Novel robust-optimal controllers based on fuzzy descriptor system

(a) The controller makes use of Parallel Distributed Compensator (PDC) because the management stratergy and Linear Matrix Inequality (LMI)-based stability circumstances to realize robust-optimal management. (b) The robust-optimal controller demonstrates decrease error values in controlling the rotary inverted pendulum. Credit: Ngoc-Tam Bui, Shibaura Institute of Know-how

Nonlinear programs have functions in lots of numerous fields from robotics to economics. In contrast to linear programs, the output shouldn’t be proportional to the enter is such programs. A traditional instance is the movement of a pendulum. As a result of inherent nature of nonlinear programs, their mathematical modeling and, consequently, management is troublesome.

On this context, the Takagi–Sugeno (T–S) fuzzy system emerges as a extremely efficient instrument. This method leverages fuzzy logic to map enter and output values to approximate a nonlinear system as a number of linear programs that are simpler to mannequin.

Fuzzy logic is a type of mathematical logic wherein, as an alternative of requiring all statements to be true (1) or false (0), the reality values will be any worth between 0 and 1. T–S fuzzy system has thus served as the inspiration for a number of nonlinear management strategies, with the Parallel Distributed Compensator (PDC) technique being probably the most distinguished.

Moreover, scientists have developed an enhanced model of this method, referred to as the fuzzy descriptor system (FDS). It combines the T–S fuzzy system with the highly effective house–state illustration, which describes a bodily system when it comes to state variables, enter variables, and output variables.

Regardless of in depth analysis, optimum management methods within the context of T–S FDSs are nonetheless largely unexplored. Moreover, whereas sturdy management strategies, which defend in opposition to disturbances, have been explored for T–S FDS utilizing strategies like Linear Matrix Inequalities (LMI), these strategies introduce extra complexity and optimization challenges.

To beat these limitations, a bunch of researchers, led by Affiliate Professor Ngoc-Tam Bui from the Revolutionary World Program of the School of Engineering at Shibaura Institute of Know-how in Japan and together with Thi-Van-Anh Nguyen, Quy-Thinh Dao, and Duc-Binh Pham, all from Hanoi University of Science and Know-how, developed novel optimum and robust-optimal controllers primarily based on the T–S fuzzy descriptor mannequin. Their examine was published in the journal Scientific Reports.

To develop the controllers, the crew first utilized the highly effective Lyapunov stability idea to ascertain the steadiness circumstances for the mathematical mannequin of the FDS. Nonetheless, these stability circumstances can’t be immediately used. As Dr. Bui explains, “The stability conditions for the FDS model make it difficult to solve using established mathematical tools. To make them more amenable, we systematically transformed them into LMI.”

These modified circumstances shaped the idea for creating three controllers: the steadiness controller which makes use of PDC to handle deviations, the optimum controller which minimizes a value operate to acquire optimum management, and the robust-optimal controller which mixes the advantages of each of them.

The researchers demonstrated the effectiveness of those controllers in controlling a rotary inverted pendulum, a difficult system comprising an inverted pendulum sitting on a rotating base. The issue is to maintain the pendulum upright by controlling the rotation of the bottom.

The researchers examined the efficiency of the controllers utilizing distinct simulation situations. Simulations revealed that the steadiness controller successfully stabilized the system when the preliminary displacement angle was small, whereas with bigger preliminary angles, there have been extra oscillations, and the settling time was larger.

The excessive settling time was successfully addressed by the optimum controller, decreasing it from 13 to 2 seconds, representing a six-fold discount. Furthermore, it additionally diminished the utmost amplitudes throughout oscillations.

The robust-optimal controller was examined utilizing two totally different situations. Within the first case, the mass of the pendulum bar was modified, whereas within the second, white noise was launched into the management enter. In comparison with the optimum controller, it carried out the identical within the first situation. Nonetheless, the controller was significantly higher within the second situation, exhibiting no oscillations whereas the optimum controller confirmed clear oscillations. Notably, the robust-optimal controller confirmed the bottom error values.

These outcomes spotlight the adaptability and potential of those controllers in sensible situations. “The research findings hold promising implications for various real-life applications where stable control in dynamic and uncertain environments is paramount. Specifically, autonomous vehicles and industrial robots can achieve enhanced performance and adaptability using the proposed controllers,” remarks Dr. Bui.

“Overall, our research opens avenues for advancing control strategies in various domains, ultimately contributing to more capable autonomous systems, making transportation safer, health care more effective, and manufacturing more efficient.”

Extra data:
Duc-Binh Pham et al, Sturdy-optimal management of rotary inverted pendulum management by fuzzy descriptor-based strategies, Scientific Reviews (2024). DOI: 10.1038/s41598-024-56202-2

Novel robust-optimal controllers primarily based on fuzzy descriptor system (2024, April 8)
retrieved 8 April 2024

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