Passivity-Based Control of Nonlinear Mechanical Systems

Passivity-based control exploits the intrinsic energy properties of mechanical structures to achieve robust stabilisation and performance in the presence of nonlinearities and uncertainties. By modelling a system as a mapping between power-conjugate variables, this approach ensures that the closed-loop interconnection preserves an energy balance, leading naturally to Lyapunov stability. Central to the methodology is the port-Hamiltonian framework, which represents dynamics in terms of stored energy, dissipation and interconnection structure. The interconnection and damping assignment passivity-based control (IDA-PBC) technique reshapes the total energy landscape and injects damping to steer system states towards a desired equilibrium. Extensions of classical theory accommodate underactuated systems—those with fewer actuators than degrees of freedom—by exploiting structural properties to assign virtual energy tanks and damping channels. Recent advances have further generalised passivity definitions to nonautonomous and discontinuous phenomena such as Coulomb friction, and to distributed-parameter devices with spatially varying energy-storage characteristics. The global significance of these developments spans high-precision robotics, aerospace platforms, microelectromechanical systems and geophysical applications, offering energy-efficient regulation, disturbance rejection and safe interaction in human-robot environments.

Research from Nature Portfolio

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Research from all publishers

Recent studies have extended passivity frameworks to accommodate frictional effects in underactuated systems, demonstrating a control synthesis that restores energy balance in models with Coulomb friction and achieves slow reference tracking in seismogenic fault scenarios. Another contribution introduces a Krasovskii passivity-based approach for voltage-actuated piezoelectric beams, yielding proportional-integral–like controllers that guarantee asymptotic stabilisation of flexible structures under dissipative loads. In the domain of sampled-data control, a discrete-time port-Hamiltonian regulator has been developed that circumvents nonlinear partial differential matching by casting the feedback synthesis into algebraic equations, enabling trajectory tracking with provable Lyapunov stability for mechanical systems under periodic sampling.

Passivity-Based Control of Nonlinear Mechanical Systems publication trend

The graph below shows the total number of articles in passivity-based control of nonlinear mechanical systems across all publications each year (not limited to Nature Index journals).

Technical terms

Passivity: A system property ensuring that the energy supplied does not exceed the sum of stored and dissipated energy, underpinning stable feedback interconnections.

Port-Hamiltonian system: A modelling paradigm that describes dynamics through energy storage (Hamiltonian), energy exchange ports, and interconnection structures preserving power continuity.

Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC): A design method that reshapes the total energy function and inserts damping channels to stabilise target equilibria in nonlinear mechanical systems.

Underactuated system: A mechanical system possessing fewer control inputs than degrees of freedom, requiring exploitation of inherent coupling for full-state regulation.

References

1. Passivity-based control of underactuated mechanical systems with Coulomb friction: Application to earthquake prevention. Automatica (2024).
2. On control of voltage-actuated piezoelectric beam: A Krasovskii passivity-based approach. European Journal of Control (2023).
3. Trajectory Tracking for Discrete-Time Port-Hamiltonian Systems. IEEE Control Systems Letters (2022).