Control Design for Saturated Linear Systems

Designing controllers for linear systems subject to actuator saturation is crucial across engineering disciplines. Saturation arises when control signals exceed physical actuator limits, introducing nonlinear behaviour into an otherwise linear plant. Uncompensated saturation can degrade performance, induce instability or provoke limit cycles. Modern control design addresses these challenges through anti-windup compensators, low-gain integral schemes, sliding-mode structures and optimisation-based formulations. Anti-windup prevents integrator windup by adjusting controller signals during saturation, preserving stability and transient response. Low-gain integral control mitigates saturation effects by constraining integration gains, ensuring accurate tracking within safe bounds. Lyapunov-based analysis and Linear Matrix Inequalities (LMIs) provide systematic tools to certify closed-loop stability and estimate regions of attraction under input constraints. Recent innovations integrate amplitude- and rate-limitation directly into the control law, broadening the set of admissible trajectories and enhancing disturbance rejection. Applications span robotics, automotive systems, power electronics and aerospace, where reliable performance under strict actuator limits is essential for safety and efficiency.

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Research from all publishers

Recent advances have refined amplitude- and rate-saturation control for single-input linear plants. A sliding-mode-inspired design employs a state-dependent parameter and a set-valued function to enforce bounds on both control amplitude and its rate of change, thereby enlarging the region of attraction and reducing residual error. A model-based implicit discretisation scheme enables practical digital implementation without sacrificing theoretical guarantees, and simulations confirm improved convergence and robustness against bounded disturbances. In multi-input multi-output settings, low-gain integral control with static anti-windup shows that by suitably limiting the integrator gain and incorporating a simple saturating element, the closed-loop system can achieve asymptotic tracking of constant references under componentwise input nonlinearities. Rigorous robustness analysis demonstrates that small integrator gains ensure stability without undue conservatism, with detailed examples illustrating straightforward gain selection. For trajectory tracking in mobile robotics, a proportional controller complemented by a limited integrator anti-windup mechanism has been formally analysed via Lyapunov methods. This work provides the first stability proof for this class of constrained integrator schemes in mobile-robot applications, showing that windup is avoided and tracking errors are significantly reduced compared with classical saturation functions. Numerical comparisons highlight the practical benefits of the proposed architecture in meeting both performance and safety requirements.

Control Design for Saturated Linear Systems publication trend

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

Technical terms

Saturation: The nonlinear constraint arising when actuator output cannot exceed predefined amplitude or rate limits.

Anti-windup: A compensation technique that prevents integrator accumulation when the actuator is saturated, preserving stability and transient performance.

Lyapunov function: A scalar function used to prove stability by demonstrating that it decreases along system trajectories.

Linear Matrix Inequality (LMI): A convex constraint on matrix variables, enabling tractable optimisation for controller synthesis under constraints.

Region of attraction: The set of initial states from which the controlled system converges to the desired equilibrium despite input limits.

References

1. An Amplitude‐ and Rate‐Saturated Controller for Linear Plants. Asian Journal of Control (2018).
2. Low-Gain Integral Control for Multi-Input Multioutput Linear Systems With Input Nonlinearities. IEEE Transactions on Automatic Control (2017).
3. Constrained Trajectory Tracking Control of a Mobile Robot by Limited Integrator Anti-Windup. IEEE Transactions on Circuits & Systems II Express Briefs (2021).