Optical Encoder for Measuring Angular Position - IT Assignment Help

Assignment Task

QueThe system 
We have an electromechanical system, which is composed by an electric motor, moving a rotational  load. The load is a pendulum. 
We have sensors installed on it. Those are: 
1) Optical encoder for measuring angular position. 
2) IMU (inertial measurement unit) 
The IMU is installed on the pendulum shaft in a way that one if the IMU’s gyros is used to measure the  angular velocity of the arm.  
The system allows us to modify the amount of friction, and to change the position of a mass which is  attached to the arm. We can also change the gain of the amplifier which drives the electric motor. Although we can modify those characteristics, the resulting parameters a b c , ,are not accurately  known by us. 
We know that the dynamics of the system can be approximated by the following ODE. 

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