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Control Systems Laboratory - Servomechanism Design Exercise

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Control Systems Laboratory - Servomechanism Design Exercise

Introduction 

In this lab, I designed three new controllers. I designed a full state feedback, partial state feedback and a partial state feedback with dynamic controller to give pole-zero cancellation. For each controller, I calculated the forward and feedback gain values, these are shown in figure 1, 2 and 3 below. I built the controllers and compared the dynamic performance of each type of control.

Performance of Finalised-gain Values

Full State Feedback

[pic 1][pic 2]

Plant transfer functions and final closed loop system with numerical values

The closed-loop transfer function of the full state feedback system is shown in Eq.1 below.

                                                                         (1)[pic 3]

Partial State Feedback

[pic 4][pic 5]

The closed-loop transfer function of the partial state feedback system is shown in Eq.2 below.

                                                                         (2)[pic 7][pic 6]

Partial State Feedback with Dynamic Controller

[pic 8]

The closed-loop transfer function of the partial state feedback with dynamic controller system is shown in Eq.3 below.

[pic 9]

Experimental Step Responses Comparison

Full State Feedback

Partial State Feedback

Partial State Feedback with Dynamic Controller

[pic 10]

[pic 11]

[pic 12]

[pic 13]

[pic 14]

[pic 15]

TP

360ms

720ms

840ms

VP

4.88V

No Peak

5.12V

VSTEADY

3.60V

3.92V

3.76V

[pic 16]

0.313

-

0.308

[pic 17]

9.19Hz

-

3.93Hz

Figure 4 - Comparison of three control strategies

When applying resistance, all three systems acted in a different way. The full state feedback was very steady, and when applying resistance, it was quite difficult, as shown in Figure 4, the full state feedback was steady even with a large amount of resistance applied.

The partial state feedback was steady, but when even a little bit of resistance was applied, as shown in Figure 4, the motor could be stopped with just using your hands. This system is designed to be under damped, and it is behaving critically damped, this is to do with the friction in the motor. The viscous friction constant is assumed to be 0, but in real life this would not be the case. The mechanical resistance provided enough resistance to damp this.

The partial state feedback with dynamic controller was also steady, but required more resistance than without the dynamic controller. But the motor could still be stopped with your hands on the motor, as shown in Figure 4.  

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