Energy-Based Nonlinear Control Algorithm for Swing-Up of Underactuated Rotary Inverted Pendulum System and Its Experimental Verification

Fatih Adıgüzel

Makale detayları

Energy-Based Nonlinear Control Algorithm for Swing-Up of Underactuated Rotary Inverted Pendulum System and Its Experimental Verification

Yazarlar:

Fatih Adıgüzel

Yayıncı:

Fırat University

Ana Başlıklar:

Kontrol Teorisi ve Uygulamaları | Kontrol Mühendisliği | Mekatronik Mühendisliği

Dergi:

Fırat Üniversitesi Mühendislik Bilimleri Dergisi Vol.36 Issue 2, pp.621-639

Belge Tipi:

Makale

Yayın Tarihi:

9/2024

Belge Dili:

Türkçe

Document ID (Org No.):

2001317069

pISSN:

1308-9072

Anahtar kelimeler:

Özet:

 This study aims to control the oscillation and increase the pendulum energy with the movable arm of the rotary inverted pendulum, swinging the pendulum up from a stable equilibrium point to an unstable equilibrium point in a restricted zone. After the nonlinear model of the rotary inverted pendulum system and the linear models at the equilibrium points are given, the pendulum swing-up algorithm is introduced. The swing-up algorithm is based on increasing energy into the pendulum with the help of an arm at certain points while the pendulum is swinging. At this point, the arm acceleration is moved by a constant acceleration. The algorithm of the swinging-up is activated when the pendulum completes its period and moves to the point of maximum speed where the stable equilibrium point. These analyses are made by taking calculated limits in these operations into account. When the pendulum swing-up is achieved, a classical full-state feedback controller obtained from the linear model comes into play and keeps the pendulum at the unstable equilibrium point. Thus, a switching control structure is obtained. To verify the proposed control algorithm, the proposed algorithm is carried out in real-time on a rotary inverted pendulum. The comparative results obtained with the different arm acceleration values are presented. When the arm acceleration is increased from 32 rads2 to 64 rads2, the pendulum swing up time decreases from approximately 9 sec to 5 sec. These results demonstrate the experimental success of the proposed algorithm.

 This study aims to control the oscillation and increase the pendulum energy with the movable arm of the rotary inverted pendulum, swinging the pendulum up from a stable equilibrium point to an unstable equilibrium point in a restricted zone. After the nonlinear model of the rotary inverted pendulum system and the linear models at the equilibrium points are given, the pendulum swing-up algorithm is introduced. The swing-up algorithm is based on increasing energy into the pendulum with the help of an arm at certain points while the pendulum is swinging. At this point, the arm acceleration is moved by a constant acceleration. The algorithm of the swinging-up is activated when the pendulum completes its period and moves to the point of maximum speed where the stable equilibrium point. These analyses are made by taking calculated limits in these operations into account. When the pendulum swing-up is achieved, a classical full-state feedback controller obtained from the linear model comes into play and keeps the pendulum at the unstable equilibrium point. Thus, a switching control structure is obtained. To verify the proposed control algorithm, the proposed algorithm is carried out in real-time on a rotary inverted pendulum. The comparative results obtained with the different arm acceleration values are presented. When the arm acceleration is increased from 32 rads2 to 64 rads2, the pendulum swing up time decreases from approximately 9 sec to 5 sec. These results demonstrate the experimental success of the proposed algorithm.

 This study aims to control the oscillation and increase the pendulum energy with the movable arm of the rotary inverted pendulum, swinging the pendulum up from a stable equilibrium point to an unstable equilibrium point in a restricted zone. After the nonlinear model of the rotary inverted pendulum system and the linear models at the equilibrium points are given, the pendulum swing-up algorithm is introduced. The swing-up algorithm is based on increasing energy into the pendulum with the help of an arm at certain points while the pendulum is swinging. At this point, the arm acceleration is moved by a constant acceleration. The algorithm of the swinging-up is activated when the pendulum completes its period and moves to the point of maximum speed where the stable equilibrium point. These analyses are made by taking calculated limits in these operations into account. When the pendulum swing-up is achieved, a classical full-state feedback controller obtained from the linear model comes into play and keeps the pendulum at the unstable equilibrium point. Thus, a switching control structure is obtained. To verify the proposed control algorithm, the proposed algorithm is carried out in real-time on a rotary inverted pendulum. The comparative results obtained with the different arm acceleration values are presented. When the arm acceleration is increased from 32 rads2 to 64 rads2, the pendulum swing up time decreases from approximately 9 sec to 5 sec. These results demonstrate the experimental success of the proposed algorithm.

