568 research outputs found

    Pole Assignment for a Vibrating System with Aerodynamic Effect

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    This paper deals with a pole assignment problem by single-input state feedback control arising from a one-dimensional vibrating system with aerodynamic effect. On the practical side, we derive explicit formulae for the required controlling force terms, which can reassign part of the spectrum to the desired values while leaving the remaining spectrum unchanged. On the mathematical side, unlike the classical Sturm–Liouville problem, our eigenvalue problem is associated with a cubic pencil with unbounded operators as coefficients and has many interesting new features, one of which is that a new controllability condition appears. This condition together with the known controllability condition in the quadratic case are necessary and sufficient. This sheds light on the adjustment of the model parameters. We also analyze the spectrum of the associated noncompact operator and in particular show that the discrete spectrums of controlled and uncontrolled systems lie outside a closed interval on the negative real axis

    State feedback control with time delay

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    In this thesis we start with an introduction to the theory of vibration control. We broadly classify the control methods into passive and active schemes. We introduce the problem of state feedback control and provide the classical solution in the form of Ackermann formula. We then identify the limitations of the classical approach and present the more elegant solution of partial pole assignment without spillover. We highlight the problem with model uncertainties and describe the method of pole assignment using data from measured receptances. This approach is extended for pole assignment for a linear vibrating system by using state feedback control delayed in time. This approach is significantly advantageous over various conventional state-space approaches which need to use information of , and matrices. Since the method relies solely on measured receptances, it negates the need to know , and matrices. It is shown that for a system with degrees of freedom, we may assign eigenvalues. Assigning eigenvalues in a time delayed system does not necessarily regulate the dynamics of the system or guarantee its stability. We separate the eigenvalues into two groups, primary and secondary, and propose method of a posteriori analysis to ensure that the primary eigenvalues have been assigned. The method is demonstrated by various examples. For state feedback control, the control is achieved by measuring the states of the system and feeding them back into the system after multiplying them with appropriate control gain. This makes it imperative to measure all the states of the system. In practical control applications, all states are not accessible for measurement. We address the problem of inaccessibility of states making it difficult to implement the state feedback control. We introduce the theory of linear state estimation also called observer design. We identify the limitations of this approach and introduce the concept of state reconstruction by delayed action. We develop a method to reconstruct the inaccessible states by introducing delay in the system and using information from accessible states. The results are demonstrated by examples

    The minimum norm multi-input multi-output receptance method for partial pole placement

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    A closed-form analytical solution is developed for the first time that fully addresses the problem of choosing feedback gains that minimize the control effort required for partial pole placement in multi-input, multi-output systems. The norm of the feedback gain matrix is shown to take the form of an inverse Rayleigh quotient, such that the optimal closed-loop system eigenvectors are given as a function of the dominant (highest)eigenvectors of the matrix in the quotient. The feedback gains that deliver the required pole placement with minimum effort may then be determined using standard procedures. The original formulation by the receptance method proposed an arbitrary choice of the closed loop eigenvectors that assigned the poles exactly but was generally wasteful of control effort that might otherwise be conserved or put to good use in satisfying additional control objectives. The analytical solution is validated against a set of numerical examples

    Multiple-Input Multiple-Output Experimental Aeroelastic Control Using a Receptance-Based Method

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    This paper presents the first experimental study of multiple-input multiple-output (MIMO) active vibration suppression by pole placement using the receptance method. The research is based on a purpose-built modular flexible wing equipped with leading- and trailing-edge control surfaces and two displacement sensors for measuring its position. The MIMO controller has the advantage of being designed entirely on frequency response functions, which are measured between the control surface position (control inputs) and the structural displacements (outputs), and include the actuator dynamics. There is no requirement to evaluate or to know the structural M, C, and K matrices or the aerodynamic loads; and the formulation eliminates the need for a state observer. The controller is first implemented numerically and then experimentally on the aeroelastic system. Both frequencies and damping are assigned (together or independently) for the first two vibration modes. The research includes a procedure for assessing the control effort required and demonstrates an effective means of increasing the flutter margin while the effort is minimized

    Active vibration control in linear time-invariant and nonlinear systems

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    Active vibration control techniques are widely used in linear time-invariant and nonlinear systems. However, there still exist many difficulties in the application of conventional active vibration control techniques, including the following: (1) In application, some of the degrees of freedom may not be physically accessible to actuation and sensing simultaneously; (2) large flexible structures are difficult in terms of isolating one substructure from the vibration of another; (3) the incomplete understanding of the effects of softening nonlinearity may put conventional active controllers at risk; and (4) global stability of under-actuated nonlinear aeroelastic systems, resulting from actuator failure or motivated by weight and cost constraints imposed on next-generation flight vehicles, is extremely challenging, especially in the case of uncertainty and external disturbances. These intellectual challenges are addressed in this research by linear and nonlinear active control techniques. A new theory for partial pole placement by the method of receptances in the presence of inaccessible degrees of freedom is proposed. By the application of a new double input control and orthogonality conditions on the input and feedback gain vectors, partial pole placement is achieved in a linear fashion while some chosen degrees of freedom are free from both actuation and sensing. A lower bound on the maximum number of degrees of freedom inaccessible to both actuation and sensing is established. A theoretical study is presented on the feasibility of applying active control for the purpose of simultaneous vibration isolation and suppression in large flexible structures by block diagonalisation of the system matrices and at the same time assigning eigenvalues to the chosen substructures separately. The methodology, based on eigenstructure assignment using the method of receptances, is found to work successfully when the open-loop system, with lumped or banded mass matrix, is controllable. A comprehensive study of the effects of softening structural nonlinearity in aeroelastic systems is carried out using the simple example of a pitch-flap wing, with softening cubic nonlinearity in the pitch stiffness. Complex dynamical behaviour, including stable and unstable limit cycles and chaos, is revealed using sinusoidal-input describing functions and numerical integration in the time domain. Bifurcation analysis is undertaken using numerical continuation methods to reveal Hopf, symmetry breaking, fold and period doubling bifurcations. The effects of initial conditions on the system stability and the destabilising effects of softening nonlinearity on aerodynamic responses are considered. The global stability of an under-actuated wing section with torsional nonlinearity, softening or hardening, is addressed using a robust passivity-based continuous sliding-mode control approach. The controller is shown to be capable of stabilising the system in the presence of large matched and mismatched uncertainties and large input disturbance. With known bounds on the input disturbance and nonlinearity uncertainty, the continuous control input is able to globally stabilise the overall system if the zero dynamics of the system are globally exponentially stable. The merits and performance of the proposed methods are exemplified in a series of numerical case studies

    Spatial damping identification and control of mechanical systems

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    L'abstract è presente nell'allegato / the abstract is in the attachmen

    Aeronautical Engineering: A continuing bibliography with indexes, supplement 97

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    This bibliography lists 420 reports, articles, and other documents introduced into the NASA scientific and technical information system in May 1978
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