Proportional-Integral-Observer With Adaptive High-Gain Design Using Funnel Adjustment Concept

This paper focuses on a novel gain design approach of Proportional-Integral-Observer (known as PI-Observer) for unknown input estimation such as disturbances. Whereas estimation of the fast dynamical behavior requires large observer gains, the effect of measurement noise is not negligible. To adjust the PIO gain adaptively, in this contribution the idea of funnel control is taken into consideration. The advantage of the proposed approach compared to previously published PIO gain design is the self adjustment of the observer gains according to the actual estimation situation. To improve the control performance and robustness, in the present contribution the proposed approach is combined with exact feedback linearization (EFL) method. The effectiveness of the proposed approach is verified by simulation results of a MIMO mass-spring system.

Application of the POD Method for Cracked Rotors

The application of the proper orthogonal decomposition (POD) method to the vibration response of a cracked Jeffcott rotor model is investigated here. The covariance matrices of horizontal and vertical whirl amplitudes are formulated based on the numerical integration response and the experimental whirl response, respectively, for the considered cracked rotor system. Accordingly, the POD is directly applied to the obtained covariance matrices of the numerical and experimental whirl amplitudes where the proper orthogonal values (POVs) and the proper orthogonal modes (POMs) are obtained for various crack depths, unbalance force vector angles and rotational speeds. It is observed that both POVs and their corresponding POMs are highly sensitive to the appearance of the crack and the unbalance angle changes at the neighborhoods of the critical. The sensitivity zones of the POVs and POMs to the crack propagation coincide with the unstable zones of the cracked system obtained by Floquets theory.

Null Space Method of Differential Equation Type for Motion Analysis of Multibody Systems

The governing equations of multibody systems are, in general, formulated in the form of differential algebraic equations (DAEs) involving the Lagrange multipliers. For efficient and accurate analysis, it is desirable to eliminate the Lagrange multipliers and dependent variables. Methods called null space method and Maggi’s method eliminate the Lagrange multipliers by using the null space matrix for the constraint Jacobian. In previous reports, one of the authors presented methods which use the null space matrix. In the procedure to obtain the null space matrix, the inverse of a matrix whose regularity may not be always guaranteed. In this report, a new method is proposed in which the null space matrix is obtained by solving differential equations that can be always defined by using the QR decomposition, even if the constraints are redundant. Examples of numerical analysis are shown to validate the proposed method.

Comparison of Control Methods for Two-Link Planar Flexible Manipulator

While the majority of terrestrial multi-link manipulators can be considered in a purely kinematic sense due to their high stiffness, the launch mass restrictions of aerospace applications such as in-orbit assembly of large space structures result in low stiffness links being employed, meaning dynamics can no longer be ignored. This paper seeks to investigate the suitability of several different open and closed loop control techniques for application to the problem of end effector position control with minimal vibration for a low stiffness space based manipulator. Simulations of a representative planar problem with two flexible links are used to measure performance and sensitivity to parameter variation of: model predictive control, command shaping, and command shaping with linear quadratic regulator (LQR) feedback. An experimental testbed is then used to validate simulation results for the recommended command shaped controller.

Model-Free Control Approach of a Three-Tank System Using an Adaptive-Based Control

For improving the dynamics of systems in the last decades model-based control design approaches are continuously developed. The task to design an accurate model is the most relevant and related task for control engineers, which is time consuming and difficult if in the case of complex nonlinear systems a complex modeling or identification problem arises. For this reason model-free control methods become attractive as alternative to avoid modeling. This contribution focuses on design methods of a model-free adaptive-based controller and modified model-free adaptive-based controller. Modified approach is based on the same adaptive model-free control algorithm performing tracking error optimization. Both approaches are designed for non-linear systems with uncertainties and in the presence of disturbances in order to assure suitable performance as well as robustness against unknown inputs. Using this approach, the controller requires neither the information about the systems dynamical structure nor the knowledge about systems physical behaviors. The task is solved using only the system outputs and inputs, which are measurable. The effectiveness of the proposed method is validated by experiments using a three-tank system.

