Optimal controller synthesis for second order time delay systems with at least one RHP pole

• Published in: ISA transactions Vol. 73; pp. 181 - 188
• Main Authors: Begum, K. Ghousiya, Rao, A. Seshagiri, Radhakrishnan, T.K.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01-02-2018
• Subjects: H2 minimization; Internal model control; Maximum sensitivity; PID controller; Process control; PID controller; Maximum sensitivity; Internal model control; Process control; H2 minimization; H minimization
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2017.12.025

An optimal H2 minimization framework is proposed in this paper for devising a controller of PID in nature, based on a refined IMC filter configuration. The tuning strategy is for controlling time delay system with at least one pole which falls on the right half of the s-plane. An underdamped model based filter is used in place of the unity damping ratio (critically damped) filter available in the literature to improve the reset action. The method has a single adjustable closed loop tuning parameter. Guidelines have been provided for choosing the pertinent tuning parameter based on the sensitivity function. Simulation work has been executed on diverse unstable models to support the advantages of the proposed scheme. The proposed controller yields improved performances over other recently reported tuning techniques in the literature. Experimental implementation is carried out on an inverted pendulum for demonstrating the practical applicability of the present method. The efficacy of the intended controller design is quantitatively analyzed using the time integral performance index.
•Optimal controller is designed based on H2 minimization for different second order unstable delay processes.•Blaschke product is used to derive the optimal H2 controller. An underdamped filter structure is used to derive the controller.•Quantitative comparison has been carried out by considering integral absolute error (IAE) and total variation (TV).•Provides significant improvement when compared to the recently reported methods in the literature.•Robustness is analyzed using small gain theorem.