Analysis of interconnected oscillators by dissipativity theory

This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. Oscillators are regarded as open systems that satisfy a particular dissipation inequality. It is shown that this characterization has implications for the global stability analysis of limit cycle oscillations: i) in isolated oscillators, ii) in interconnections of oscillators, and iii) for the global synchrony analysis in interconnections of identical oscillators. © 2007 IEEE.

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This note analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a Stable nonlinear system. It is shown that the instability of the zeros of the linear System can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static-state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Robust stabilization of a nonlinear cement mill model

Plugging is well known to be a major cause of instability in industrial cement mills. A simple nonlinear model able to simulate the plugging phenomenon is presented. It is shown how a nonlinear robust controller can be designed in order to fully prevent the mill from plugging.

Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

Lyapunov functions for stable cascades and applications to global stabilization

This paper generalizes recent Lyapunov constructions for a cascade of two nonlinear systems, one of which is stable rather than asymptotically stable. A new cross-term construction in the Lyapunov function allows us to replace earlier growth conditions by a necessary boundedness condition. This method is instrumental in the global stabilization of feedforward systems, and new stabilization results are derived from the generalized construction.

Output feedback H2 model matching for decentralized systems with delays

This paper gives a new solution to the output feedback H2 model matching problem for a large class of delayed information sharing patterns. Existing methods for similar problems typically reduce the decentralized problem to a centralized problem of higher state dimension. In contrast, this paper demonstrates that the decentralized model matching solution can be constructed from the original centralized solution via quadratic programming. © 2013 AACC American Automatic Control Council.

Designing output-feedback predictive controllers by reverse-engineering existing LTI controllers

An approach to designing a constrained output-feedback predictive controller that has the same small-signal properties as a pre-existing output-feedback linear time invariant controller is proposed. Systematic guidelines are proposed to select an appropriate (non-unique) realization of the resulting state observer. A method is proposed to transform a class of offset-free reference tracking controllers into the combination of an observer, steady-state target calculator and predictive controller. The procedure is demonstrated with a numerical example. © 2013 IEEE.

A differential lyapunov framework for contraction analysis

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. © 2013 IEEE.

Towards soft self-reconfigurable robots

Modular self-reconfigurable robots have previously demonstrated that automatic control of their own body shapes enriches their behavioural functions. However, having predefined rigid modules technically limits real-world systems from being hyper-redundant and compliant. Encouraged by recent progress using elastically deformable material for robots, we propose the concept of soft self-reconfigurable robots which may become hyper-flexible during interaction with the environment. As the first attempt towards this goal, the paper proposes a novel approach using viscoelastic material Hot-Melt Adhesives (HMAs): for physical connection and disconnection control between bodies that are not necessarily predefined rigid modules. We present a model that characterizes the temperature dependency of the strength of HMA bonds, which is then validated and used in a feedback controller for automatic connection and disconnection. Using a minimalistic robot platform that is equipped with two devices handling HMAs, the performance of this method is evaluated in a pick-and-place experiment with aluminium and wooden parts. © 2012 IEEE.