 Bu çalışmada, döner ters sarkaç sistemi hareketli koluyla sınırlı bir bölge içinde, salınımı kontrol edilerek ve sarkaç enerjisi artırılarak, kararlı denge noktasından kararsız denge noktasına çıkarılması hedeflenmektedir. Döner ters sarkaç sisteminin doğrusal olmayan modeli ve denge noktalarındaki doğrusal modelleri verildikten sonra sarkaç yukarı yükseltme algoritması tanıtılmaktadır. Yukarı yükseltme algoritması, sarkaç salınırken belli noktalarda kol yardımıyla sarkaca enerji yüklemesine dayanmaktadır. Burada kol ivmelendirilmesi sabit bir ivme ile hareket ettirilmektedir. Yukarı yükseltme işlemindeki algoritma, sarkacın hızının en fazla olduğu yere yani kararlı denge noktasına ilerlerken ve periyodunu tamamlarken devreye girmektedir. Bu analizler hesaplanmış sınırlar dikkate alınarak yapılmaktadır. Sarkacın yukarı yükselmesi gerçekleştiğinde doğrusal model üzerinden elde edilmiş temel bir tam durum geri beslemeli kontrolcü devreye girmektedir ve sarkacı kararsız denge noktasında tutmaktadır. Böylece, anahtarlamalı bir kontrol yapısı elde edilmektedir. Önerilen kontrol algoritmasının doğrulaması için önerilen algoritma bir döner sarkacı üzerinde gerçek zamanlı olarak test edilmiştir. Farklı kol ivmelendirme değerleri ile elde edilen karşılaştırmalı sonuçlar sunulmuştur. Kol ivmesi 32 rads 2 den 64 rads 2 ye çıkarıldığında sarkacın yukarı yükselme süresi yaklaşık 9 sden 5 sye düşmektedir. Bu sonuçlar, önerilen algoritmanın deneysel başarısını göstermektedir.

Makale detayları

Energy-Based Nonlinear Control Algorithm for Swing-Up of Underactuated Rotary Inverted Pendulum System and Its Experimental Verification

Yazarlar:

Fatih Adıgüzel

Yayıncı:

Fırat University

Ana Başlıklar:

Kontrol Teorisi ve Uygulamaları | Kontrol Mühendisliği | Mekatronik Mühendisliği

Dergi:

Fırat Üniversitesi Mühendislik Bilimleri Dergisi Vol.36 Issue 2, pp.621-639

Belge Tipi:

Makale

Yayın Tarihi:

9/2024

Belge Dili:

Türkçe

Document ID (Org No.):

2001317069

pISSN:

1308-9072

Rotary Pendulum

energy-based swing-up

arm acceleration

nonlinear control algorithm

LQR.Döner sarkaç

enerji tabanlı yukarı yükseltme

kol ivmelendirme

doğrusal olmayan kontrol algoritması

LQR

Sayı

Makale detayları

Yazarlar: Fatih Adıgüzel

Yayıncı: Fırat University

Ana Başlıklar: Kontrol Teorisi ve Uygulamaları | Kontrol Mühendisliği | Mekatronik Mühendisliği

Dergi: Fırat Üniversitesi Mühendislik Bilimleri Dergisi Vol.36 Issue 2, pp.621-639

Belge Tipi: Makale

Yayın Tarihi: 9/2024

Belge Dili: Türkçe

Document ID (Org No.): 2001317069

pISSN: 1308-9072

Sayı

Yazarlar:

Fatih Adıgüzel

Yayıncı:

Fırat University

Ana Başlıklar:

Kontrol Teorisi ve Uygulamaları | Kontrol Mühendisliği | Mekatronik Mühendisliği

Dergi:

Fırat Üniversitesi Mühendislik Bilimleri Dergisi Vol.36 Issue 2, pp.621-639

Belge Tipi:

Makale

Yayın Tarihi:

9/2024

Belge Dili:

Türkçe

Document ID (Org No.):

2001317069

pISSN:

1308-9072