Integral MRAC with Minimal Controller Synthesis and bounded adaptive gains: The continuous-time case

Model reference adaptive controllers designed via the Minimal Control Synthesis (MCS) approach are a viable solution to control plants affected by parameter uncertainty, unmodelled dynamics, and disturbances. Despite its effectiveness to impose the required reference dynamics, an apparent drift of the adaptive gains, which can eventually lead to closed-loop instability or alter tracking performance, may occasionally be induced by external disturbances. This problem has been recently addressed for this class of adaptive algorithms in the discrete-time case and for square-integrable perturbations by using a parameter projection strategy [1]. In this paper we tackle systematically this issue for MCS continuous-time adaptive systems with integral action by enhancing the adaptive mechanism not only with a parameter projection method, but also embedding a s-modification strategy. The former is used to preserve convergence to zero of the tracking error when the disturbance is bounded and L2, while the latter guarantees global uniform ultimate boundedness under continuous L8 disturbances. In both cases, the proposed control schemes ensure boundedness of all the closed-loop signals. The strategies are numerically validated by considering systems subject to different kinds of disturbances. In addition, an electrical power circuit is used to show the applicability of the algorithms to engineering problems requiring a precise tracking of a reference profile over a long time range despite disturbances, unmodelled dynamics, and parameter uncertainty.Postprint (author's final draft

Proportional and derivative control for steady-state vibration mitigation in a piecewise linear beam system

A control using Proportional and/or Derivative feedback (PD-control) is applied on a piecewise linear beam system with a flushing one-sided spring element for steady-state vibration amplitude mitigation. Two control objectives are formulated: (1) minimize the transversal vibration amplitude of the midpoint of the beam at the frequency where the first harmonic resonance occurs, (2) achieve this in a larger (low) excitation frequency range, where the lowest nonlinear normal mode dominates the response. Experimentally realizable combinations of PD-control are evaluated for both control objectives. Eventually objective (1) is realized by applying proportional control only, whereas derivative control is selected to realize objective (2). The vibration reduction that is achieved in simulations and validated by experiments is very significant for both objectives. Current results obtained with active PD-control are compared with earlier results obtained using a passive dynamic vibration absorber

Exponential Stabilisation of Continuous-time Periodic Stochastic Systems by Feedback Control Based on Periodic Discrete-time Observations

Since Mao in 2013 discretised the system observations for stabilisation problem of hybrid SDEs (stochastic differential equations with Markovian switching) by feedback control, the study of this topic using a constant observation frequency has been further developed. However, time-varying observation frequencies have not been considered. Particularly, an observational more efficient way is to consider the time-varying property of the system and observe a periodic SDE system at the periodic time-varying frequencies. This study investigates how to stabilise a periodic hybrid SDE by a periodic feedback control, based on periodic discrete-time observations. This study provides sufficient conditions under which the controlled system can achieve pth moment exponential stability for p > 1 and almost sure exponential stability. Lyapunov's method and inequalities are main tools for derivation and analysis. The existence of observation interval sequences is verified and one way of its calculation is provided. Finally, an example is given for illustration. Their new techniques not only reduce observational cost by reducing observation frequency dramatically but also offer flexibility on system observation settings. This study allows readers to set observation frequencies according to their needs to some extent

Sensitivity analysis of hybrid systems with state jumps with application to trajectory tracking

This paper addresses the sensitivity analysis for hybrid systems with discontinuous (jumping) state trajectories. We consider state-triggered jumps in the state evolution, potentially accompanied by mode switching in the control vector field as well. For a given trajectory with state jumps, we show how to construct an approximation of a nearby perturbed trajectory corresponding to a small variation of the initial condition and input. A major complication in the construction of such an approximation is that, in general, the jump times corresponding to a nearby perturbed trajectory are not equal to those of the nominal one. The main contribution of this work is the development of a notion of error to clarify in which sense the approximate trajectory is, at each instant of time, a firstorder approximation of the perturbed trajectory. This notion of error naturally finds application in the (local) tracking problem of a time-varying reference trajectory of a hybrid system. To illustrate the possible use of this new error definition in the context of trajectory tracking, we outline how the standard linear trajectory tracking control for nonlinear systems -based on linear quadratic regulator (LQR) theory to compute the optimal feedback gain- could be generalized for hybrid systems

