Dynamic modeling of structures from measured complex modes

ABSTRACTA new type of large semi-rigid solar array structure with a new structural concept of rigid-flexible combination has developed for space application. Due to the good features of large scale and lightweight, such structure can well satisfy to the large power requirements of spacecraft and thus has drawn increasing attention recently. However, its structural weakness of inherently flexibility makes low frequency vibrations happen much easier. It is highly required to obtain an accurate dynamic model for predicting the dynamic characteristics of this kind of semi-rigid space structure. Because this structure is composed of different components that have quite different stiffness properties respectively, it is very difficult to build up an accurate dynamic model of this complex structure. In this paper, a novel analytical dynamic model is developed for solving this problem. To validate the correctness of the proposed model, experiment studies are conducted. By comparing the simulation results with experimental results, it can be concluded that this dynamic modeling method presented in the paper is credible. The present study is significant for the structural construction and application of this special structure.

A mechanical-magnetic-electro bidirectional coupled dynamic model of a composite cantilever with magnetostrictive shunt damper is established, and the system's transfer functions and a key impedance impact factor are derived. For shunt vibration damping, H2 optimization criterion and the Nelder-Mead search method are used to obtain the optimal parameters of three circuits: resistance shunt (RS), capacitance shunt (CS), and resistance-CS (RCS). Comparisons between the calculated and measured results show that the proposed model can accurately describe the transmissibility vibration frequency responses of the system under RS and CS, and can predict the changing laws of the resonant frequency and the resonant peak with the shunt impedance. It is found that the RCS with negative shunt resistance can provide the peak attenuation rate 90.78%, which is higher than 70.44% of CS and 53.29% of RS, and has wider frequency broadband and faster vibration damping performances than CS and RS.

This paper analyses design and performance aspects of a brushless doubly fed three-phase induction machine with wound rotor circuit accessed by rotary transformer. It focuses firstly on the advantages of substituting brushes and slip-rings by rotary transformers. Secondly it shows the device operation conditions and rotary transformer calculation by using Finite Element Software in 2D domain. In sequence are presented analytical dynamic and steady state models for prediction of machine behavior. The analytical dynamic model is obtained by transforming the equations written in machine variables into equations written in arbitrary reference frame. The steady state model considers electrical circuit techniques to obtain information about current, power factor and efficiency on load. Design data of a 90kW prototype were considered for numerical results presented on this study.

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The Robot with nonlinear and stochastic dynamic challenges optimal control that relying on an analytical model. Model-free reinforcement learning algorithms have shown their potential in robot learning control without an analytical or statistical dynamic model. However, requiring numerous samples hinders its application. Model-based reinforcement learning that combines dynamic model learning with model predictive control provides promising methods to control the robot with complex dynamics. Robot exploration generates diverse data for dynamic model learning. Model predictive control exploits the approximated model to select an optimal action. There is a dilemma between exploration and exploitation. Uncertainty provides a direction for robot exploring, resulting in better exploration and exploitation trade-off. In this paper, we propose Model Predictive Control with Posterior Sampling (PSMPC) to make the robot learn to control efficiently. Our PSMPC does approximate sampling from the posterior of the dynamic model and applies model predictive control to achieve uncertainty directed exploration. In order to reduce the computational complexity of the resulting controller, we also propose a PSMPC guided policy optimization algorithm. The results of simulation in the high fidelity simulator "MuJoCo" show the effectiveness of our proposed robot learning control scheme.

Discrete event models are widely used to replicate, analyze, and understand complex systems. DEVS (Discrete Event System Specification) formalism enables hierarchical modeling, so it provides an efficiency in the model development of complex models. However, the hierarchical modeling incurs prolonged simulation executions due to indirect event exchanges through the model hierarchy. Although direct event paths are applied to mitigate this overhead, the situation becomes even worse when a model changes its structures during simulation execution, called a dynamic structure model. This article suggests Coupling Relation Graph (CRG) and Strongly Coupled Component (SCC) concepts to improve hierarchical and dynamic structure DEVS simulation execution. CRG is a directed graph representing DEVS model structure, and SCC is a group of connected components in a CRG. Using CRG and SCC, this article presents (1) how to develop CRG from a DEVS model and (2) how to construct and update direct event paths with respect to dynamic structural changes. In particular, compared to the previous works, the proposed method focuses on the reduction of the updating costs for the direct event paths. Through theoretical and empirical analyses, this article shows that the proposed method significantly reduces the simulation execution time, especially when a simulation model contains lots of components and changes its model structures frequently. We expect that the proposed method would support the faster simulation executions of complex hierarchical and dynamic structure models.

