An Application of DC Motor Modelled Classical Sliding Mode Control with Moving Sliding Surface to Rotary Inverted Pendulum System

Year 2024, , 337 - 349, 31.10.2024

Muhammet Aydın , Oğuz Yakut

https://doi.org/10.62520/fujece.1445734

Abstract

The rotary inverted pendulum system (RIP), which is highly favored in control applications, is examined in this work. By determining the coordinates of the Rip elements' centers of gravity, the system's total kinetic and potential energies were determined. The kinetic and potential energy expressions were used to generate the Lagrangian function. Expressions providing the system's equations of motion were discovered by taking the Lagrangian approach into consideration. The motor's equations, which will initiate the system, have also been considered. Through the use of state variables and a Matlab program, the system's pendulum angle was managed by using a moving sliding surface and the traditional sliding mode control technique. Based on the dynamics, the slip surface's slope was computed. The sliding surface's slope was computed based on the system's dynamics. The genetic algorithm was utilized to determine the ideal values for the coefficients employed in the control structure. The findings showed that the inaccuracy was roughly zero and that the pendulum angle took around 1.5 seconds to reach the intended reference value. Furthermore, it noted that the motor torque and current values are 12 Nm and 2.5 amps, respectively. The findings show that the motor values are reasonably similar to the values seen in real-world applications. Control in real-time applications won't be an issue if the motor is chosen based on these values.

Keywords

Rotary inverted pendulum, Moving sliding mode control, Sliding surface, Motor model

Hareketli Kayma Yüzeyli DC Motor Modelli Klasik Kayan Kipli Kontrolün Dönel Ters Sarkaç Sistemine Uygulanması

Abstract

Bu çalışmada kontrol uygulamalarında çok tercih edilen dönel ters sarkaç sistemi (DTS) ele alınmıştır. DTS elemanlarının ağırlık merkezi koordinatları bulunarak sistemin toplam kinetik ve potansiyel enerjileri elde edilmiştir. Kinetik ve potansiyel enerji ifadeleri kullanılarak Lagrange fonksiyonu oluşturulmuştur. Lagrange yöntemi dikkate alınarak sistemin hareket denklemlerini veren ifadeler bulunmuştur. Ayrıca sistemi harekete geçirecek olan motorun denklemleri dikkate alınmıştır. Durum değişkenleri kullanılarak Matlab da yazılan program yardımıyla sistemin sarkaç açısı, kayma yüzeyi hareketli klasik kayan kipli kontrol yöntemiyle kontrol edilmiştir. Kayma yüzeyinin eğimi sistemin dinamiklerine bağlı olarak hesaplatılmıştır. Kontrol yapısında kullanılan katsayıların optimum değerleri genetik algoritma yardımıyla bulunmuştur. Sonuçlardan sarkaç açısının istenilen referans değere yaklaşık 1.5 sn civarında ulaştığı ve hatanın yaklaşık sıfır olduğu görülmüştür. Ayrıca motor tork değerinin 12 Nm seviyelerinde ve motor akım değerinin 2.5 amper seviyelerinde olduğu gözlemlenmiştir. Motor değerlerinin pratik uygulamalardaki değerlere yakın makul seviyelerde olduğu sonuçlardan elde edilmiştir. Elde edilen bu değerlere göre motor seçimi yapıldığında gerçek zamanlı uygulamalarda kontrol için sorun yaşanmayacaktır.

Keywords

Dönel ters sarkaç, Hareketli kayan kipli kontrol, Kayma yüzeyi, Motor model

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