Mech 215

Question 1

Newton’s 2nd law in a non-inertial frame

Answer 1

∑Fext + Ffict = ma, where Ffict is the fictitious force, and a is the acceleration of the mass within the moving frame.

Question 2

Ffict

Answer 2

-ma, where a is the acceleration of the moving frame.

Question 3

Damping ratio > 1

Answer 3

Amplification

Question 4

Damping ratio < 1

Answer 4

Mitigation

Question 5

Phase shift < 0

Answer 5

Output delayed

Question 6

Phase shift > 0

Answer 6

Output in advance

Question 7

Harmonic forced response

Answer 7

Output is always delayed and mitigated with respect to the input.

Question 8

When does resonance occur?

Answer 8

When the system is excited at the resonance frequency.

Question 9

Requirement of frequency analysis

Answer 9

All initial conditions are set to zero.

Question 10

Output delay of a first order system

Answer 10

Phase shift of the FRF/ input frequency

Question 11

Output amplitude of a first order system

Answer 11

alphamodulus(FRF), where alpha is the coefficient of the harmonic input.

Question 12

Bode plot positive gain

Answer 12

Amplification of the harmonic forced response.

Question 13

Bode plot negative gain

Answer 13

Mitigation of the harmonic forced response.

Question 14

If T(s) = T1(s)T2(s), then then gain and phase are (respectively)…

Answer 14

gain1(w) + gain2(w) and phiH1 + phiH2

Question 15

If T(s) = T1(s)/T2(s), then then gain and phase are (respectively)…

Answer 15

gain1(w) - gain2(w) and phiH1 - phiH2

Question 16

Bode stability criterion

Answer 16

A system is stable if the open loop gain is negative at the critical frequency, wc.

Question 17

Critical frequency, wc

Answer 17

The frequency when the phase is -π.

Question 18

Gain margin

Answer 18

GM = -Gain(wc). This corresponds to the gain that can be added to the system whilst preserving its stability.

Question 19

Phase margin

Answer 19

PM = π + phase(wgo), where wgo is the frequency at zero gain. This corresponds to the phase delay that can be added to a system whilst preserving its stability.

Question 20

Steady state error, ess

Answer 20

lim(s->0)(SU(s)/1 + T1(s)T2(s))

Question 21

What does gamma represent in the open-loop transfer function equation?

Answer 21

The system type number.

Question 22

First order rise time, Tr

Answer 22

2.2 tau

Question 23

First order 2% settling time, Ts

Answer 23

4 tau

Question 24

Second order 2% settling time, Ts

Answer 24

4/xiwn, where xi is the damping ratio and wn is the natural frequency.

Question 25

Second order peak time, Tp

Answer 25

π/wd

Question 26

Second order percentage overshoot, D%

Answer 26

100e^(-πxi/√(1-xi^2))

Question 27

Three effects of increasing the damping ratio

Answer 27

The settling time and overshoot decrease, which is good. The peak time increases, which is bad.

Question 28

Optimal damping ratio

Answer 28

xi = 0.7, which gives an overshoot of D% = 5%.

Question 29

Proportional controller, Kp

Answer 29

Improves rapidity, but can introduce a steady state error. This error can be reduced by increasing Kp, but this reduces stability margins.

Question 30

Proportional integral controller, Kp + Ki/s

Answer 30

The integral action can suppress the steady state error, but it also reduces the stability margins. It increases the order of the system, so it can introduce undesirable oscillations.

Question 31

Proportional derivative controller, Kp + Kds

Answer 31

Increases the stability margins, but introduces a steady state error. This can be reduced by increasing Kp and Kd, while still keeping good stability margins. The main drawback is that it introduces high frequency noise.

Question 32

Proportional integral-derivative controller

Answer 32

Kp + Ki/s + Kds