Feedback linearization-based cascade control of an underactuated rotary inverted pendulum system

Abstract

The cascaded control is a multi-loop control structure that is particularly favored to improve performance against disturbances. It is usually a feedback control consisting of an inner loop (slave controller) and an outer loop (master controller), where the set point of the slave controller is set by this master controller. In this paper, a cascaded control strategy is employed to control a rotary inverted pendulum system with nonlinear dynamics due to gravitational, Coriolis and centripetal forces acting on it. Herein, a feedback linearization-based Proportional-Derivative (PD) controller is used for the slave controller and a linear quadratic regulator is used for the master controller. The feedback linearization employed in the inner loop has a relative degree of two and has unstable zero dynamics. These unstable dynamics are addressed in the main controller design and the whole cascaded control becomes stable. In the nonlinear dynamic equation of the inverted pendulum, the torque applied to the pendulum is formulated as a disturbance factor. The proposed feedback linearization-based cascade controller is compared with two different controllers in the presence of disturbances and shown to perform better.

Keywords

• Cascaded control
• Feedback linearization
• Rotary inverted pendulum
• Underactuated
• Nonlinear System

Eksik tahrikli döner ters sarkaç sisteminin geribeslemeli doğrusallaştırma tabanlı kademeli kontrolü

Abstract

Kademeli kontrol, özellikle bozanetkenlere karşı performansı iyileştirmek için tercih edilen çok döngülü bir kontrol yapısıdır. Genellikle, iç döngü kontrolü (bağımlı kontrolör) ve dış döngü kontrolünden (ana kontrolör) oluşan ve bağımlı kontrolörün ayar noktasının, bu ana kontrolör tarafından ayarlandığı bir geri beslemeli kontroldür. Bu çalışmada, üzerine etki eden yerçekimi kuvvetleri, Coriolis ve merkezcil kuvvetlerden dolayı doğrusal olmayan dinamiğe sahip döner ters sarkaç sisteminin denetlenmesinde kademeli kontrol kullanılmıştır. Burada, bağımlı kontrolcü için geribeslemeli doğrusallaştırma tabanlı oransal-türevsel (PD) denetleyici ve ana kontrolcü içinse doğrusal karesel düzenleyici (DKD) kullanılmıştır. İç döngüde kullanılan geri beslemeli doğrusallaştırmanın bağıl derecesi ikidir ve kararsız sıfır dinamiklere sahiptir. Bu kararsız dinamikler ana kontrolcü tasarımında ele alınmış ve kademeli kontrolün kararlı olması sağlanmıştır. Ters sarkacın doğrusal olmayan dinamik denkleminde sarkaca uygulanabilen tork bozanetken olarak formüle edilmiştir. Önerilen geribeslemeli doğrusallaştırma tabanlı kademeli denetleyici, bozan etken varlığında iki farklı denetleyici ile karşılaştırılmış ve daha iyi performans sergilediği gösterilmiştir.

Keywords

• Kademeli kontrol
• Geribeslemeli doğrusallaştırma
• Döner ters sarkaç
• Eksik tahrik
• Doğrusal olmayan sistem

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