Eigenvalue Assignment in Vibration Control Systems

Eigenvalue assignment is a cornerstone of modern vibration control, enabling the deliberate shaping of a system’s natural frequencies and damping characteristics to achieve stability, suppress unwanted resonances and enhance performance. By adjusting feedback gains or modifying structural elements, control engineers relocate the closed-loop poles of mechanical systems to desired positions in the complex plane. This process may involve full pole placement, where all eigenvalues are reassigned, or partial eigenvalue assignment, in which only a subset of critical modes is shifted while others remain unchanged. Techniques range from classical state-feedback algorithms and receptance-based methods to advanced optimisation frameworks that balance robustness, control effort and uncertainty. Recent trends emphasise concurrent design of mechanical properties and control laws, the treatment of time delays and underactuated configurations, and the incorporation of convex programming to guarantee performance margins. Applications span aerospace structures, precision robotics, civil-engineering systems and renewable-energy devices, underlining the global significance of eigenvalue assignment for ensuring safety, efficiency and resilience of critical mechanical and structural systems.

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Eigenvalue Assignment in Vibration Control Systems publication trend

The graph below shows the total number of articles in eigenvalue assignment in vibration control systems across all publications each year (not limited to Nature Index journals).

Technical terms

Eigenvalue assignment: The process of relocating the natural frequencies and damping ratios of a dynamic system by altering its feedback or structural parameters.

Pole placement: A control-design technique that positions the closed-loop system poles at specified locations in the complex plane to achieve desired transient and stability characteristics.

Eigenstructure assignment: An extension of pole placement that also prescribes the shapes of the system’s eigenvectors, enabling mode-shape regulation and decentralised control.

Receptance: The frequency-domain measure of a system’s response displacement per unit harmonic force, used to infer dynamic flexibility and guide feedback gain computation.

Partial eigenvalue assignment: A strategy that shifts only a subset of system eigenvalues—typically the most critical modes—while leaving the remainder unchanged to simplify design and reduce control effort.

References

1. Pole-zero placement through the robust receptance method for multi-input active vibration control with time delay. Journal of Sound and Vibration (2025).
2. A Review on Eigenstructure Assignment Methods and Orthogonal Eigenstructure Control of Structural Vibrations. Shock and Vibration (2009).
3. Pole Assignment for Active Vibration Control of Linear Vibrating Systems through Linear Matrix Inequalities. Applied Sciences (2020).
4. Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems. Structural and Multidisciplinary Optimization (2020).