Implementing & Testing an Observer - Engineering Assignment Help

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Assignment Task

 

Part A: Parameter estimation (Offline)
Part B: Implementing and testing an observer.

Part A, expected to be solved during weeks 7 and 8. (relevance: 45%)
Part B, expected to be solved during weeks 9 and 10. (relevance 55%)

The 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.

Based on the measurements provided by the encoder, and on the knowledge of the input being applied, we want to infer the values of the parameters of the model. Those parameters are the ODE’s coefficients a b c , , .

We are in condition to measure the angular position and the applied input. That sampling rate is more than enough for a slow system like this one. We have the intention to infer the parameters a b c, by exploiting the information provided by those measurements. However, we have an additional problem, which is related to noise polluting the measurements provided by the encoder. The encoder has a resolution of 360 degrees /2048 (~0.1758 degrees), which introduces a quantization error of(360/4096) degrees. (The angular rate measurements are also polluted by noise; however, we do not uses those measurements in part A.) This fact can be appreciated as “small steps” in the plots of the angular measurements.

 

Which one is my dataset?
There are 56 sets of datasets, indexed from 0 to 55. Your datasets will be DatasetNumber=mod( ID, 56 ), in which DatasetNumber is the index of your assigned dataset, and ID is your student ID number. Those files are located in the folder “DataForPartA”

Report
The assignment involves the processing of data and preparing a brief report. There will be a section in the report for Part A, and another for Part B. For Part A, we expect the following subsections:
A.1) A brief introduction describing this part of the assignment; then a brief explanation about the approach you have used for estimating (a,b,c). If you used a toolbox or any third-party software solution for that purpose, you must cite that source, and give a brief explanation of it.
A.2) You will indicate in a small table the estimated parameters, mentioning the number of dataset you have used.
A.3) You will simulate you estimated model, using the same inputs which had been applied in the experiments, and you will include those plots in your report, comparing the simulated one and the real ones. In Part A, we only have interest about the angular position.

 

 

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