Numerical analysis of a multistable capsule system under the delayed feedback control with a constant delay

The vibro-impact capsule system is a self-propelled mechanism that has abundant coexisting attractors and moves rectilinearly under periodic excitation when overcoming environmental resistance. In this paper, we study the control of coexisting attractors in this system by using a delayed feedback controller (DFC) with a constant delay. The aim of our control is to steer this complex system toward an attractor with preferable performance characteristics among multiple coexisting attractors, e.g., a periodically fast forward progression. For this purpose, we give an example of a feedback-controlled transition from a period-3 motion with low progression speed to a period-1 motion with high progression speed at the system parameters where both responses coexist. The effectiveness of this controller is investigated numerically by considering its convergence time and the required control energy input to achieve transition. We combine pseudo-spectral approximation of the delay, event detection for the discontinuities and path-following (continuation) techniques for non-smooth delay dynamical systems to carry out bifurcation analysis. We systematically study the dynamical performance of the controlled system when varying its control gain and delay time. Our numerical simulations show the effectiveness of DFC under a wide range of system parameters. We find that the desired period-1 motion is achievable in a range of control delays between a period-doubling and a grazing bifurcation. Therefore, two-parameter continuation of these two bifurcations with respect to the control delay and control gain is conducted to identify the delay-gain parameter region where the period-1 motion is stable. The findings of this work can be used for tuning control parameters in experiments, and similar analysis can be carried out for other non-smooth dynamical systems with a constant delay term.Comment: submitted to International Journal of Nonlinear Mechanic

Exact methods for modal transient response analysis including feedback control

This paper presents a modal method for the analysis of controlled structural systems that retains the uncoupled nature of the classical transient response analysis of a structure subjected to a prescribed time-varying load. The control force is expanded as a Taylor series that remains on the right side of the equations, and it does not lead to a computational approach that requires coupling between modes on the left side. Retaining a sufficient number of terms in the series produces a solution to the modal equations that is accurate to machine precision. The approach is particularly attractive for large problems in which standard matrix exponential methods become computationally prohibitive. Numerical results are presented to show the accuracy and efficiency of the proposed approach for dynamic feedback compensation of a truss structure with local member modes in the controller bandwidth

On the Influence of Piecewise Defined Contact Geometries on Friction Dampers

Diese Arbeit betrachtet Dämpfer, die sich nicht auf eine Schwingungsreduktionsstrategie beschränken, sondern mehrere kombinieren, um optimale Ergebnisse zu erzielen. Die Möglichkeiten herkömmlicher Reibungsdämpfer werden durch stetige, stückweise definierten Kontaktgeometrien erweitert. Dies führt zu Reibungsdämpfern, die ihr Verhalten je nach Amplitude der Schwingungen ändern. Der passive, abgestimmte Keildämpfer wird entworfen und untersucht. Dieser Dämpfer bringt Dämpfung bei hohen Schwingungsamplituden in System ein und nutzt Tilgung bei niedrigen Schwingungsamplituden aus. Es werden numerische und analytische Untersuchungen durchgeführt. Um das qualitative Verhalten des Dämpfers zu validieren, wird ein Dämpferprototyp konstruiert und erprobt. Zudem wurde auch eine aktive Variante des abgestimmten Keildämpfers betrachtet. Es werden zwei Regelstrategien entworfen, die adaptive Mehrmodellregelung und die langsame, frequenzbasierte Regelung. Diese werden mit einer State-of-the-Art- Regelungsstrategie in transienten, quasistationären und Anwendungsszenarien verglichen. Die Untersuchungen zum passiven, abgestimmten Keildämpfer zeigen, dass Dämpfung und Tilgung entkoppelt werden. Eine Optimierung der Dämpferparameter ergibt im Frequenzgang eine Reduktion der Maximalamplitude von 87.47% unter Beibehaltung der Tilgung. Die Experimente validieren den Entkopplungseffekt sowie den qualitativen Einfluss der Parameter. Die aktiven Systeme erreichen mit Amplitudenabsenkungen von 91.11% das beste Ergebnis

Self-synchronization and controlled synchronization

An attempt is made to give a general formalism for synchronization in dynamical systems encompassing most of the known definitions and applications. The proposed set-up describes synchronization of interconnected systems with respect to a set of functionals and captures peculiarities of both self-synchronization and controlled synchronization. Various illustrative examples are give