Controls/Spring 2012/Test 1/RSR

This is the equations page for Controls/Spring_2012/Test_1

Approved

Here is a link to the equation sheet: Equation Sheet The draft includes the following:

Chapter 2

• Motor equation (2.153, p. 81)
• Motor transfer function constants (2.159, 2.162 & 2.163, p. 82)

Chapter 4

• 1st Order Rise Time (4.9, p. 167)
• 1st Order Settling Time (4.10, p. 167)
• 2nd Order Peak Time (4.34, p. 179)
• 2nd Order %OS (4.38, p. 180)
• 2nd Order Damping Ratio (4.39, p. 180)
• 2nd Order Settling time (4.42, p. 181)
• 2nd Order Damped Frequency (in 4.44, p. 182)
• 2nd Order Normalized Rise Time (footnote 5, p. 181)

Other

• T from Geq for unity feedback

\(\begin{align} T&=\frac{G_{eq}}{1+G_{eq}}\\ G_{eq}&=\frac{N_G}{D_G}\\ T&=\frac{N_G}{D_G+N_G} \end{align}\)

Denied / Must Memorize / Not Needed

• Laplace Transform Table (Table 2.1, p. 36)? - not needed
• Op amp general gains (2.97, p. 59 and 2.103, p.60) - must memorize inverting/non-inverting paradigms and gains
• Mechanical rotation and translation impedances (Table 2.4 on p.62 and Table 2.5 on p. 70) - must memorize
• General 2nd order transfer function (4.22, p. 174) - need to memorize - note that to be truly general there needs to be a multiplicative constant \(K\) in front of all that.
• Mason's Rule (5.28, p. 252) - need to memorize that and what the terms mean.