Model-free practical PI-Lead control design by ultimate sensitivity principle

TL;DR

The paper tackles model-free tuning of PI-Lead controllers for type-one integrating dynamics common in motion control. It introduces a three-step procedure based on ultimate sensitivity: (i) experimentally determine the integrator time constant $T_i$ from the ultimate gain using $T_i=\dfrac{10}{\max\{\bar{\omega}_{gc}, \bar{\omega}_{pi}^c\}}$, (ii) adjust the proportional gain $K_p$ to achieve a target transient overshoot via $M=\exp(-\pi\zeta/\sqrt{1-\zeta^2})$, and (iii) apply a Lead compensator with $\alpha=0.1$ to provide phase lead around the critical frequency, e.g., $L(s)=\dfrac{(10^{1.5}/T_i)s+1}{(10^{0.5}/T_i)s+1}$. The method was validated experimentally on a noise-perturbed electro-mechanical actuator, producing a final PI controller $C(s)=\dfrac{139.5\,s+450}{0.31\,s}$ and Lead $L(s)=\dfrac{0.031\,s+1}{0.0031\,s+1}$ that improve disturbance rejection and robustness compared to a PID tuned by the Ziegler– Nichols approach. The overall approach is fully model-free, relying solely on experimental observations, and offers practical guidance for tuning in motion-control contexts with uncertain or unknown dynamics.

Abstract

Practical design and tuning of feedback controllers has to do often without any model of the given dynamic process. Only some general assumptions about the process, in this work type-one stable behavior, can be available for engineers, in particular in motion control systems. This paper proposes a practical and simple in realization procedure for designing a robust PI-Lead control without modeling. The developed method derives from the ultimate sensitivity principles, known in the empirical Ziegler-Nichols tuning of PID control, and makes use of some general characteristics of loop shaping. A three-steps procedure is proposed to determine the integration time constant, control gain, and Lead-element in a way to guarantee a sufficient phase margin, while all steps are served by only experimental observations of the output value. The proposed method is also evaluated with experiments on a noise-perturbed electro-mechanical actuator system with translational motion.

Figures (10)

• Figure 1: Typical configuration of the model-free controller tuning for type-one dynamic system process: 'monitor' includes the sensor and data processing, and 'tuning' includes closing the loop for $u(t)$ and computation of the control parameters based on the measured $x(t)$ and the set of the tuning rules.
• Figure 2: Example of shift and reduction of the phase advance of PI controller $C(j\omega)$ by continuously decreasing the integrator time constant $T_i$.
• Figure 3: Loop phase advance with phase margin depending on unknown $\omega_{gc}$.
• Figure 4: Exemplary loop transfer function with i.e. $C(j\omega)L(j\omega)G(j\omega)$ and without i.e. $C(j\omega)G(j\omega)$ the designed Lead-compensator.
• Figure 5: Experimental setup of electro-mechanical actuator system ruderman2022motionruderman2025loop with one translational degree of freedom $x$ (in laboratory environment).