arXiv subjects

Pablo Borja

Publications and source records attributed to Pablo Borja.

15 recordsLinked to original sources

arXiv2026

Introduction to Passivity-based Control

Passivity-based control (PBC) is a nonlinear control design framework that has proven adequate for controlling a wide range of systems, especially physical ones. Their main ingredients are physical quantities such as energy and dissipation, making the control design more intuitive and endowing the controllers with a physical interpretation. In contrast to other, mathematically-based nonlinear control approaches, the energy-based viewpoint and physical intuition of PBC often make this strategy more robust and energy efficient. This chapter provides an overview of PBC, revisiting the basic aspects of this powerful nonlinear control framework and the most common PBC approaches.

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arXiv2026

Passivity-Based Nonlinear Control

The passivity-based control (PBC) framework focuses on understanding and modifying the energy storage and dissipation in the system to be controlled. To this end, PBC techniques often proceed in two steps: (i) ensuring that the closed-loop system's energy is minimum at the desired point, and then (ii) forcing the system to dissipate energy until reaching that point. These control methods have proven effective in controlling a wide range of systems, especially physical ones, even when they exhibit highly nonlinear behaviors. This chapter discusses the main aspects of some PBC strategies for nonlinear systems.

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arXiv2023

Contraction-based Tracking Control of Electromechanical Systems

This paper addresses the trajectory-tracking problem for a class of electromechanical systems. To this end, the dynamics of the plants are modeled in the so-called port-Hamiltonian framework. Then, the notion of contraction is exploited to design the desired closed-loop dynamics and the corresponding tracking controller. Notably, the proposed control design method does not require solving partial differential equations or changing the coordinates of the plant, which permits preserving the physical interpretation of the controller. The applicability of the proposed approach is illustrated in several electromechanical systems via simulations.

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arXiv2023

Angle-based formation stabilization and maneuvers in port-Hamiltonian form with bearing and velocity measurements

This paper proposes a port-Hamiltonian framework for angle-based formation stabilization and maneuvers using bearing and velocity measurements with an underlying triangulated Laman graph. The corresponding port-Hamiltonian controller is designed using virtual couplings on the errors of angle constraints in angle space and then the angle constraints and agent actuators are mapped by the constraint Jacobian, which can be applied to other formation constraints. In addition, due to the fact that the port-Hamiltonian model allows for complex and heterogeneous agent dynamics, our framework can be extended to networks with different agent dynamics and formation constraints. To avoid unavailable distance terms in the control law, an estimator is designed based on port-Hamiltonian theory and the property that energy is coordinate-free for different sensor modalities using bearing and velocity measurements, which permits our framework to inject damping for the formation maneuvers. Furthermore, several maneuvers are analyzed under both considerations of stabilization and transient performance. Simulations are performed to illustrate the effectiveness of the approach.

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arXiv2023

Physics-informed Neural Networks to Model and Control Robots: a Theoretical and Experimental Investigation

This work concerns the application of physics-informed neural networks to the modeling and control of complex robotic systems. Achieving this goal required extending Physics Informed Neural Networks to handle non-conservative effects. We propose to combine these learned models with model-based controllers originally developed with first-principle models in mind. By combining standard and new techniques, we can achieve precise control performance while proving theoretical stability bounds. These validations include real-world experiments of motion prediction with a soft robot and of trajectory tracking with a Franka Emika manipulator.

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arXiv2022

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.

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arXiv2022

Tuning of passivity-based controllers for mechanical systems

This manuscript describes several approaches to tune the parameters of a class of passivity-based controllers for standard nonlinear mechanical systems. In particular, we are interested in controllers that preserve the mechanical system structure in 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 while prescribing the rise time. Additionally, we propose a methodology to tune the gyroscopic-related parameters. We also provide remarks on the damping phenomena to facilitate the practical implementation of our approaches. We conclude this paper with experimental results obtained from applying our tuning rules to an underactuated and a fully-actuated mechanical configuration.

