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"ABSTRACTWe considered the problem in which a DC motor was controlled to track a given trajectory when the corresponding driven load was associated with uncertain time-varying mass moment of inertia. With the existence of such inertia variation, the corresponding system matrix and input matrix of the control system were simultaneously uncertain and time-varying. Accordingly, stability of the control system could not be guaranteed by simply locating all the poles of the linearized model in the LHP at all time. Based on Lyapunov stability theorem, we came up with a robust PID controller design technique that yielded satisfactory results for this problem. Our robust PID controller was easy to implement, and guaranteed uniform input-to-state stability for the system. It appeared in our investigation on a large Maxxon DC motor that our controller allowed as high as 100% variation of equivalent inertia loading with respect to rotor inertia. We provided a tool to facilitate controller tuning so that the resulting control signal stayed within practical bounds, while achieving a satisfactory level of performance. By selecting an appropriate transmission ratio, our tracking control system could be employed in demanding applications such as independent joint control of robots, and spindle control of modern machining machines."

"Perkembangan teknologi UAV yang pesat menyebabkan teknologi UAV semakin marak digunakan dalam kehidupan sehari-hari. Quadrotor UAV menjadi populer akibat fleksibilitas dan utilitas nya yang tinggi dan bermanfaat di kehidupan masyarakat luas. Penelitian ini membahas permasalahan pengendalian trajectory tracking menggunakan Pengendali MPC Non-Linier pada model Quadrotor UAV. Model dinamik quadrotor yang digunakan merupakan model non linier, yang sensitif terhadap perubahan input dan gangguan. proses pengendalian sistem dengan pengendali MPC non-linier dilakukan dengan mengubah model sistem continuous kedalam bentuk diskrit yang kemudian diselesaikan dengan pemecah pemrograman kuadratik sekuensial sembari memperhitungkan batasan input, output dan keadaan sistem. Ditampilkan hasil simulasi dengan variasi referensi trajektori dan parameter pengendali untuk mencapai keadaan optimal. Hasil simulasi menunjukan bahwa MPC non-linier dapat melakukan pengendalian trajectory tracking dengan baik, dengan nilai RMSE pada trajektori garis lurus sebesar 0.0168, pada trajektori kotak sebesar 0.0207, pada trajektori helix sebesar 0.4215, pada trajektori spiral sebesar 0.0084, dan pada trajektori lingkaran sebesar 0.4687.

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The rapid development of UAV technology causes UAV technology to be increasingly used in everyday life. Quadrotor UAV is becoming popular due to its flexibility and high utility and is useful in people's lives. This study discusses the problem of controlling trajectory tracking using a Non-Linear MPC controller on the Quadrotor UAV model. The quadrotor dynamic model used is a non-linear model, which is sensitive to input changes and disturbances. the process of controlling the system with non-linear MPC controller is done by changing the continuous system model into a discrete form which is then solved by a sequential quadratic programming solver while taking into account input, output and system state constraints. The simulation results with variations of the trajectory reference and control parameters are displayed to achieve the optimal state. The simulation results show that non-linear MPC can control trajectory tracking well, with an RMSE value of 0.0168 for straight-line trajectory, 0.0207 for square trajectory, 0.4215 for helix trajectory, 0.0084 for spiral trajectory, and 0.4687 for circle trajectory. "

"Mobile robot dalam aplikasinya sering dimanfaatkan dalam membantu kehidupan manusia. Tetapi mobile robot yang bekerja sendiri tidak bisa diandalkan dalam mengerjakan pekerjaan yang lebih kompleks, maka diperlukan robot yang saling berkoordinasi satu sama lain. Dalam koordinasi robot ini diperlukan kendali formasi. Kendali formasi ini dapat direalisasikan dengan beberapa metode, salah satunya adalah dengan leader-follower. Namun sebelumnya, untuk memastikan multi-mobile robot dapat bekerja dengan baik perlu dipastikan setiap mobile robot dapat mengikuti trayektori yang diperintahkan. Untuk itu pertama kali dilakukan pengujian kemampuan mobile robot dalam mengikuti trayektori garis lurus, sinusoidal, dan triangular. Selanjutnya dilakukan perancangan sistem kendali dengan metode leader-follower untuk mempertahankan formasi berdasarkan kecepatan leader dan jarak relatif follower terhadap leader. Sistem lalu diuji dengan simulasi dan perangkat keras menggunakan ROS (Robot Operating System) dan Gazebo. Hasil eksperimen menunjukkan bahwa mobile robot dapat mengikuti skenario trayektori yang diperintahkan dengan kesalahan mutlak rata-rata maksimal adalah ±5.681 cm dan mampu mempertahankan formasi ketika leader mengikuti trayektori yang diinginkan dengan kesalahan mutlak rata-rata jarak antar-mobile robot adalah ±7.327 cm.

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Mobile robots are often used to help human life. But mobile robots that work alone cannot be relied upon to do more complex work, so robots are needed to coordinate with each other. In coordination this robot requires formation control. This formation control can be realized by several methods, one of which is leader-follower. But beforehand, to ensure multi-mobile robots can work properly it is necessary to ensure that each mobile robot can follow the trajectory that is ordered. For the first, one mobile robot is tested to follow a straight line, sinusoidal, and triangular trajectory. Then the control system with leader-follower method is designed to maintain formation based on leader speed and relative distance of the follower to the leader. The system is then tested with simulations and hardware using ROS (Robot Operating System) and Gazebo. The experimental results show that the mobile robot can follow the desired trajectory with the maximum mean absolute error of ±5.681 cm and is able to maintain the formation as the leader follows the desired trajectory with mean absolute error of ±7.327 cm"