Abstract:

The pendulum model is one of the famous examples of control statements that are generally studied and it is considered one of the systems that have non-linear properties because it is characterized as a single-input multi-output system. The position in which the pendulum is stable is vertical up or down. Examples of its applications include walking robots, personal baggage transport robots, and wheelchair robots, So, the goal of this study is to achieve the stability of the system (The arm should be at zero angle with the plumb axis). In addition to achieving tracing of the required reference signal (Chase the cart to the desired position), the problem of optimal control takes into account these two conditions by finding the gain constants for the law of control after solving the Riccati equation. Whereas, the solution of the Riccati equation is based on Lyapunov’s laws of stability, in addition to minimizing the cost function, as this achieves reducing the static error to the lowest possible value. In this paper the optimal control system was designed to control the Cart-inverted Pendulum. The simulation results showed the effectiveness of the proposed system and its ability to achieve the desired purpose.

Keywords: Swing arm – inverted pendulum – optimal control – Modeling and
Simulation

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A quarterly peer-reviewed scientific journal, issued in Arabic by a university in the liberated areas, the subject of scientific research and academic studies in various disciplines, in which the conditions of scientific research are applied in briefing and investigation and the methodology and steps of scientific research.

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