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ABSTRAK Makalah ini memaparkan proses pemodelan robot inverted pendulum beroda dua (IPBD) menggunakan dinamika Lagrange. Setelah sistem model robot IPBD diperoleh, teknik kendali optimal dalam hal ini menggunakan linear quadratic regulator (LQR) digunakan untuk melihat step respon sistem dan tanggapan respon sistem terhadap gangguan. Sebelum kendali LQR diimplementasikan, simulasi menggunakan Simulink Matlab dilakukan untuk mendapat parameter gain K pada kendali LQR. Selanjutnya, dengan mengubah-ubah matriks pembobot Q akan diperoleh variasi gain K. Pada penelitian ini dilakukan variasi matriks pembobotan Q sebanyak lima jenis. Sedangkan matriks elemen R dituning dengan nilai satu. Dari hasil pengujian diperoleh bahwa dengan membesarkan pembobotan matriks Q, dihasilkan respon menuju keadaan steady lebih cepat dan overshoot berkurang. Parameter gain K dari hasil simulasi selanjutnya akan diimplementasikan secara embedded programming ke dalam Arduino Uno pada sistem robot IPBD. Kata kunci: Inverted pendulum beroda, Pemodelan, LQR ABSTRACT This paper describes the process of modeling two-wheeled pendulum inverted robots (IPBD) using the Lagrange dynamics. After the IPBD robot model system was obtained, the optimal control technique in this case using a linear quadratic regulator (LQR) was used to see the system response step and the response of the system response to interference. Before the LQR control is implemented, simulation using Matlab Simulink is conducted to get the gain K parameter on the LQR control. Furthermore, by varying the weighting matrix Q, the gain variation K will be obtained. There are five types of Q weighting matrix in this research and the R element matric is tuned with a value of 1. From the test, obtained results show that by raising the weighting matrix Q is produced a faster response to the steady state and overshoot is reduced. At the final stage, the gain K parameter from the simulation results will be implemented by embedded programming into Arduino Uno on the IPBD robot system. Keywords: Wheeled inverted pendulum, Modelling, LQR

Robot Inverted Pendulum Beroda Dua (IPBD) dengan Kendali Linear Quadratic Regulator (LQR)