State-space system identification with physically motivated residual states and throughput rank constraint

<div class="htmlview paragraph">An investigation was made of the problem of providing an automatic control system for a large booster subject to severe mode interaction. This interaction is defined as a strong aerodynamic coupling between the rigid body motion and one or more elastic modes of the vehicle and can appear as a flutter phenomenon between rigid and elastic degrees of freedom as opposed to “classical” flutter between two or more elastic degrees of freedom. For the booster considered, the interaction resulted in a rigid-body mode static divergence for an aerodynamically statically stable rigid configuration in the uncontrolled or forward-loop-only system. It was shown that preliminary control system design must include the significant elastic modes when mode interaction is present. A rigid-body-only synthesis will not yield “ballpark” values for the control element gains.</div> <div class="htmlview paragraph">The investigation revealed that the active control philosophy of using auxiliary control inputs to increase the frequencies of the elastic modes sufficient to reduce the mode interaction in the forward-loop is a false notion. It is the free-free bending modes which interact with the rigid-body motion, and input forces cannot alter their mode shapes and frequencies. They can be altered only by mass and structural stiffness changes to the basic vehicle. The input forces result in changes to elastic mode coupled frequencies and damping ratios which do not effect the mode interaction phenomenon as defined herein.</div> <div class="htmlview paragraph">Analysis has shown that it is meaningless to specify desired transient response in terms of closed-loop short-period frequency and damping ratio as a criterion for control system synthesis when the vehicle is subject to severe mode interaction. In general, the closed-loop modes cannot be identified as being elastic or rigid-body in the conventional sense. In this case new synthesis criteria are needed. Perhaps a better approach would be to specify desired time histories for the various output variables.</div>

Determination Of Rigid Body Characteristics From Time Domain Modal Test Data

The 5# arc working gate of Jiangshan Wanyao Reservoir is composed of the suspension system of the gate and the steel wire rope, which has a serious vibration phenomenon when running without water. Firstly, the rigid body modal analysis of the gate suspension system is analyzed, the position size of key components such as gate support hinge shaft, gate motion guide embedded parts, and main beam position state is measured and evaluated on site, and the dynamic stress and vibration of the support arm are tested and analyzed during gate operation. It is concluded that the influence rule and weight of the steel wire rope on the rigid body mode of the gate, the torsional position of the gate, and the uneven operation condition of the side guide lead to the rigid body mode of the gate. It is suggested to improve the twisting state of the gate, adjust the unevenness of the embedded parts, and weaken the factors that induce the modal vibration of the rigid body.

Integral resonant control (IRC) is an effective vibration control technique for flexible structures including multiple vibration modes, even though the controller is a simple first-order system. However, IRC can not be directly applied to flexible structures with rigid body modes. This paper proposes a new method to apply IRC by choosing an angle difference output in which the rigid body modes are unobservable but only elastic modes observable. The proposed method is effective for applying IRC to torsional vibration systems where the control objective is to reduce only torsional vibration modes while leaving the rigid body mode preserved. However, side effects such as an inverse response and a brake effect occur depending on the choice of the controller parameter. This paper clarifies the condition for the inverse response and the magnitude of the brake effect on the rigid body motion analytically. A new design method for the IRC controller is then presented based on the trade-off between the brake effect and the vibration suppression performance.

In the wireless sensor network (WSN) based rigid body target localization systems, the error caused by the non-line-of-sight (NLoS) transmission of wireless signal can seriously deteriorate the localization accuracy. To improve the estimation performance of rigid body posture, including the parameters of the position and the direction, a rigid body localization (RBL) technology is proposed based on the semi-definite programming (SDP) with NLoS error elimination. By taking the unknown NLoS errors as the balancing parameters in the received signal strength (RSS) model, the results of the maximum likelihood estimation (MLE) is obtained according to a nonlinear least squares (NLS) problem, which is solved by using the semi-definite relaxation (SDR) method. The obtained balancing parameters are then re-substituted into the model to refine the parameters in the semi-definite programming problem to mitigate the effect of the NLoS error on the localization performance. Finally, the singular value decomposition (SVD) is used to solve the parameters of rigid body posture. The effectiveness of the algorithm is verified by computer simulation.

The Laplace problem subject to the Dirichlet or Neumann boundary condition in the direct and indirect boundary element methods (BEM) sometimes both may result in a singular or ill-conditioned system (some special situations) for the interior problem. In this paper, the direct and indirect BEMs are revisited to examine the uniqueness of the solution by introducing the Fichera’s idea and the self-regularized technique. In order to construct the complete range of the integral operator in the BEM lacking a constant term in the case of a degenerate scale, the Fichera’s method is provided by adding the constraint and a slack variable to circumvent the problem of degenerate scale. We also revisit the Fredholm alternative theorem by using the singular value decomposition (SVD) in the discrete system and explain why the direct BEM and the indirect BEM are not indeed equivalent in the solution space. According to the relation between the SVD structure and Fichera’s technique, a self-regularized method is proposed in the matrix level to deal with non-unique solutions of the Neumann and Dirichlet problems which contain rigid body mode and degenerate scale, respectively, at the same time. The singularity and proportional influence matrices of 3 by 3 are studied by using the property of the symmetric circulant matrix. Finally, several examples are demonstrated to illustrate the validity and the effectiveness of the self-regularized method.

