Question

Experiment 1 Consider the open-loop system, modelled as V (s) 6(s) GM(s) where GM(s) is given by equation7 In this experiment, we will find the responise and investigate the characteristics of this open-loop system. a) Write instructions to create the ILTI (linear time-invariant) transfer function representing the motor GM(s). b) Plot the open-loop response for step voltage input (step response). c) Find the finite poles afid zeros of GM(s) c) Answer questions for experiment 1 in the worksheet. Simplifying, gives the transfer function θ(s) sition - inline %3B%20filename%2A%3DUTF-8%, G(s) i(o) Op(s) Figure 6: Closed-loop system for PI control of DC motor. Experiment 1 Consider the open-loop system, modelled as V(s) Grs) where GM(s) is given by equation7 In this experiment, we will find the response and investigate the characteristics of this open-loop system a) Write instructions to create the LTI (linear time-invariant) transfer function representing the motor Gu(s) b) Plot the open-loop response for step voltage input (step response) c) Find the finite poles and zeros of GM(s). c) Answer questions for experiment 1 in the worksheet. Experiment 2 To improve control over the speed of the motor's rotation, we put the motor in a feedback conigs- ration as shown in Figure 4. C(o) is the transfer function of the coitroller. Initially, proportional control is being used, which means that C(o) is equal to a gain, ie. C(o) - Kp where Kp is a constant gain value. In this experiment we are going to find the response and investigate the characteristics of the closed-loop system.

Answer 1

The solution is given in these 15 pages

First, the motor transfer function is derived for field current controlled.

Equations from field current controller are used to derive armature current controlled which is desired G(s).

Then the roots are found from the derived transfer function.

The Matlab code and plot for specific values is attached in the end.

It is verified that the Matlab plot has the same steady-state value as the one derived from the equation.

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