Nonovershooting Control Strategies for Linear Dynamic Systems

Nonovershooting control seeks to drive a linear dynamic system from one equilibrium to another without exceeding the target, thereby ensuring monotonic response profiles. Such strategies are crucial in applications where overshoot may cause damage, compromise safety or induce instability, including aerospace guidance, precision robotics and power electronics. At their core, these approaches manipulate pole and zero locations in the closed-loop transfer function to enforce externally positive behaviour, guaranteeing non-negative impulse responses and thus monotonic step responses. Key methodologies encompass state-feedback designs, pole-zero placement via optimal or convex programming, and synthesis based on logarithmically completely monotonic functions. Dominant-pole techniques isolate a real pole and complex conjugate pair to shape transient response, while discretisation schemes preserve monotonicity in sampled-data implementations. Advances in computational algorithms now enable real-time tuning and robust performance amidst plant uncertainties and time delays, broadening the global impact of nonovershooting control.

Research from Nature Portfolio

Recent studies have introduced simple nonovershooting controllers for high-order systems with or without time delay. They establish three design propositions and propose a dominant-pole control structure comprising one real pole and a pair of complex conjugate poles placed to dominate nondominant dynamics. The controller architecture combines a first-order filter with PD-PID elements to stabilise and shape the response. A computational procedure verifies pole dominance and ensures zeros lie sufficiently to the left in the complex plane. Two illustrative examples demonstrate the method’s effectiveness and robustness under time-delay conditions.

Nonovershooting Control Strategies for Linear Dynamic Systems publication trend

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

Technical terms

Nonovershooting control: A control design ensuring system outputs reach the setpoint without exceeding it, yielding monotonic transient responses.

Dominant poles: Selected closed-loop poles whose location governs the overall speed and damping of the system response.

Externally positive system: A linear system whose impulse response remains non-negative, guaranteeing monotonic step responses.

Logarithmically completely monotonic function: A rational function whose derivatives alternate in sign under a logarithm, used to characterise monotonic response properties.

Transmission zero: A frequency or complex-plane value at which the system’s transfer function becomes zero, influencing transient overshoot.

References

1. Logarithmically completely monotonic rational functions. Automatica (2023).
2. Design of simple nonovershooting controllers for linear high order systems with or without time delay. Scientific Reports (2024).
3. Preservation of external positivity in discretization of linear systems. European Journal of Control (2021).
4. Determination of the Overshoot Scalar Control Systems with Transfer Zero and Binomial Law of Poles Distribution. Indian Journal of Science and Technology (2017).