Discrete-time system conditional optimization based on Takagi-Sugeno fuzzy model using the full transfer function
2022
Authors
Jovanović, RadišaZarić, Vladimir
Bučevac, Zoran
Bugarić, Uglješa
Contributors
Božek, PavolKrenicky, Tibor
Nikitin, Yury
Article (Published version)
Metadata
Show full item recordAbstract
The study proposes a novel method for synthesis of a discrete-time parallel distributed
compensation (PDC) controller for the nonlinear discrete-time Takagi–Sugeno (TS) fuzzy plant model. For each of the fuzzy plant model linear subsystems, a local linear first order proportional-sum (PS) controller is designed. The algebraic technique is used in two-dimensional parameter space, utilizing the characteristic polynomial of the row nondegenerate full transfer function matrix. Each system’s relative stability is accomplished in relation to the selected damping coefficient. The supplementary criterion is the minimal value of the performance index in the form of the sum of squared errors (SSE). However, unlike the traditional technique, output error is influenced by all simultaneous actions on the system: nonzero inputs and nonzero initial conditions. The full transfer function matrix of the system allows for the treatment of simultaneous actions of the input vector and unknown unpredictabl...e initial conditions. In order to show the improvement caused by the application of a new optimization method that considers nonzero initial conditions, a comparison of PDC controllers designed under zero and nonzero initial conditions is given, where the system in both cases starts from the same nonzero initial conditions, which is often the case in practice. The simulation and experimental results on a DC servo motor are shown to demonstrate the suggested method efficiency.
Keywords:
Takagi–Sugeno / parallel distributed compensation / fuzzy control / full transfer function matrix / conditional optimization / nonzero initial conditions / discrete-time systems / DC servo motorSource:
Applied Sciences, 2022, 12, 7705, 1-22Publisher:
- MDPI
Funding / projects:
- Ministry of Science, Technological Development and Innovation of the Republic of Serbia, institutional funding - 200105 (University of Belgrade, Faculty of Mechanical Engineering) (RS-MESTD-inst-2020-200105)
- An innovative ecologically based approach to implementation of intelligent manufacturing systems for production of sheet metal parts (RS-MESTD-Technological Development (TD or TR)-35004)
- Development of Methodology for Improvement of Operational Performance, Reliability and Energy Efficiency of Machine Systems used in the Resource Industry (RS-MESTD-Technological Development (TD or TR)-35029)
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Mašinski fakultetTY - JOUR AU - Jovanović, Radiša AU - Zarić, Vladimir AU - Bučevac, Zoran AU - Bugarić, Uglješa PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4524 AB - The study proposes a novel method for synthesis of a discrete-time parallel distributed compensation (PDC) controller for the nonlinear discrete-time Takagi–Sugeno (TS) fuzzy plant model. For each of the fuzzy plant model linear subsystems, a local linear first order proportional-sum (PS) controller is designed. The algebraic technique is used in two-dimensional parameter space, utilizing the characteristic polynomial of the row nondegenerate full transfer function matrix. Each system’s relative stability is accomplished in relation to the selected damping coefficient. The supplementary criterion is the minimal value of the performance index in the form of the sum of squared errors (SSE). However, unlike the traditional technique, output error is influenced by all simultaneous actions on the system: nonzero inputs and nonzero initial conditions. The full transfer function matrix of the system allows for the treatment of simultaneous actions of the input vector and unknown unpredictable initial conditions. In order to show the improvement caused by the application of a new optimization method that considers nonzero initial conditions, a comparison of PDC controllers designed under zero and nonzero initial conditions is given, where the system in both cases starts from the same nonzero initial conditions, which is often the case in practice. The simulation and experimental results on a DC servo motor are shown to demonstrate the suggested method efficiency. PB - MDPI T2 - Applied Sciences T1 - Discrete-time system conditional optimization based on Takagi-Sugeno fuzzy model using the full transfer function EP - 22 IS - 7705 SP - 1 VL - 12 DO - 10.3390/app12157705 ER -
@article{ author = "Jovanović, Radiša and Zarić, Vladimir and Bučevac, Zoran and Bugarić, Uglješa", year = "2022", abstract = "The study proposes a novel method for synthesis of a discrete-time parallel distributed compensation (PDC) controller for the nonlinear discrete-time Takagi–Sugeno (TS) fuzzy plant model. For each of the fuzzy plant model linear subsystems, a local linear first order proportional-sum (PS) controller is designed. The algebraic technique is used in two-dimensional parameter space, utilizing the characteristic polynomial of the row nondegenerate full transfer function matrix. Each system’s relative stability is accomplished in relation to the selected damping coefficient. The supplementary criterion is the minimal value of the performance index in the form of the sum of squared errors (SSE). However, unlike the traditional technique, output error is influenced by all simultaneous actions on the system: nonzero inputs and nonzero initial conditions. The full transfer function matrix of the system allows for the treatment of simultaneous actions of the input vector and unknown unpredictable initial conditions. In order to show the improvement caused by the application of a new optimization method that considers nonzero initial conditions, a comparison of PDC controllers designed under zero and nonzero initial conditions is given, where the system in both cases starts from the same nonzero initial conditions, which is often the case in practice. The simulation and experimental results on a DC servo motor are shown to demonstrate the suggested method efficiency.", publisher = "MDPI", journal = "Applied Sciences", title = "Discrete-time system conditional optimization based on Takagi-Sugeno fuzzy model using the full transfer function", pages = "22-1", number = "7705", volume = "12", doi = "10.3390/app12157705" }
Jovanović, R., Zarić, V., Bučevac, Z.,& Bugarić, U.. (2022). Discrete-time system conditional optimization based on Takagi-Sugeno fuzzy model using the full transfer function. in Applied Sciences MDPI., 12(7705), 1-22. https://doi.org/10.3390/app12157705
Jovanović R, Zarić V, Bučevac Z, Bugarić U. Discrete-time system conditional optimization based on Takagi-Sugeno fuzzy model using the full transfer function. in Applied Sciences. 2022;12(7705):1-22. doi:10.3390/app12157705 .
Jovanović, Radiša, Zarić, Vladimir, Bučevac, Zoran, Bugarić, Uglješa, "Discrete-time system conditional optimization based on Takagi-Sugeno fuzzy model using the full transfer function" in Applied Sciences, 12, no. 7705 (2022):1-22, https://doi.org/10.3390/app12157705 . .