Nonlinear Control Strategies for Balancing Systems

Balancing systems, exemplified by inverted pendulums, self-erecting poles and underactuated robotic platforms, present a canonical challenge in control theory due to their intrinsic instability and highly nonlinear dynamics. Nonlinear control strategies address these challenges by exploiting energy-based formulations, Lyapunov-shaped stability proofs and adaptive estimation of uncertain parameters. Techniques such as backstepping permit systematic controller synthesis by transforming the original system into a cascade of subsystems, while passivity-based designs guarantee robust performance against bounded disturbances by enforcing energy dissipation properties. Fractional-order and complex-order regulators enhance structural flexibility, improving disturbance rejection and robustness to parametric uncertainties. Hybrid and switched approaches, including fuzzy logic and neural-network approximators, accommodate model uncertainties and unmodelled friction characteristics. Across applications from robotic manipulators through vibration suppression in wind turbines to stabilisation of aerial drones, these strategies underpin advances in real-time implementation and global stability verification, thereby driving both theoretical insight and industrial adoption of underactuated and high-precision balancing mechanisms.

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Recent studies have introduced a nonlinear controller with friction compensation for a Furuta pendulum subject to dynamic friction. By integrating a modified energy-shaping law with an observer to estimate unmeasurable friction states and employing a Lyapunov-based analysis, the controller achieves full swing-up and stable regulation under realistic friction dynamics, demonstrating both rapid convergence and closed-loop stability in experimental prototypes.

Model-free backstepping techniques have been devised for rotary inverted pendulums, circumventing the need for detailed system models. By utilising only structural insights and measured states, the approach estimates unknown dynamics and control coefficients online. Comparative trials against linear–quadratic regulators show equivalent or superior performance, with the key advantage of adaptability to varying system parameters without explicit identification.

A complex fractional-order linear quadratic integral regulator has been developed for inverted-pendulum–type mechanisms, assigning calibrated complex exponents to differential and integral operators. This design augments a baseline regulator to strengthen robustness against bounded disturbances and parametric uncertainties. Real-time experiments confirm enhanced disturbance rejection and rapid settling while maintaining control-input economy, outperforming both integer-order and conventional fractional-order counterparts.

Nonlinear Control Strategies for Balancing Systems publication trend

The graph below shows the total number of articles in nonlinear control strategies for balancing systems across all publications each year (not limited to Nature Index journals).

Technical terms

Underactuated system: A mechanical system with fewer control inputs than degrees of freedom, requiring specialised strategies to achieve full state regulation.

Lyapunov stability: A method for proving that system trajectories remain close to an equilibrium by constructing a scalar energy-like function that monotonically decreases.

Backstepping: A recursive controller design procedure that stabilises complex nonlinear systems by decomposing them into simpler subsystems and designing virtual controls.

Passivity: A property indicating that a system does not generate energy, enabling robust control designs based on energy dissipation arguments.

Fractional-order controller: A control law employing non-integer differentiation and integration orders to provide additional tuning flexibility and robustness.

Observer: An algorithm that estimates unmeasurable system states or parameters based on available measurements and a mathematical model.

Radial basis function neural network (RBFN): A type of artificial neural network using radial basis functions as activation functions, often employed for nonlinear function approximation in control tasks.

References

1. Nonlinear control with friction compensation to swing-up a Furuta pendulum. ISA Transactions (2023).
2. Control of Rotary Inverted Pendulum Using Model-Free Backstepping Technique. IEEE Access (2019).
3. Complex Fractional-Order LQIR for Inverted-Pendulum-Type Robotic Mechanisms: Design and Experimental Validation. Mathematics (2023).