shown to be intrinsic to PI passivity-based
control. Fourth, motivated by the latter, an outer-loop that overcomes the
aforementioned limitations is proposed. The performance limitation of the PI,
and its drastic improvement using outer-loop controls, are verified via
simulations on a three-terminals benchmark example. A final contribution is a
novel formulation of the power flow equations for the centralized references
calculation
Towards control by interconnection of port-thermodynamic systems
Power conserving interconnection of port-thermodynamic systems via their power ports results in another port-thermodynamic system, and the same holds for any rate of entropy increasing interconnection via the entropy flow ports. Control by interconnection seeks to control the port-thermodynamic system by the interconnection with a controller port-thermodynamic system. The stability of the interconnected port-thermodynamic system is investigated by Lyapunov functions that are based on generating functions for the submanifold characterizing the state properties, as well as additional conserved quantities. Crucial tool is the use of point transformations of the symplectized thermodynamic phase space
Energy-based Stabilization of Network Flows in Multi-machine Power Systems
This paper considers the network flow stabilization problem in power systems
and adopts an output regulation viewpoint. Building upon the structure of a
heterogeneous port-Hamiltonian model, we integrate network aspects and develop
a systematic control design procedure. First, the passive output is selected to
encode two objectives: consensus in angular velocity and constant excitation
current. Second, the non-Euclidean nature of the angle variable reveals the
geometry of a suitable target set, which is compact and attractive for the zero
dynamics. On this set, circuit-theoretic aspects come into play, giving rise to
a network potential function which relates the electrical circuit variables to
the machine rotor angles. As it turns out, this energy function is convex in
the edge variables, concave in the node variables and, most importantly, can be
optimized via an intrinsic gradient flow, with its global minimum corresponding
to angle synchronization. The third step consists of explicitly deriving the
steady-state-inducing control action by further refining this sequence of
control-invariant sets. Analogously to solving the so called regulator
equations, we obtain an impedance-based network flow map leading to novel error
coordinates and a shifted energy function. The final step amounts to decoupling
the rotor current dynamics via feedback-linearziation resulting in a cascade
which is used to construct an energy-based controller hierarchically.Comment: In preparation for MTNS 201
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