On Excessive Transverse Coordinates for Orbital Stabilization of Periodic Motions

This paper explores transverse coordinates for the purpose of orbitally stabilizing periodic motions of nonlinear, control-affine dynamical systems. It is shown that the dynamics of any (minimal or excessive) set of transverse coordinates, which are defined in terms of a particular parameterization of the motion and a strictly state-dependent projection operator recovering the parameterizing variable, admits a (transverse) linearization along the target motion, with explicit expressions stated. Special focus is then placed on a generic excessive set of orthogonal coordinates, revealing a certain limitation of the "excessive" transverse linearization for the purpose of control design. To overcome this limitation, a linear comparison system is introduced, and conditions are stated for when the asymptotic stability of its origin corresponds to the asymptotic stability of the origin of linearized transverse dynamics. This allows for the construction of feedback controllers utilizing this comparison system which, when implemented on the dynamical system, renders the desired motion asymptotically stable in the orbital sense.Comment: Extended version with proofs of paper accepted to the IFAC World Congress 202

Periodic Motion Planning for Virtually Constrained (Hybrid) Mechanical Systems

The paper presents sufficient and almost necessary conditions for the presence of periodic solutions for zero dynamics of virtually constrained under-actuated Euler-Lagrange system. This result is further extended to detect periodic solutions for a class of hybrid systems in the plane and analyze their orbital stability and instability. Illustrative examples are given

Global Stabilization for a Class of Coupled Nonlinear Systems with Application to Active Surge Control

We propose here a new procedure for output feedback design for systems with nonlinearities satisfying quadratic constraints. It provides an alternative for the classical observer-based design and relies on transformation of the closed-loop system with a dynamic controller of particular structure into a special block form. We present two sets of sufficient conditions for stability of the transformed block system and derive matching conditions allowing such a representation for a particular challenging example. The two new tests for global stability proposed for a class of nonlinear systems extend the famous Circle criterion applied for infinite sector quadratic constraints. The study is motivated and illustrated by the problem of output feedback control design for the well-known finite dimensional nonlinear model qualitatively describing surge instabilities in compressors. Assuming that the only available measurement is the pressure rise, we suggest a constructive procedure for synthesis of a family of robustly globally stabilizing feedback controllers. The solution relies on structural properties of the nonlinearity of the model describing a compressor characteristic, which includes earlier known static quadratic constraints and a newly found integral quadratic constraint. Performance of the closed-loop system is discussed and illustrated by simulations

Criteria for Global Stability of Coupled Systems with Application to Robust Output Feedback Design for Active Surge Control

The well-known and commonly accepted finite dimensional model qualitatively describing surge instabilities in centrifugal (and axial) compressors is considered. The problem of global output feedback stabilization for it is solved. The solution relies on two new criteria for global stability proposed for a class of nonlinear systems exploiting quadratic constraints for infinite sector nonlinearities. Two families of robust output feedback controllers are proposed. Controllers from the first family ensure global exponential stabilization. The ones from the second family provide integral action but only ensure local exponential and global asymptotic stability. Performance is verified by simulations

Observer-based strict positive real (SPR) switching output feedback control

This paper considers switching output feedback control of linear systems and variablestructure systems. Theory for stability analysis and design for a class of observer-based feedback control systems is presented. It is shown how a circlecriterion approach can be used to design an observerbased state feedback control which yields a closedloop system with speci ed robustness characteristics. The approach is relevant for variable structure system design with preservation of stability when switching feedback control or sliding mode control is introduced in the feedback loop. It is shown that there exists a Lyapunov function valid over the total operating range and this Lyapunov function has also interpretation as a storage function of passivity-based control and a value function of an optimal control problem. The Lyapunov function can be found by solving a Lyapunov equation. Important applications are to be found in hybrid systems with switching control and variable structure systems with high robustness requirements

Explicit formulas for general integrals of motion for a class of mechanical systems subject to virtual constraints

The paper suggests an explicit form of a general integral of motion for some classes of dynamical systems including n-degree-of-freedom mechanical systems subject to (n-1) virtual holonomic constraints. The computation of this integral opens several possibilities for generating and further exponential orbital stabilization of solutions in nonlinear feedback systems. An illustrative example is given

Efficacy and Comparison of Different Strategies for Selenium Biofortification of Tomatoes

At appropriate concentrations, selenium (Se) is beneficial for humans. Tomato appears to be one of the best commodities for producing Se-biofortified fruit for dietary supplementation. To assess the efficacy of different enrichment protocols, a total of four on-plant and off-plant trials were conducted. Hydroponically grown tomato plants were sprayed with: (i) chemically synthesized Se nanoparticles (SeNPs) at 0, 1, and 1.5 mg Se L−1 at blooming; (ii) sodium selenate (Na2SeO4) or SeNPs solution at 0, 5, and 10 mg Se L−1 when the fruit entered the immature green stage. With regard to the off-plant trials, harvested mature green fruit were immersed in Na2SeO4 solution: (iii) at 0, 5, 10, and 20 mg Se L−1 for 15 s under a vacuum; (iv) at 0, 40, and 80 mg Se L−1 for 1 h. Spraying Na2SeO4 induced higher Se accumulation in plant tissue than SeNPs: both protocols were effective in enriching tomatoes. Postharvest Se enrichment via vacuum infiltration caused textural damage, whereas passive immersion in solution induced fruit Se accumulation without causing any damage. SeNPs appear to be quantitatively less effective than Na2SeO4, but might be environmentally safer. Elemental Se carried by NPs may be more easily incorporated into organic forms, which are more bioavailable for humans. Passive immersion may represent an alternative Se-enrichment strategy, allowing for the biofortification of harvested tomato fruit directly, with lower risks of environmental pollution

Orbital Stabilization of Point-to-Point Maneuvers in Underactuated Mechanical Systems

The task of inducing, via continuous static state-feedback, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to a so-called point-to-point maneuver in an underactuated mechanical system. Namely, to a smooth curve in its state--control space, which is consistent with the system dynamics and connects two (linearly) stabilizable equilibrium points. The proposed method uses a particular parameterization, together with a state projection onto the maneuver as to combine two linearization techniques for this purpose: the Jacobian linearization at the equilibria on the boundaries and a transverse linearization along the orbit. This allows for the computation of stabilizing control gains offline by solving a semidefinite programming problem. The resulting nonlinear controller, which simultaneously asymptotically stabilizes both the orbit and the final equilibrium, is time-invariant, locally Lipschitz continuous, requires no switching, and has a familiar feedforward plus feedback--like structure. The method is also complemented by synchronization function--based arguments for planning such maneuvers for mechanical systems with one degree of underactuation. Numerical simulations of the non-prehensile manipulation task of a ball rolling between two points upon the "butterfly" robot demonstrates the efficacy of the synthesis.Comment: 21 pages, 8 figures, 1 table. Substantial changes made to sections 2, 3 and 5. Results unchange

Virtual environment-based teleoperation of forestry machines : designing future interaction methods

Virtual environment-assisted teleoperation has great potential as a human-robot interaction paradigm for field robotic systems, in particular when combined with elements of automation. Unstructured outdoor environments present a complex problem with many challenging elements. For the specific application of forestry machines, we investigate which steps are required in order to implement such a system, what potential benefits there are, and how individual components can be adapted to efficiently assist forestry machine operators in their daily work in the near future. An experimental prototype of a teleoperation system with virtual environment-based feedback is constructed using a scenario-based design process. The feasibility of the implementation is partly verified through experimental studies