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arXiv2021

Exponential Stability and Tuning for a Class of Mechanical Systems

In this paper, we prove the exponential stability property of a class of mechanical systems represented in the port-Hamiltonian framework. To this end, we propose a Lyapunov candidate function different from the Hamiltonian of the system. Moreover, we study how the proposed analysis can be used to determine the exponential stability and the rate of convergence of some (nonlinear)-mechanical systems stabilized by two passivity-based control techniques, namely, PID passivity-based control and interconnection and damping assignment. We implement the former control approach to stabilize a three degrees-of-freedom robotic arm at the desired equilibrium point to illustrate the mentioned analysis.

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arXiv2021

Stabilization of physical systems via saturated controllers with only partial state measurements

This paper provides a constructive passivity-based control approach to solve the set-point regulation problem for input-affine continuous nonlinear systems while considering saturation in the inputs. As customarily in passivity-based control, the methodology consists of two steps: energy shaping and damping injection. In terms of applicability, the proposed controllers have two advantages concerning other passivity-based control techniques: (i) the energy shaping is carried out without solving partial differential equations, and (ii) the damping injection is performed without measuring the passive output. The proposed methodology is suitable to control a broad range of physical systems, e.g., mechanical, electrical, and electro-mechanical systems. 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.

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arXiv2021

Passivity-based control of mechanical systems with linear damping identification

We propose a control approach for a class of nonlinear mechanical systems to stabilize the system under study while ensuring that the oscillations of the transient response are reduced. The approach is twofold: (i) we apply our technique for linear viscous damping identification of the system to improve the accuracy of the selected control technique, and (ii) we implement a passivity-based controller to stabilize and reduce the oscillations by selecting the control parameters properly in accordance with the identified damping. Moreover, we provide an analysis for a particular passivity-based control approach that has been shown successfully for reducing such oscillations. Also, we validate the methodology by implementing it experimentally in a planar manipulator.

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arXiv2020

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.

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arXiv2020

Trajectory Tracking for Robotic Arms with Input Saturation and Only Position Measurements

In this work, we propose a passivity-based control approach that addresses the trajectory tracking problem for a class of mechanical systems that comprises a broad range of robotic arms. The resulting controllers can be naturally saturated and do not require velocity measurements. Moreover, the proposed methodology does not require the implementation of observers, and the structure of the closed-loop system permits the identification of a Lyapunov function, which eases the convergence analysis. To corroborate the effectiveness of the methodology, we perform experiments with the Philips Experimental Robot Arm.

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arXiv2020

Tuning Rules for a Class of Port-Hamiltonian Mechanical Systems

In this extended abstract, we propose a tuning approach for nonlinear mechanical systems to modify the behavior of the closed-loop system, where we are particularly interested in attenuating oscillations from the transient response. Towards this end, we inject damping into the system, and we provide two tuning methods to select the gains that are appropriate for our purposes. Furthermore, we apply these tuning rules to a 2DoF planar manipulator and present its simulation results.

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arXiv2020

Extended balancing of continuous LTI systems: a structure-preserving approach

In this paper, we treat extended balancing for continuous-time linear time-invariant systems, and we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model.

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arXiv2016

Energy Shaping Control of an Inverted Flexible Pendulum Fixed to a Cart

Control of compliant mechanical systems is increasingly being researched for several applications including flexible link robots and ultra-precision positioning systems. The control problem in these systems is challenging, especially with gravity coupling and large deformations, because of inherent underactuation and the combination of lumped and distributed parameters of a nonlinear system. In this paper we consider an ultra-flexible inverted pendulum on a cart and propose a new nonlinear energy shaping controller to keep the pendulum at the upward position with the cart stopped at a desired location. The design is based on a model, obtained via the constrained Lagrange formulation, which previously has been validated experimentally. The controller design consists of a partial feedback linearization step followed by a standard PID controller acting on two passive outputs. Boundedness of all signals and (local) asymptotic stability of the desired equilibrium is theoretically established. Simulations and experimental evidence assess the performance of the proposed controller.

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