The calculation of modal cross-section properties for use in the generalized beam theory

Analytical derivation and numerical experiments of degenerate scales for regular N-gon domains in two-dimensional Laplace problems

A theoretical analysis of free dry and wet vibration of a trapezoidal, 2-way tapered, marine spade rudder, is presented. The rudder is considered as a hollow Kirchhoff’s plate, with the chord section as a NACA profile. The chord length and the thickness taper from the top to the bottom, over the vertical span. The rudder is pivoted at the top, with the pivot behind the leading edge. The pivot is modeled as a combination of a translational and a rotational spring, in order to include the rigid body modes of the rudder vibration. The span-wise and chord-wise non-uniform beam vibration is first analyzed by the Rayleigh-Ritz method, in order to establish the non-uniform beam mode shapes. The span-wise beam is a linearly tapered vertical cantilever, with non-classical edge at the top and free at the bottom. The chord-wise section is a 2-span beam with the ends free, and four continuity conditions at the pivot. The non-uniform mode shapes, in either direction, are a weighted summation of the uniform beam mode shapes, which also satisfy the boundary/continuity conditions. They now act as admissible spatial functions to the plate vibration, which is analyzed by the Galerkin’s method. Eigenvalue analysis generates the plate natural frequencies. A weighted superposition, of the product of the beam mode shapes, in either direction, generates the plate mode shapes. Alternately, uniform beam mode shapes are used as admissible functions into the Galerkin’s method for the plate natural frequencies and mode shapes. The natural frequencies are generated for various positions of the rudder stock along the chord length. The pivot conditions (in both translational and rotational rigid body degree of freedom) influence the prominence of the rigid body mode shapes. The natural frequencies are analyzed for various pivot fixities, taper ratios, and aspect ratios of the plate. This is followed by the wet vibration analysis of the rudder. First, 2D strip theory is used to generate the added mass of each chord section. Constant strength source distribution technique is used to generate the added mass in sway and yaw of a 2D aerofoil. Each flexural and torsional mode is associated with its own added mass. Various empirical corrections are done to account for the 3D flow. Finally, 3D panel method is used to generate the modal added masses, and hence the wet natural frequencies. The added mass coefficient is generated for various aerofoil fineness ratios, pivot fixities, taper ratios, and aspect ratios of the plate.

: New handling qualities specifications are currently being developed for attack helicopters. Most unaugmented helicopters will not meet these specifications and feedback control is necessary to improve handling qualities so that safe operation close to the earth in poor weather conditions and/or at night is possible. In this paper a methodology for the direct design of helicopter flight control systems which meet handling qualities specifications is presented. This methodology uses full state feedback to place closed loop eigenvalues to achieve bandwidth specifications and to shape closed loop eigenvectors to decouple lateral and longitudinal responses to control inputs. Full state feedback requires that all state variables be known; however, only angular rates and normal acceleration are measured by sensors. Thus, a state estimator is required in the feedback loop in order to convert sensor outputs to control inputs. This estimator is designed using eigenstructure assignment so as to achieve loop transfer recovery. Design of a feedback system for use in precise hovering control for a modern attack helicopter is used to illustrate the method. Control law synthesis is accomplished using an eighth order model which includes only rigid body modes. Control law performance is evaluated using a 37th order model which includes rigid body, actuator, rotor, sensor, and flexure dynamics. It is found that a notch filter must be added to the design in order to eliminate a high frequency instability. Once this is accomplished, both the time and frequency response characteristics of the augmented helicopter are much improved compared with the unaugmented helicopter.

Evaluation of the performance of a passive–active vibration isolation system

In this paper, an improved wedge damper model is presented, based on which the effects of wedge dampers on the forced response of frictionally constrained blades are investigated. In the analysis, while the blade is modeled as a constrained structure, the damper is considered as an unconstrained structure. The model of the damper includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the damper is not artificially constrained. When modeling the contact surfaces of the wedge damper, discrete contact points along with contact stiffness are evenly distributed on the two contact surfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the engine rpm, quasi-static contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the centrifugal force. A friction model is employed to determine the three-dimensional nonlinear contact forces and the relationship between the contact forces and the relative motion is utilized by the Harmonic Balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations, in the Harmonic Balance method is in proportion to the number of modes employed, and therefore the number of contact points used is irrelevant. The developed method is applied to tuned bladed disk system and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that, the effect of rotational motion is significant, particularly for the in-phase vibration modes.

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

In order to achieve better performances and reduce fuel consumption, the new generation of turbomachines uses larger and lighter design, for instance the “open-rotor” concept, and is conceived to rotate at higher speeds. Parts of the structure become then even more likely to undergo large amplitude vibrations. Consequently, the conception of future aero-engine requires a sound and robust technique to predict the rotating machine vibrations considering geometrical nonlinearities (large displacements and large deformation). In this paper, the nonlinear vibrations of rotating beams with large displacements is investigated by the use of the Co-Rotational (C-R) finite element method. In the C-R approach, the full motion of each element is decomposed into a rigid body part and a pure deformational part by introducing a local coordinate system attached to the element. The utilization of the C-R method offers the possibility to treat geometrical nonlinearity directly with pre-extracted rigid body motion displacements. The originality we propose in this study is to derive its formulation in a rotating reference frame and include both centrifugal and gyroscopic effects. The nonlinear governing equations are obtained from Lagrange’s equations using a consistent expression for the kinetic energy. With this formulation, the spin-stiffening effect from geometrical nonlinearities due to large displacements is accurately handled. The proposed approach is then applied to several types of mechanical analysis (static large deformation, modal analysis at different spin speeds, and transient analysis after an impulsive force) to verify its accuracy and demonstrate its efficiency.

Two finite-element models, one derived from the principle of minimum total potential energy and the other derived from a modification of the same, are considered for linear analysis of shells of revolution. The first is a compatible displacement model in which an element interior displacement field that generates compalible interelement boundary displacements and rotations is assumed, but no rigid-body displacement modes are included in the element displacement field; the second is a hybrid displacement model in which rigid-body modes are included explicitly in the displacement field in the interior of the element and a Lagrangian multiplier technique is needed to satisfy the