Conditions for the Existence of Stabilizing PID Controllers in Unstable Systems

https://doi.org/10.58571/CNCA.AMCA.2025.053

Resumen: This paper analyzes the stabilization of a class of linear time-invariant systems with one or two unstable poles using simple PID controllers. By applying the Nyquist stability criterion, algebraic conditions are derived for the existence of stabilizing P, PI, PD, and PID controllers in systems without time delay. These conditions are formulated as corollaries of previously reported results for delayed systems, showing that the absence of delay simplifies transcendental conditions into closed-form inequalities. The findings provide a unified framework for PID design in unstable systems with real or complex stable poles.

¿Cómo citar?

Gómez Jurado, I., del Muro Cuellar, B., Duchén, G., Hernández Pérez, M. & Novella Rodríguez, D. (2025). Conditions for the Existence of Stabilizing PID Controllers in Unstable Systems. Memorias del Congreso Nacional de Control Automático 2025, pp. 307-312. https://doi.org/10.58571/CNCA.AMCA.2025.053

Palabras clave

PID control, Stability analysis, Frequency domain analysis, Linear control systems, Control design.

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