MATLAB_motor_modeling_control3

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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. It is believed that the system can be represented using a first-order transfer function model.

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

If you cannot complete the modelling exercise of Task 1, you will need to assume a suitable second

order system for G1(s), with arbitrarily chosen parameters. Choose values to 1 decimal place, and not

simple integer values.

It is possible that you have developed a model for G1(s) which contains a right-half plane (unstable)

pole. This is a legitimate outcome, depending on the measurements and calculations from Task 1,

but also may be the result of an error in the working. In such as case, it is still possible that the

control engineering problem is a perfectly reasonably one, however it may be more difficult to solve,

and it some cases (depending on the value of the pole) the problem may be unsolvable, for example

in Task 2. If you have deduced a model with a right-half plane pole, you should first modify it simply

by taking the mirror image value of a left-half plane pole instead. Move forward with this modified

G1(s).

It is also possible you have produced a model with complex poles for G1(s). In this case, there is no

need to modify the poles as outlined above. In trying to modify such models students often make

mistakes, and come up with models that do not make sense.

It is known that the parameters of the production motors differ from those of the test rig version. In

order to reflect some differences, you should present another motor model, G2(s) as follows:

Illustrate how additional velocity feedback, from a tacho-generator, may be incorporated into the

closed-loop system. Investigate the effect of integrating such a scheme with a proportional controller

K(s) = Kp, and investigate the design of such a Proportional + Derivative or P+D controller.

This is also an open investigation, there is no set specification to meet. Reflect on advantages and

disadvantages compared to proportional control alone.

[20 Marks]

Instead of using velocity feedback, closed-loop performance may be achieved by the introduction of

an in-series compensator (or filter) in the forward path. The compensator may be seen as K(s) in

Figure 3, so in this case the P+D controller structure of Task 3 is removed from Task 4.

Investigate how the parameters of such an in-series compensator maybe designed, and how they affect

the performance characteristics of the closed-loop system, compared with the methods of Tasks 2 and

3. Investigate the design of suitable compensators, and present your findings. You should base your

designs on the frequency response methods presented in the module.

The structure of the compensator is up to you, and more than one choice can be made.

Again, this is an open specification. You need to consider what factors to take into account in setting

objectives.

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