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

Stabilization of Physical Systems via Saturated Controllers With Partial State Measurements

This article provides a constructive passivity-based control (PBC) approach to solve the set-point regulation problem for input-affine continuous nonlinear systems while considering bounded inputs. As customary in PBC, the methodology consists of two steps: energy shaping and damping injection. In terms of applicability, the proposed controllers have two advantages concerning other PBC techniques: 1) the energy shaping is carried out without solving partial differential equations and 2) the damping injection is performed without measuring the passive output. As a result, the proposed methodology is suitable to control a broad range of physical systems, e.g., mechanical, electrical, and electromechanical systems, with saturated control signals. We illustrate the applicability of the technique by designing controllers for systems in different physical domains, where we validate the analytical results via simulations and experiments

Passivity-Based Trajectory Tracking and Formation Control of Nonholonomic Wheeled Robots Without Velocity Measurements

This note proposes a passivity-based control method for trajectory tracking and formation control of nonholonomic wheeled robots without velocity measurements. Coordinate transformations are used to incorporate the nonholonomic constraints, which are then avoided by controlling the front end of the robot rather than the center of the wheel axle into the differential equations. Starting from the passivity-based coordination design, the control goals are achieved via an internal controller for velocity tracking and heading control and an external controller for formation in the port-Hamiltonian framework. This approach endows the resulting controller with a physical interpretation. To avoid unavailable velocity measurements or unreliable velocity estimations, we derive the distributed control law with only position measurements by introducing a dynamic extension. In addition, we prove that our approach is suitable not only for acyclic graphs but also for a class of non-acyclic graphs, namely, ring graphs. Simulations are provided to illustrate the effectiveness of the approach

Dead-zone compensation via passivity-based control for a class of mechanical systems

This manuscript introduces a passivity-based control methodology for fully-actuated mechanical systems with symmetric or asymmetric dead-zones. To this end, we find a smooth approximation of the inverse of the function that describes such a nonlinearity. Then, we propose an energy and damping injection approach — based on the PI-PBC technique — that compensates for the dead-zone. Moreover, we provide an analysis of the performance of the proposed controller near the equilibrium. We conclude this paper by experimentally validating the results on a two degrees-of-freedom planar manipulator

A Novel Reduced Model for Electrical Networks With Constant Power Loads

We consider a network-preserved model of power networks with proper algebraic constraints resulting from constant power loads. Both for the linear and the nonlinear differential algebraic model of the network, we derive explicit reduced models which are fully expressed in terms of ordinary differential equations. For deriving these reduced models, we introduce the "projected incidence" matrix which yields a novel decomposition of the reduced Laplacian matrix. With the help of this new matrix, we provide a complementary approach to Kron reduction, which is able to cope with constant power loads and nonlinear power flow equations

Online parameters estimation schemes to enhance control performance in DC microgrids

This is the final version. Available on open access from Elsevier via the DOI in this recordThis paper addresses the problem of achieving current sharing and voltage balancing in DC microgrids when the filter parasitic resistances of the Distributed Generation Units (DGUs) are unknown and potentially time-varying. Two schemes are proposed for current sharing and voltage balancing, which use only generated current and voltage measurements. The first scheme is a novel distributed adaptive control utilising the principles of back-stepping and passivity-based control design, intended for the case of constant parasitic resistances. The second scheme alters an existing stabilising controller for current sharing and voltage balancing by incorporating the estimation of the unknown, possibly time-varying, parasitic resistance. A Super-Twisting Sliding Mode Algorithm (STA) estimates the parasitic resistance and its bounded variations in finite-time. The simulation results using a DC microgrid composed of 4 DGUs demonstrate the performance of the proposed schemes.Dutch Research Council (NWO)European Union Horizon 2020Innovate U

Model Reduction Methods for Complex Network Systems

Network systems consist of subsystems and their interconnections and provide a powerful framework for the analysis, modeling, and control of complex systems. However, subsystems may have high-dimensional dynamics and a large number of complex interconnections, and it is therefore relevant to study reduction methods for network systems. Here, we provide an overview of reduction methods for both the topological (interconnection) structure of a network and the dynamics of the nodes while preserving structural properties of the network. We first review topological complexity reduction methods based on graph clustering and aggregation, producing a reduced-order network model. Next, we consider reduction of the nodal dynamics using extensions of classical methods while preserving the stability and synchronization properties. Finally, we present a structure-preserving generalized balancing method for simultaneously simplifying the topological structure and the order of the nodal dynamics

A new controllability Gramian for semistable systems and its application to approximation of directed networks

In this paper, we propose a new definition of a controllability Gramian for semistable systems, which is then used for model reduction of network systems. The system under consideration is modeled as single integrators that interconnected with each other according to a connected directed network. In the proposed method, the complexity of the network is reduced through a graph clustering method which aggregates the vertices if they respond similarly with respect to external inputs. Here, the similarity of the vertices is computed based on the new Gramian. The reduced-order model is obtained by a Petrov-Galerkin projection where the projection matrices are constructed from the resulting clustering. The reduced system preserves the network structure, and the approximation error between the full-order and reduced-order models is shown to be always bounded. Finally, the proposed approach is illustrated by an example