Abstract
The present study proposes a new design method for a proportional-integral-derivative (PID) control system for first-order plus dead-time (FOPDT) and over-damped second-order plus dead-time (SOPDT) systems. What is presented is an optimal PID tuning constrained to robust stability. The optimal tuning is defined for each one of the two operation modes the control system may operate in: servo (reference tracking) and regulation (disturbance rejection). The optimization problem is stated for a normalized second-order plant that unifies FOPDT and SOPDT process models. Different robustness levels are considered and for each one of them, the set of optimal controller parameters is obtained. In a second step, suitable formulas are found that provide continuous values for the controller parameters. Finally, the effectiveness of the proposed method is confirmed through numerical examples.
Highlights
Proportional-integral-derivative (PID) control has been widely used because the control structure is simple and the role of tuning parameters is clear
The epoch-making rule of PID control has been investigated as the Ziegler and Nichols (ZN) method [2]
The stabilizing regions in the PID parameter space are decided for a fixed proportional gain, and the boundaries for stabilizing the proportional gain are provided
Summary
Proportional-integral-derivative (PID) control has been widely used because the control structure is simple and the role of tuning parameters is clear. Has been studied for more than half a century [3,4,5,6]. Stability is crucially important, and robust PID control has been studied [7,8]. Söylemez et al have proposed a fast calculation method [9]. In this method, the stabilizing regions in the PID parameter space are decided for a fixed proportional gain, and the boundaries for stabilizing the proportional gain are provided. Works [10,11,12] have proposed methods for the computation of all stabilizing PI(D) controllers, where the stability regions of PI(D)
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