Bifurcation Trees of Periodic Motions in a Parametrically Excited Pendulum

In this paper, the bifurcation trees of periodic motions in a parametrically excited pendulum are studied using discrete implicit maps. From the discrete maps, mapping structures are developed for periodic motions in such a parametric pendulum. Analytical bifurcation trees of periodic motions to chaos are developed through the nonlinear algebraic equations of such implicit maps in the specific mapping structures. The corresponding stability and bifurcation analysis of periodic motions is carried out. Finally, numerical results of periodic motions are presented. Many new periodic motions in the parametrically excited pendulum are discovered.

Advancement of Contact Dynamics Modeling for Human Spaceflight Simulation Applications

Pong is a new software tool developed at the NASA Johnson Space Center that advances interference-based geometric contact dynamics based on 3D graphics models. The Pong software consists of three parts: a set of scripts to extract geometric data from 3D graphics models, a contact dynamics engine that provides collision detection and force calculations based on the extracted geometric data, and a set of scripts for visualizing the dynamics response with the 3D graphics models. The contact dynamics engine can be linked with an external multibody dynamics engine to provide an integrated multibody contact dynamics simulation. This paper provides a detailed overview of Pong including the overall approach, modeling capabilities, which encompasses force generation to computational performance, and example applications.

Parallel Time-Integration of Flexible Multibody Dynamics Based on Newton-Waveform Method

Traditionally, the time integration algorithms for multibody dynamics are in sequential. The predictions of previous time steps are necessary to get the solutions at current time step. This time-marching character impedes the application of parallel processor implementation. In this paper, the idea of computing a number of time steps concurrently is applied to flexible multi-body dynamics, which makes parallel time-integration possible. In the present method, the solution at the current time step is computed before accurate values at previous time step are available. This method is suitable for small-scale parallel analysis of flexible multibody systems.

Control of Nonlinear Systems in Normal Form by Complementary Lyapunov Functions

If a Lyapunov function is known, a dynamic system can be stabilized. However, the search for a Lyapunov function is often challenging. This paper takes a new approach to avoid such a search; it assumes a basic Control Lyapunov Function [CLF] then seeks to numerically diminish the value of the Lyapunov function. If a singularity arises during calculations with the default CLF, a complementary function is used. The complementary function eliminates a common cause of singularities with the default CLF. While many other algorithms from the literature use switched or time-varying CLF’s, the presented method is unique in that the CLF’s do not require prior calculation and the technique applies globally. The method is proven and demonstrated for SISO systems in normal form and then demonstrated on a higher-order system of a more general type.

On Mode Coupling Analysis and Stability Regions to Energy Harvesting in a Two-Degrees-of-Freedom Portal Frame Platform

This work aims to study the modal coupling of a nonlinear two-degrees-of-freedom portal frame platform and a numerical analysis of the system with a nonlinear piezoelectric (PZT) material coupled to one of its columns, both externally base-excited. The nonlinear platform possesses two-to-one internal resonance between its two vibration modes and presenting the saturation phenomenon. The nonlinearities of the piezoelectric material are considered by a nonlinear mathematical relation. Here, it is considered an electro-dynamical shaker with harmonic output. The employed methodology to carry out the analysis of this work was: the application of the method of multiple scales to find the best configuration of the parameters, and to find some kind of phenomena due to the two-to-one internal resonance; several numerical simulations were carried out to optimize the energy harvesting through parametrical variations, bifurcation diagrams, stability diagrams. It will be analyzed: the influence of the nonlinearity of the piezoelectric material and of the electro-dynamical shaker on the energy harvesting. Results showed great influence of the nonlinearity of the material and using the electro-dynamical device. It was possible to gain considerably in energy harvesting and stability of the system.