Dynamic analysis and comparison of the performance of linear and nonlinear controllers applied to a nonlinear non-interactive and interactive process

José M. Campos-Salazar; Pablo Lecaros; Rodrigo Sandoval-García; José M. Campos-Salazar; Pablo Lecaros; Rodrigo Sandoval-García

doi:10.3934/electreng.2024021

AIMS Electronics and Electrical Engineering

2024, Volume 8, Issue 4: 431-455. doi: 10.3934/electreng.2024021

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Research article Topical Sections

Dynamic analysis and comparison of the performance of linear and nonlinear controllers applied to a nonlinear non-interactive and interactive process

1.
Electronic Engineering Department, Universitat Politècnica de Catalunya, Barcelona, Spain
2.
Process Engineering Department, Celulosa Arauco y Constitución S.A, Concepción, Chile
3.
Control Engineering Department, Celulosa Arauco y Constitución S.A, Concepción, Chile

Academic Editor: Kourosh Kalantar-Zadeh

Received: 06 April 2024 Revised: 24 July 2024 Accepted: 18 September 2024 Published: 23 September 2024

This article presents an in-depth dynamic analysis and comparative evaluation of three distinct control strategies—proportional-integral (PI) compensator, linear quadratic regulator (LQR), and sliding mode control (SMC)—applied to a nonlinear process in two configurations: non-interactive system (NIS) and interactive system (IS). The primary objective was to optimize the regulation of fluid levels in a dual-tank system subject to external disturbances and varying operational conditions. The process dynamics were initially modeled using nonlinear differential equations, which were subsequently linearized to facilitate the design of the PI and LQR controllers. The PI compensator design was rooted in state-space representation and was tuned using the Ziegler-Nichols method to achieve the desired transient and steady-state performance. The LQR design employed optimal control theory, minimizing a quadratic cost function to derive the state feedback gain matrix, ensuring system stability by shifting the eigenvalues of the closed-loop system matrix into the left half of the complex plane. In contrast, the SMC leveraged the full nonlinear dynamics of the process, establishing a sliding surface to drive the system states toward a desired trajectory with robustness against model uncertainties and external disturbances. The SMC's performance was evaluated by analyzing the existence and stability of the sliding mode using the derived switching laws for the actuation signal. The comparative study was conducted through simulations in MATLAB/Simulink environments, where each controller's performance was assessed based on transient response, robustness to disturbances, and computational complexity. The results indicate that while the PI compensator and LQR provide satisfactory performance under linearized assumptions, the SMC demonstrates superior robustness and precision in managing the nonlinearities inherent in the IS configuration. This comprehensive analysis underscores the critical trade-offs between simplicity, computational overhead, and control efficacy when selecting appropriate control strategies for nonlinear, multi-variable processes.
- cascade connection,
- level control,
- nonlinear process,
- series connection,
- simulation results
Citation: José M. Campos-Salazar, Pablo Lecaros, Rodrigo Sandoval-García. Dynamic analysis and comparison of the performance of linear and nonlinear controllers applied to a nonlinear non-interactive and interactive process[J]. AIMS Electronics and Electrical Engineering, 2024, 8(4): 431-455. doi: 10.3934/electreng.2024021

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Abstract

This article presents an in-depth dynamic analysis and comparative evaluation of three distinct control strategies—proportional-integral (PI) compensator, linear quadratic regulator (LQR), and sliding mode control (SMC)—applied to a nonlinear process in two configurations: non-interactive system (NIS) and interactive system (IS). The primary objective was to optimize the regulation of fluid levels in a dual-tank system subject to external disturbances and varying operational conditions. The process dynamics were initially modeled using nonlinear differential equations, which were subsequently linearized to facilitate the design of the PI and LQR controllers. The PI compensator design was rooted in state-space representation and was tuned using the Ziegler-Nichols method to achieve the desired transient and steady-state performance. The LQR design employed optimal control theory, minimizing a quadratic cost function to derive the state feedback gain matrix, ensuring system stability by shifting the eigenvalues of the closed-loop system matrix into the left half of the complex plane. In contrast, the SMC leveraged the full nonlinear dynamics of the process, establishing a sliding surface to drive the system states toward a desired trajectory with robustness against model uncertainties and external disturbances. The SMC's performance was evaluated by analyzing the existence and stability of the sliding mode using the derived switching laws for the actuation signal. The comparative study was conducted through simulations in MATLAB/Simulink environments, where each controller's performance was assessed based on transient response, robustness to disturbances, and computational complexity. The results indicate that while the PI compensator and LQR provide satisfactory performance under linearized assumptions, the SMC demonstrates superior robustness and precision in managing the nonlinearities inherent in the IS configuration. This comprehensive analysis underscores the critical trade-offs between simplicity, computational overhead, and control efficacy when selecting appropriate control strategies for nonlinear, multi-variable processes.

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