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# Automatic Control 2

### definitions 2

cyclone | convection current | condensation | eye | CATEGORY 4 | HURRICANE | GULF STREAM |
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Describe the procedure for plotting the Nyquist plot | 1.Plot KG(s) for –j(infinity)2.Evalunate the number of clockwise encirclements of -1, and call that number N3. Determine the number of unstable (RHP) poles of G(s) and call that number P4. Calculate the number of unstable closed-loop <= s <= +j(infinity) | |||||

vector margin? | The distance to the -1 point from the closest approach of the nyquist plot | |||||

Discuss closed-loop frequency response | A specification related to the closed-loop frequency response is the resonant-peak magnitude Mr, generally related to the damping of the system. | |||||

Discuss PD compensation | Compensator transfer function, D(s)=(Tds+1), has a stabilizing effect on the root locus of a second order system | |||||

lead compensation (design procedure, p. 375); | 1.Determine open-loop gain K to satisfy error 2.Evaluate the phase margin of the uncompensated system using K 3. Allow for extra margin 4. Determine alpha from Eq (6.40) | |||||

lead compensation (design procedure, 2 | 5. Pick wmax to be at the crossover frequency 6. Draw the compensated frequency response and check the PM 7. Iterate on the design | |||||

PI compensation | PI has the transfer function D(s) = K/s(s+ 1/T1) | |||||

lag compensation (design procedure | 1.Determine the open-loop gain K 2. Draw the bode plot of the uncompensated system 3. Determine alpha to meet the low-frequency gain 4. Choose the corner frequency w=1/T 5. The other corner frequency is then w=1/alphaT 6.Iterate on the design | |||||

give a summary of compensation characteristics (p. 390); | PD control adds phase lead at all frequencies above the break point. 2. Lead compensation adds phase lead at a frequency band between the two break points 3. PI control increases the frequency-response magnitude at frequencies below the breakpoint 4. Lag | |||||

M and N circles | The contours of constant closed-loop magnitude and phase are circles when G(jw) is presented in the linear Nyquist plot | |||||

Resonant frequency | the frequency associated with the magnitude and phase at the point of tangency | |||||

What is the Inverse Nyquist plot (p. 397)? | The reciprocal of the Nyquist plot. It is obtained most easily by computing the inverse of the magnitude from the bode plot and plotting that quantity at an angle in the complex plane. | |||||

Sensitivity function | S(jw) = 1/(1+DG) | |||||

Time-delay magnitude | |Gd(jw)|=|e^-jwTd|=1 for all w | |||||

What is state-space design? | Aim is to find a compensation D(s) that satisfies the design specifications | |||||

Give the steps of the design method | 1.Select closed-loop pole locations and develop the control law for the closed-loop system 2.Design an estimator 3.Combine the control law and the estimator 4.Introduce the reference input | |||||

Describe the advantages of state-space (p. 440)? | 1.The study more general models 2.To introduce the ideas of geometry into differential equations 3.To connect internal and external descriptions | |||||

What are normal form?; | The state-variable form | |||||

modern control design?; | use of the state-space approach | |||||

classical control design? | Use of transfer-function-based methods, such as root locus and frequency response |

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delafuente