Johannes Schröck

Motion Planning for Piezo-Actuated Flexible Structures: Modeling, Design, and Experiment

We consider motion planning and feedforward control for a cantilevered flexible plate-like structure actuated by a finite number of surface-mounted piezoelectric patches to realize prescribed highly dynamic trajectories for the deflection profile in open loop. For this, a distributed-parameter mathematical model including damping and localized effects originating from the spatially distributed patch actuators is derived by means of the extended Hamiltons principle. With this, a flatness-based design methodology is proposed for motion planning and feedforward control, which directly exploits the distributed-parameter system description. In particular, differential state, input, and output parameterizations are systematically constructed in terms of a basic output to achieve a one-to-one correspondence between system trajectories. Finite element methods are incorporated into the design to account for structures with nontrivial domain and nonisotropic material behavior. In addition, the convergence of the system parameterization is analyzed analytically and by means of numerical results. Finally, measurement results demonstrate the applicability of this approach for the realization of highly dynamic rest-to-rest transitions of the deflection profile of an orthotropic plate structure with macro-fiber composite patch actuators.

Control of a flexible beam actuated by macro-fiber composite patches: I. Modeling and feedforward trajectory control

This paper considers a systematic approach for motion planning and feedforward control design for a flexible cantilever actuated by piezoelectric macro-fiber composite (MFC) patches. For accurate feedforward tracking control, special attention has to be paid to the inherent nonlinear hysteresis and creep behavior of these actuators. In order to account for these effects an appropriate compensator is applied which allows us to perform the tracking controller design on the basis of a linear infinite-dimensional model. A detailed analysis of the nonlinear actuator behavior as well as the compensator design and the overall experimental validation is presented in the companion paper (Schrock et al 2011 Smart Mater. Struct. 20 015016). The governing equations of motion of the hysteresis and creep compensated cantilever are determined by means of the extended Hamiltons principle. This allows us to consider the influence of the bonded patch actuators on the mechanical properties of the underlying beam structure in a straightforward manner and results in a model with spatially varying system parameters. For the solution of the motion planning and feedforward control problem a flatness-based methodology is proposed. In a first step, the infinite-dimensional system of the MFC-actuated flexible cantilever is approximated by a finite-dimensional model, where all system variables, i.e. the states, input and output, can be parameterized in terms of a so-called flat output. In a second step, it is shown by numerical simulations that these parameterizations converge with increasing system order of the finite-dimensional model such that the feedforward control input can be directly calculated in order to realize prescribed output trajectories.

Non-collocated feedback stabilization of a non-uniform Euler-Bernoulli beam with in-domain actuation

For the stabilization of a flexible beam actuated by piezoelectric patches a Lyapunov-based control strategy is presented in terms of a non-collocated dynamic output feedback control. Thereby, a distributed-parameter Luenberger observer is incorporated to provide an estimate of the variables required by the control law. Besides the proof of asymptotic stability of the closed-loop system, the derived control concept is validated by experimental results.

Motion planning for a damped euler-bernoulli beam

The motion planning problem is considered for a Euler-Bernoulli beam with viscous damping. For its solution, a systematic spectral approach is proposed, which is based on the Riesz spectral properties of the system operator. This enables to analyze both boundary and in-domain control in a common framework.

Motion planning for an adaptive wing structure with macro-fiber composite actuators

A systematic approach for flatness-based motion planning and feedforward control is presented for the transient shaping of a piezo-actuated rectangular cantilevered plate modeling an adaptive wing. In the first step the consideration of an idealized infinite-dimensional input allows to determine the state and input parametrization in terms of a flat or basic output, which is used for a systematic motion planning approach. Subsequently, the obtained idealized input function is projected onto a finite number of suitably placed Macro-fiber Composite (MFC) patch actuators. The tracking performance of the proposed approach is evaluated in a simulation scenario.

Infinit-dimensionaler Reglerentwurf für Euler-Bernoulli Balken mit Macro-Fibre Composite Aktoren

Zusammenfassung Dieser Beitrag beschäftigt sich mit der Regelung eines einseitig eingespannten Euler-Bernoulli Balkens mit piezoelektrischen Aktoren, die in Form von Macro-Fibre Composite Patches realisiert sind. Auf Basis des verteilt-parametrischen mathematischen Modells wird eine nicht-kollokierte dynamische Ausgangsregelung entworfen, die die asymptotische Stabilität des geschlossenen Regelkreises gewährleistet. Neben der mathematischen Analyse werden die entwickelten Methoden an einem Versuchsstand experimentell validiert. Die Messergebnisse zeigen die Machbarkeit des vorgestellten Ansatzes. Abstract

Motion planning for an elastic Kirchhoff plate

The motion planning problem is considered for a cantilevered orthotropic Kirchhoff plate with spatially varying coefficients and distributed piezoelectric patch actuators. For this, the spectral representation of the corresponding equations of motion is utilized to systematically construct a flatness-based parametrization of state and inputs. These enable a very intuitive motion planning to realize prescribed high-speed rest-to-rest motions as is illustrated in simulation scenarios.

Trajektorienplanung für eine piezo-aktuierte elastische Kirchhoff-Platte

SummaryThe motion planning problem is considered for a cantilevered orthotropic Kirchhoff plate with spatially varying coefficients and distributed piezoelectric patch actuators. For this, the spectral representation of the corresponding equations of motion is utilized to systematically construct a flatness-based parametrization of state and inputs. These enable a very intuitive motion planning to realize prescribed high-speed rest-to-rest motions. Moreover, the incorporation of weighted residuals approaches yields a very efficient computational implementation. Simulation results confirm the applicability of the design approach and the achievable tracking performance.ZusammenfassungDie Trajektorienplanungsaufgabe für verteilt-parametrische Systeme wird anhand des Beispiels einer einseitig eingespannten orthotropen Kirchhoff-Platte mit örtlich verteilten Patch-Aktoren analysiert. Hierzu wird auf Basis der spektralen Darstellung der Bewegungsgleichung ein systematischer Ansatz zur flachheitsbasierten Parametrierung des Auslenkungsprofils und der Stellgrößen vorgestellt. Dies ermöglicht einen intuitiven Zugang zur Trajektorienplanung und zur Realisierung hochdynamischer Übergänge zwischen stationären Auslenkungsprofilen. Die Verwendung gewichteter Residuenverfahren ermöglicht zudem eine effiziente Computer-gestützte Umsetzung des Entwurfsverfahrens. Simulationsergebnisse bestätigen die Anwendbarkeit der entwickelten Methodik und illustrieren das erzielbare Folgeverhalten.

Motion Planning for a Flexible Link Manipulator with Macro-Fiber Composite Actuators

Abstract The motion planning and feedforward control design is considered for the realization of highly dynamic output trajectories for the deflection and the angle of the tip of a lightweight flexible link manipulator that is actuated by piezoelectric actuators (macro-fiber composite patches). For this, a systematic flatness-based approach based on the distributed parameter model is presented, whose applicability is verified by experimental results of the tracking performance.