ABSTRAKTema Inverted pendulum banyak diteliti oleh peneliti dunia, salah satu temanya adalah
pemodelan dan perancangan pengendali. Tema inilah yang diambil sebagai tema penelitian
dalam tesis ini. Dalam tesis ini dimodelkan tiga jenis inverted pendulum yaitu Single Inverted
Pendulum, Double Inverted Pendulum, dan Dual Inverted Pendulum. Model matematik dari
ketiga jenis inverted pendulum ini diturunkan dari persamaan Euler- Lagrange. Model matematik
yang didapatkan disimulasikan menggunakan matlab simulink. Dari hasil simulasi didapatkan
bahwa ketiga jenis inverted pendulum ini tidak stabil namun demikian ketiga jenis inverted
pendulum ini dapat dikendalikan sehingga ketiga jenis inverted pendulum ini dapat distabilkan.
Untuk menstabilkan sistem inverted pendulum digunakan pengendali LQR. Dari hasil simulasi
terlihat bahwa sistem inverted pendulum dapat distabilkan, namun kestabilan sistem hanya dapat
dipenuhi dalam batasan nilai variabel keadaan yang tertentu.
ABSTRACTInverted pendulum is widely studied by researchers around the world. One of its research themes
is modeling and control design. This theme also becomes the research focus of this thesis. In the
research, three types of inverted pendulum have been studied. That are Single Inverted
Pendulum, Double Inverted Pendulum and Dual Inverted Pendulum. Mathematical models of
these inverted pendulums are derived from the Euler-Lagrange equation. Based on these models,
simulation is carried out by using Matlab/Simulink. Simulation results showed that the inverted
pendulums are not stable but controllable. Therefore the inverted pendulums can be stabilized.
In this research, LQR controller is used to stabilize the inverted pendulum systems. Simulation
results show that the inverted pendulum systems could be stabilized only within limited range of
the state variable values.