Design, Construction, Control and Implementation of Unstable Nonlinear One Degree of Freedom Cube with Reaction Wheel Actuator

In this paper, the mathematical modeling, construction, control, and implementation of a one-degree-of-freedom cube dynamic system with a reaction wheel actuator will be discussed. The innovation of this paper is the implementation of the proportional-integral-derivative controller on the experimental system of one degree of freedom with a reaction wheel. First, equations of system are expressed, then the system is analyzed in time and frequency domain. Then, the proportional-integral-derivative controller will be designed and implemented on the constructed system. The system response is compared in six steps for different control gains. The control gains of the best answer are proportional gain of -20, integral gain of -30 and derivative gain of 3- in system theory answers it has 1 degree of superiority and in experimental answer it has 7 degrees of overshoot. The steady-state error is zero for both experimental and theoretical system. The rise time of the simulation theory is 10 time steps, each time step is equal to 0.001 seconds, and the experimental response of the system is 10 time steps. The simulation session time is 180 time steps and the experimental response is 100 time steps.. In the next step, the stability of the control designed with the selected gains from the previous step is tested by inserting the perturbation, and the system is stabilized by 4 degrees overshoot. By changing the angle of the bottom plane, the response will have 3 degrees overshoot, but the system will remain stable.