Investigation into the Modelling and Control of a D.C. Motor - Engineering Assignment Help

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Assignment Task :

Task 1 - Modelling 

A d.c. motor is to be controlled using a variety of methods. Unfortunately, the control engineer does not have any suitable transfer function model of the system as a basis for controller design. In order to tackle this problem, a simple experimental feedback test rig is constructed, and various data are collected from the system. The data is noisy and uncertain, due to limitations of the methods used to collect it. 

Speed Response - Finding P(s) 

The first test is an open-loop test measuring motor speed (shown in Figure 1). An amplifier gain k = 2 is used, and the driving input is a step, by coincidence of 2 volts. Use the data of Figure 4 to deduce an appropriate transfer function model P(s). The model for P(s) does not need to be taken forward to any other tasks.

Rig

 

Position Response - Finding G1(s) 

The engineer adjusts the rig, so that the motor position is now controlled under feedback, with the motor represented by G1(s), and with a simple proportional gain (amplifier) in series with the motor, as shown in Figure 2. k is set to 12 for these experiments. 

Position

 

Step response data is collected from the closed-loop rig and shown in Figure 5. The step input ?i is 2V for this experiment. The experiment is not considered to provide any sort of a benchmark for the upcoming control problem, and the value of k is chosen without any careful consideration. Frequency response data is also collected from the closed-loop rig and shown in the form of a Bode diagram in Figure 6. 

Use the provided data to determine a transfer function for the closed-loop experimental rig, and - recalling that k is set to 12 - propose a suitable transfer function model for G1(s) (refer again to Figure 2). A second order transfer function will be adequate - you may like to justify this in your submission - and such a second order system will also enable analytical work to be undertaken in Tasks 2 and 3. Present your methods, analysis and your findings. You may download MATLAB .fig files of the experimental data from the ENG644D1 Moodle page, these may be helpful in both undertaking and reporting on this task. You may, if you prefer, include the scan of appropriately annotated hard copies of these graphs in your report if you cannot work with the versions in MATLAB.

 

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