# Simulated Adaptive Control of a Propeller Levitated Arm

The objective of the project was to simulate control of a 1 DOF propeller levitated arm system. Adaptive control was portrayed using a MRAC (Model Reference Adaptive Control) architecture.

The system consists of a rod hinged at a point by means of a pin joint. On the other end of the rod a propeller is attached. The goal is to control the angular velocity and the thrust of the propeller so that the arm can reach the desired position in space. In practicality, this control can be achieved by regulating the voltage to the propeller by means of controller pulse width modulation and this in-turn would change the angular velocity of the propeller. The angular position of the arm is the system input while the propeller thrust is the system output. A model capturing the system dynamics by Newton Euler methods was established and the corresponding state space and transfer function forms were formulated to demonstrate control using MATLAB Simulink.

The controller scheme used was MRAC (Model Reference Adaptive Control) and two control laws were illustrated namely:

1) MIT Rule

2) Lyapunov Stability Criteria

Additionally, since MIT rule does not guarantee stability an inner PD and PID loop was considered for control. In order to simulate adaptive control a step disturbance was introduced in the system at a fixed sample time after system stabilization. The implemented control law shows successful disturbance rejection.

**Abstract:**

This report documents the background, methods, results and conclusions for the propeller levitated arm system using adaptive control. The rationale behind the propeller levitated system was that it was used as a preliminary-study for the more complex quadcopter system since both the systems have comparable dynamics. The propeller levitated arm system is documented in Part A; while quadcopter model is documented in part B. The methods used highlight the Model Reference Adaptive Control (MRAC) scheme using 2 adaptive laws namely MIT rule and Lyapunov stability criteria. It was observed that MIT rule lacks stability due to apparent reasons discussed in the subsequent text; hence it was necessary to employ an inner closed loop PID (Proportional Integral Derivative) control for the levitated

arm system using MIT rule. The Lyapunov stability criteria gave satisfactory results guaranteeing stability with system

states converging or following the model states thus driving error to zero. The report further summarizes the developments for the proposed quadcopter control in Part B thus giving an insight on the control theory for a quadcopter and various control cases that can be considered to simplify and simulate the highly non-linear 6 DOF (degrees of freedom) model. From the system dynamics, it was apparent that no progress would’ve been made unless the system had been linearized. Hence, three control cases had to be considered where linearization and model simplification was applicable. Though adaptive control using MRAC gave unacceptable results for the 3 DOF system, it was possible to employ closed loop PID control for all the mentioned cases.

Refer the pdf report for additional details

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