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

Öz

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 rad/s^2 to ±64 rad/s^2, the pendulum swing up time decreases from approximately 9 sec to 5 sec. These results demonstrate the experimental success of the proposed algorithm.

Anahtar Kelimeler

• Rotary Pendulum
• energy-based swing-up
• arm acceleration
• nonlinear control algorithm
• LQR.

Eksik Tahrikli Döner Ters Sarkaç Sisteminin Yukarı Yükseltilmesi için Enerji Tabanlı Doğrusal Olmayan Kontrol Algoritması ve Deneysel Doğrulaması

Öz

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 rad/s²’den ±64 rad/s²’ye çıkarıldığında sarkacın yukarı yükselme süresi yaklaşık 9 s’den 5 s’ye düşmektedir. Bu sonuçlar, önerilen algoritmanın deneysel başarısını göstermektedir.

Anahtar Kelimeler

• Döner sarkaç
• enerji tabanlı yukarı yükseltme
• kol ivmelendirme
• doğrusal olmayan kontrol algoritması
• LQR

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