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<p>This paper proposes a novel optimization-based design methodology for a five-parameter, expanded-form PID controller (PIDC). The controller is structurally equivalent to a PID cascaded with a first-order lead/lag compensator, corresponding to a causal third-order transfer function. The design methodology combines prototype pole placement approach with the max(<i>k</i>)-based optimality criterion, constrained by the maximum modulus of the sensitivity function and the maximum modulus of the sensitivity function with respect to measurement noise, to ensure effective suppression of unmeasurable load disturbances, quantified via the Integrated Absolute Error (IAE). Through the pole placement technique, the locations of the closed-loop system’s dominant poles are assigned based on the poles of two types of reference prototype polynomials characterized by negligible overshoot and short settling time. Using the Lagrange multiplier method, the constrained optimization problem is reduced to a system of four nonlinear algebraic equations, simplifying computational demands. Comprehensive simulation studies demonstrate the effectiveness of the method across broad class of industrial processes, modeled by transfer functions, including stable, integrating, and unstable systems—with and without dead time and of both minimum and non-minimum phase—as well as distributed parameter systems. Comparative analyses with existing PIDC tuning techniques highlight its advantages in disturbance rejection and robustness to model uncertainties.</p>

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Optimization of PIDC controller via pole placement under constraints on robustness and sensitivity to measurement noise for broad class of industrial processes

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Tomislav B. Šekara,
  • Petar D. Mandić,
  • Marko Č. Bošković,
  • Mihailo P. Lazarević

摘要

This paper proposes a novel optimization-based design methodology for a five-parameter, expanded-form PID controller (PIDC). The controller is structurally equivalent to a PID cascaded with a first-order lead/lag compensator, corresponding to a causal third-order transfer function. The design methodology combines prototype pole placement approach with the max(k)-based optimality criterion, constrained by the maximum modulus of the sensitivity function and the maximum modulus of the sensitivity function with respect to measurement noise, to ensure effective suppression of unmeasurable load disturbances, quantified via the Integrated Absolute Error (IAE). Through the pole placement technique, the locations of the closed-loop system’s dominant poles are assigned based on the poles of two types of reference prototype polynomials characterized by negligible overshoot and short settling time. Using the Lagrange multiplier method, the constrained optimization problem is reduced to a system of four nonlinear algebraic equations, simplifying computational demands. Comprehensive simulation studies demonstrate the effectiveness of the method across broad class of industrial processes, modeled by transfer functions, including stable, integrating, and unstable systems—with and without dead time and of both minimum and non-minimum phase—as well as distributed parameter systems. Comparative analyses with existing PIDC tuning techniques highlight its advantages in disturbance rejection and robustness to model uncertainties.