A Novel Nonlinear PID Controller for Improved Performance and Robust Control of Nonlinear Systems

Charkoutsis, S (2025) A Novel Nonlinear PID Controller for Improved Performance and Robust Control of Nonlinear Systems. Doctoral thesis, Liverpool John Moores University.

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Abstract

The Proportional, Integral, and Derivative (PID) controller is the most common control algorithm in industry because of its simplicity, well-understood behaviour, and ease of design. PID is a linear controller with trade-offs between performance and robustness that cause performance compromises and a limited operating region in highly nonlinear industrial systems, which require iterative tuning for each operating region. This process is time-consuming, and the literature indicates that nonlinear PID controllers are a better alternative. However, a nonlinear PID controller that is simple, model-free, and easy to implement is required with an extensive analysis of stability. This thesis proposes a novel Nonlinear PID (NLPID) controller using a unique set of nonlinear gain functions that can improve performance and robustness and eliminate step input derivative kicks, making the controller more energy efficient. The proposed controller is tuned using a Particle Swarm Optimization (PSO) algorithm with an objective function prioritising fast performance with minimum overshoot. An indicative stability analysis has also been conducted through extensive simulations to justify the constraints region, which allows for the determination of stable control gain parameters. The proposed NLPID controller is simulated for a Nonlinear Continuous Stirred Tank Reactor (NCSTR) model with saturation and disturbances at various operating regions. The proposed controller is also benchmarked against the conventional PID, two degrees of freedom PID, and Smith predictor PID controllers in the three linearised dynamics, which are, a First Order Plus Time Delay (FOPTD), a Negative Gain Second Order Plus Time Delay (NG-SOPTD), and a Non-minimum Phase SOPTD (NmP-SOPTD) systems. The benchmarking results show that the proposed NLPID controller improves the performance in all nominal systems, and improves robustness against parametric, additive, and multiplicative uncertainties. In summary, the proposed NLPID controller improves performance and robustness, expanding the operating region of PID in nonlinear systems, using the proposed unique set of nonlinear gain functions. The proposed controller provides an alternative control algorithm to the literature that is model-free, nonlinear, and supported with an indicative stability analysis. Future work can be done to expand the stability analysis with a rigorous mathematical approach for linearisations and to a class of nonlinear systems and potentially include an observer to improve robustness.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	PID; Nonlinear Systems; Nonlinear PID; FOPTD; SOPTD; Robust Control
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Divisions:	Engineering
Date of acceptance:	4 April 2025
Date of first compliant Open Access:	7 May 2025
Date Deposited:	07 May 2025 15:25
Last Modified:	07 May 2025 15:25
DOI or ID number:	10.24377/LJMU.t.00026314
Supervisors:	Kara-Mohamed, M, Stancioiu, D and Yu, D
URI:	https://researchonline.ljmu.ac.uk/id/eprint/26314

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