Eigenvalue sensitivity minimisation for robust pole placement by the receptance method

The problem of robust pole placement in active structural vibration control by the method of receptance is considered in this paper. Expressions are derived for the eigenvalue sensitivities to parametric perturbations, which are subsequently minimised to improve performance robustness of the control of a dynamical system. The described approach has application to a vibrating system where variations are present due to manufacturing and material tolerances, damages and environment variabilities. The closed-loop eigenvalue sensitivities are expressed as a linear function of the velocity and displacement feedback gains, allowing their minimisation with carefully calculated feedback gains. The proposed algorithm involves curve fitting perturbed frequency response functions, FRFs, using the rational fraction polynomial method and implementation of a polynomial fit to the individual estimated rational fraction coefficients. This allows the eigenvalue sensitivity to be obtained entirely from structural FRFs, which is consistent with the receptance method. This avoids the need to evaluate the M,C,K matrices which are typically obtained through finite element modelling, that produces modelling uncertainty. It is also demonstrated that the sensitivity minimisation technique can work in conjunction with the pole placement and partial pole placement technique using the receptance method. To illustrate the working of the proposed algorithm, the controller is first implemented numerically and then experimentally

Robust active vibration control by the receptance method

In recent years, the pursuit of lighter and more energy-efficient structures has fuelled research and development efforts focused on creating innovative, flexible, and lightweight structures. While these advancements promise benefits, such as enhanced fuel efficiency, they often encounter challenges in the form of unwanted vibrations, particularly unstable oscillations known as resonance. Resonance occurs when external loads excite the structure near its natural frequencies, raising safety concerns such as mechanical deterioration, fatigue, and structural failure.Conventional methods for suppressing structural vibrations involve passive modifications, such as physically altering the structural stiffness or adding supplementary damping properties, like dashpots. However, these modifications usually lead to additional weight penalties for the structure. Fortunately, with technological advancements, active vibration control (AVC) has emerged as a promising solution. AVC strategies deploy strategically placed actuators and sensors on the structure to dynamically adjust the damping levels and natural frequencies, thereby mitigating vibrations.While the theory of AVC is well-established, practical implementations on various structures in real-world applications remain rare. This scarcity is primarily due to their reliance on highly accurate models of the structures, which are challenging to obtain due to the complexities associated with achieving precise numerical or analytical models. This thesis explores an experimental-based approach to AVC known as the Receptance Method, eliminating the need for numerical modelling and mitigating issues related to modelling accuracies.However, owing to the experimental nature of the Receptance Method, the controller is sensitive to the measurement process. Therefore, this thesis aims to investigate and design a control system that can maintain robust performance in the presence of uncertainties. The formulation proposed in this thesis builds upon the Receptance Method, addressing the practical limitations associated with uncertain system parameters. It is demonstrated that when the proposed formulation is applied in conjunction with the Receptance Method, the controller maintains a predefined level of performance in the presence of uncertainties.Furthermore, to facilitate the experimental implementation of the proposed method, this thesis presents an experimental procedure for quantifying uncertainties in a system using only a single measured nominal receptance dataset. This technique eases the implementation of the proposed robust controller in experimental settings. Experiment validations have demonstrated improvements in system performance and have proven effective in preventing the propagation of uncertainties in its poles. Finally, a series of numerical analyses on a continuous system are conducted to investigate the implications of employing suboptimally measured datasets in designing a receptance controller

Eigenvalue sensitivity minimisation for robust pole placement by the receptance method

The problem of robust pole placement in active structural vibration control by the method of receptance is considered in this paper. Expressions are derived for the eigenvalue sensitivities to parametric perturbations, which are subsequently minimised to improve performance robustness of the control of a dynamical system. The described approach has application to a vibrating system where variations are present due to manufacturing and material tolerances, damages and environment variabilities. The closed-loop eigenvalue sensitivities are expressed as a linear function of the velocity and displacement feedback gains, allowing their minimisation with carefully calculated feedback gains. The proposed algorithm involves curve fitting perturbed frequency response functions, FRFs, using the rational fraction polynomial method and implementation of a polynomial fit to the individual estimated rational fraction coefficients. This allows the eigenvalue sensitivity to be obtained entirely from structural FRFs, which is consistent with the receptance method. This avoids the need to evaluate the matrices which are typically obtained through finite element modelling, that produces modelling uncertainty. It is also demonstrated that the sensitivity minimisation technique can work in conjunction with the pole placement and partial pole placement technique using the receptance method. To illustrate the working of the proposed algorithm, the controller is first implemented numerically and then experimentally

Eigenvalue sensitivity minimisation for robust pole placement by the receptance method

The problem of robust pole placement in active structural vibration control by the method of receptance is considered in this paper. Expressions are derived for the eigenvalue sensitivities to parametric perturbations, which are subsequently minimised to improve performance robustness of the control of a dynamical system. The described approach has application to a vibrating system where variations are present due to manufacturing and material tolerances, damages and environment variabilities. The closed-loop eigenvalue sensitivities are expressed as a linear function of the velocity and displacement feedback gains, allowing their minimisation with carefully calculated feedback gains. The proposed algorithm involves curve fitting perturbed frequency response functions, FRFs, using the rational fraction polynomial method and implementation of a polynomial fit to the individual estimated rational fraction coefficients. This allows the eigenvalue sensitivity to be obtained entirely from structural FRFs, which is consistent with the receptance method. This avoids the need to evaluate the M,C,K matrices which are typically obtained through finite element modelling, that produces modelling uncertainty. It is also demonstrated that the sensitivity minimisation technique can work in conjunction with the pole placement and partial pole placement technique using the receptance method. To illustrate the working of the proposed algorithm, the controller is first implemented numerically and then experimentally