A Linear Quadratic Regulator (LQR)-based least-squares output feedback control procedure using a complex mode procedure is developed for the optimal vibration control of high-order asymmetric discrete system. An LQ Regulator is designed for a reduced-order model obtained by neglecting high-frequency complex modes of the original system. The matrix transformations between physical coordinates and complex mode coordinates are derived. The complex mode approach appears to provide more accurate reduced-order models than the normal mode approach for asymmetric discrete systems. The proposed least-squares output feedback control procedure takes advantage of the fact that a full-state feedback control is possible without using an observer. In addition, the lateral vibration of a high-order rotor system can be effectively controlled by monitoring one single location along the rotor shaft, i.e., the number of measured states can be much less than the number of eigenvectors retained in producing the reduced-order model while acceptable performance of the controller is maintained. The procedure is illustrated by means of a 52 degree-of-freedom finite element based rotordynamic system. Simulation results show that LQ regulators based on a reduced-order model with 12 retained eigenvalues can be accurately approximated by using feedback of four measured states from one location along the rotor shaft. The controlled and uncontrolled transient responses, using various numbers of measured states, of the original high-order system are shown. Comparisons of reduced-order model results using normal modes and complex modes are presented. The spillover problem is discussed for both collocated and noncollocated cases based on this same example.

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Multirotor analytical dynamic inflow models in the literature, such as pressure potential superposition inflow model or velocity potential superposition inflow model (VPSIM), have been shown to capture the fundamental inflow interference effects between the rotors. Some of the differences in inflow predictions seen between these analytic models and high-fidelity wake models are attributed to missing real flow effects such as wake distortion, contraction, decay, swirl, etc. As such, correction terms are needed in the analytically derived multirotor finite-state inflow models, because of the potential flow and rigid wake assumptions they are based on, in order to capture some of the missing real flow effects in them. This paper develops a systematic methodology for arriving at the needed correction terms in the VPSIM through comparisons of its inflow predictions with those of a viscous vortex particle model (VVPM). Also, a procedure is developed to assess the relative importance of individual real flow effects and the associated corrections needed for improving the overall fidelity of the VPSIM. The developed methodology is applied to the Harrington coaxial rotor using its geometric and aerodynamic data from the literature. It is shown that the addition of swirl coupling correction terms to the VPSIM significantly improves its correlations with the VVPM. Further, it is shown that the required corrections are reasonably insensitive to thrust sharing ratio conditions between the rotors.

There is still lack of effective modelling, simulation and optimisation methods for complex electromechanical system. In this paper, the dynamics model of the PMSM-precision reducer system is established using Lagrange-Maxwell equation. The simulation model and optimisation model of this system are set up with Modelica language. The simulation and optimisation of the system are realised in Dymola and JModelica.org platforms respectively. Simulation results show that the dynamics model of the system is correct. Optimisation results show that the system can quickly respond to the given speed and loads. The proposed modelling, simulation and optimisation method based on Modelica may be commonly applied to other complex electromechanical systems.

Modeling of tire friction is one of the central problems for vehicle control systems design. LuGre-type dynamic tire model has been proposed and well discussed in previous studies, because it offers a compact form of dynamic model that is convenient in advanced control studies. It has been successfully used in tire slip control design and vehicle state estimation problems. In this article, a concept of time-constrained Stribeck effect is introduced to interpret the mechanism of the LuGre friction model in predicting tire friction characteristics. A modified two-dimensional (2D) dynamic LuGre friction model is introduced to make it compatible with the governing theorem in the steady state. An analytical 2D modified LuGre-type dynamic tire model is developed, in which some fundamental limitations of classical LuGre models are eliminated. The main modifications involve a change in the structure of the 2D LuGre friction model, introduction of load-dependent parameters in 1D and 2D tire models, and a changed structure in the distributed parameter model. The proposed model is compared, in the steady state, to both the Magic Formula and the classical LuGre model. It improves model accuracy in the steady state and gives a physically reasonable distribution of the bristle deflection. A first-order lumped parameter (LP) nonlinear model, which has simpler structure than the distributed parameter model and the classical LP LuGre model, is then derived. Numerical simulations show that the proposed LP model has a good estimation for tire transient dynamics. Thus, the proposed model retains the merits of LuGre-type models and improves the agreement with observation and experimental data on friction force distribution along the patch and on the steady-state friction prediction.