Tuning a PI/PID Controller with Direct Synthesis to Obtain a Non-Oscillatory Response of Time-Delayed Systems

Abstract

The article presents a method for tuning PI/PID regulators controlling inertial time-delayed plants. The method was formulated on the basis of direct synthesis using the FOPDT (First-Order Plus Dead-Time) and the SOPDT (Second-Order Plus Dead-Time) models to represent the dynamics of the object. The performance objective is to achieve the non-oscillatory response of the system in the shortest time possible while set-point tracking. By employing a novel approach to the synthesis of the control systems with a time delay based on a root-locus analysis, the method eliminates errors resulting from the omission of high-order terms in the Taylor series expansion or the Padé approximation in simplified mathematical descriptions of the process. Consequently, the proposed method makes it possible to precisely determine controller settings to achieve the set control objective. The method was tested with a computer simulation, and the results obtained were compared with those of other methods designed to ensure specific system responses in the designed control systems. The comparisons confirm the proposed method’s ability to achieve the desired reference response and demonstrate its effectiveness in overcoming the limitation of permissible time delays present in other similar methods.

Keywords

• PID controller
• time-delayed systems
• analytic design