Lab 2 Digital Simulation: Analyzing the Effects of Zeros and Poles on H1(s) and H2(s), Lab Reports of Control Systems

A lab report for a digital simulation course, focusing on the analysis of h1(s) and h2(s) transfer functions. The report covers three parts: comparing the effects of zeros on the state space model, discussing the impact of zeros on mp, tr, and ts, and analyzing the effects of an extra pole. Tables, plots, and instructions for filling in missing data.

Typology: Lab Reports

Pre 2010

Uploaded on 03/10/2009

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Lab 2 DIGITAL SIMULATION 1 of 3
Report By: Alan Gostin
Lab Partner: Vlad Vladimerou
Lab TA: Alan Gostin
Section: Thursday at 10:00
Part I. ___/8
State Space Model Representation of H1(s) ___/8
Compare the plots of y_dot and y obtained in Part 1 of the lab with the plots previously made for
the prelab. Why are they identical? Attach plots – if your prelab plot was wrong, fix it and
attach the corrected plot.
Part II. ___/22
Effects of a Zero on Mp, tr, and ts. ___/2
Fill the table and attach plot for part II.
Property No Zero
H1(s)
H2(s) with
Zero at s = -30
H2(s) with Zero
at s = -3
H2(s) with Zero
at s = -1.5
H2(s) with Zero
at s = 1.8
H2(s) with Zero
at s = 18
Mp obs % % % % % % %
tr obs (s)
ts obs (s)
Table 1: Effects of Zero
Discuss the Effects of a LHP Zero ___/4
Explain how Mp, tr, and ts are affected by the zero’s location. When can the zero be ignored?
Effects of a Non-minimum Phase Zero ___/2
What is unique in this situation? Explain how Mp, tr, and ts are affected by the zero’s location.
Total: ____/50
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Report By: Alan Gostin Lab Partner: Vlad Vladimerou Lab TA: Alan Gostin Section: Thursday at 10:

Part I. ___/

State Space Model Representation of H 1 (s) ___/

Compare the plots of y_dot and y obtained in Part 1 of the lab with the plots previously made for the prelab. Why are they identical? Attach plots – if your prelab plot was wrong, fix it and attach the corrected plot.

Part II. ___/

Effects of a Zero on Mp, tr, and ts. ___/

Fill the table and attach plot for part II. Property No Zero H 1 (s) H 2 (s) with Zero at s = - H 2 (s) with Zero at s = - H 2 (s) with Zero at s = -1. H 2 (s) with Zero at s = 1. H 2 (s) with Zero at s = 18 Mp obs % % % % % % % tr obs (s) ts obs (s) Table 1: Effects of Zero

Discuss the Effects of a LHP Zero ___/

Explain how Mp, tr, and ts are affected by the zero’s location. When can the zero be ignored?

Effects of a Non-minimum Phase Zero ___/

What is unique in this situation? Explain how Mp, tr, and ts are affected by the zero’s location.

Total: ____/

Decomposition of H 2 (s) __/

Split H 2 into 2 fractions. Discuss how this decomposition helps to explain the effect of the zero location. Also discuss α’s effect. What happens when α is negative?

Part III. ___/

Effects of an Extra Pole on Mp, tr, and ts. ___/

Fill the table and attach plot for part III. Attach Plots. Property No Zero H 1 (s) H 3 (s) with Pole at s = - H 3 (s) with Pole at s = - H 3 (s) with Pole at s = -1. Mp obs % % % % % tr obs (s) ts obs (s) Table 2: Effects of Extra Pole

Discuss the Effects of an Extra Pole ___/

Explain how Mp, tr, and ts are affected by the location of the additional pole. When can the extra pole be ignored?

Decomposition of H 3 (s) ___/

Use partial fraction expansion. Discuss how this decomposition helps to explain the effect of the location of an additional pole.