ECE 415 Control Systems, Fall 2018 Final Project 4-Dec-2015 Due: Saturday, 15-Dec-2018 by 11:55 pm via Isidore

Instructions:

1. You may not use any reference source other than your own class notes, your own homework and the homework solutions I have provided. You may not refer to any other textbook, other course notes, or other published material, including the web.

2. You may not consult another human being. This is your work, and yours alone.

3. There are four questions, out of which you need to choose three. Submit your solutions to three problems only, for a total of 75 points.

4. Work neatly and be precise, concise and to the point. Because this is a formal project, I will not struggle to grade a poorly organized or messy solution, and will automatically assign a grade of zero to any problem I cannot easily read.

5. All the problems are design problems, and they require you to use MATLAB to solve them. Provide all your MATLAB code, uncompressed, via Isidore, as .m or .slx files.

6. Write a report on the results using the following outline (the page limits are strict): • Title page (with your name and the date and an Executive Summary (abstract) which

is a short paragraph description of what the report is about). • Design Problem Descriptions (for the three problems): ≤ 2 pages. • Controller Design Approach: ≤ 3 pages

o Describe your approach to designing the compensators. o Provide the final compensators that you designed (the ones that meet the

specifications). • Verification of Specifications: ≤ 3 pages

o Provide simulations / analysis to verify that you meet the specifications. You may organize these elements problem by problem, or one by one. It is your choice.

7. Make sure your all your final control designs are clearly marked, and in the form

“

It is essential that you provide clear evidence of having followed a design procedure. Failing to do so will cause you to lose points.

8. Turn in your report in PDF format via Isidore. It should be at most 9 pages long.

9. Only turn in your report if the paragraph below applies to you.

I certify that I have worked on this test exclusively on my own, and that all the work I am turning in is completely my own. I have not given any help, received any help, nor witnessed anyone else giving or receiving help to solve this test. I understand that cheating on this test will automatically result in a failing grade for the test and for the class.

C (s) = K s + z s + pOwner铅笔

For all problems below we will use the standard negative unity feedback system shown here:

1. (25 pts) The plant is given by ” . Design a controller that achieves

” and a settling time (2% criterion) ” . In addition, the steady-state requirement for tracking a ramp is ” . Your controller should be of first order (it can be either a lead or a lag controller).

2. (25 pts) The plant is given by ” . Using the design approach of

your choice, design a controller that yields a percent overshoot to a step input ” , and ” for a ramp input. Hint: consider first designing a lead compensator, and then a lag compensator, to arrive at a lead-lag design.

3. (25 pts) The plant is given by ” . Using frequency domain methods, design

a controller that achieves a steady-state error less than 10% for a step input, a phase margin ” and a settling time (2% criterion) ” for a step input. Your controller should be of first order (it can be either a lead or a lag controller).

4. (25 pts) Using the approach of your choice, design a lead or lag controller for the purpose of dc motor position control. The transfer function modeling the motor, from input voltage ” to shaft angle ” , is given by ” . We assume to be able

to accurately measure the angle, and your controller should produce a voltage signal to be output to the motor. The reference signal to track is a train of steps with amplitude 1 (that is, alternating between -1 and 1) and frequency equal to 0.5 Hz. You are given the task of achieving a peak time ” , and a maximum percent overshoot to a step input ” .

Be sure to show a plot of your design tracking a train of steps (not a single step response!) with the characteristics specified. Show three complete periods in your plot.

P (s) = 4

s (s + 1)(s + 4) PM ≥ 50∘ Ts ≤ 4s

Kv ≥ 2

P (s) = 81

s ( 14895 s2 + 169 s + 1) P . O . ≤ 10 %

Kv ≥ 20

P (s) = 0.5(s + 9.8) s2 + 2s + 21

PM ≥ 45∘ Ts ≤ 5s

V (s) θ (s) P (s) = θ (s) V (s)

= 1

s (0.0093s + 0.5369)

Tp ≤ 0.05s P . O . ≤ 4.6 %

+

− C(s) P (s)

R(s) Y (s)