Term
1. What is a root locus?
(8) 

Definition
The plot of a system's closedloop poles as a function of gain 


Term
2. Do the zeros of a system change with a change in gain? Why or why not?
(8) 

Definition


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3. What are two ways to find where the root locus crosses the imaginary axis?
(8) 

Definition
(1) Apply RouthHurwitz to the closedloop transfer function's denominator. (2) Search along the imaginary axis for 180 degrees. 


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4. How can you tell from the root locus if a system is unstable?
(8) 

Definition
7. If any branch of the root locus is in the rhp, the system is unstable. 


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5. How can you tell from the root locus if the settling time does not change over a region of gain?
(8) 

Definition
If the branch of the root locus is vertical, the settling time remains constant for that range of gain on the vertical section. 


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6. How can you tell from the root locus that the natural frequency does not change over a region of gain?
(8) 

Definition
If the root locus is circular with origin at the center 


Term
7. How would you determine whether or not a root locus plot crossed the real axis?
(8) 

Definition
Determine if there are any breakin or breakaway points 


Term
8. Briefly describe how the zeros of the openloop system affect the root locus and the transient response.
(8) 

Definition
The zeros of the open loop system help determine the root locus. The root locus ends at the zeros. Thus, the zeros are the closedloop poles for high gain. 


Term
1. Name two major advantages of the design techniques of Chapter 9 over the design techniques of Chapter 8.
(9) 

Definition
A. Permits design for transient responses not on original root locus and unattainable through simple gain adjustments. B. Transient response and steadystate error specifications can be met separately and independently without the need for tradeoffs 


Term
2. What kind of compensation improves the steadystate error?
(9) 

Definition


Term
3. What kind of compensation improves both steadystate error and transient response?
(9) 

Definition
PID or laglead compensation 


Term
4. Cascade compensation to improve the steadystate error is based upon what pole zero placement of the compensator? Also, state the reasons for this placement.
(9) 

Definition
A pole is placed on or near the origin to increase or nearly increase the system type, and the zero is placed near the pole in order not to change the transient response. 


Term
5. What are the advantages and disadvantages of using a passive lead network instead of an active PD controller?
(9) 

Definition
A PD controller yields a single zero, while a lead network yields a zero and a pole. The zero is closer to the imaginary axis. 


Term
6. In order to speed up a system without changing the percent overshoot, where must the compensated system's poles on the splane be located in comparison to the uncompensated system's poles?
(9) 

Definition
Further out along the same radial line drawn from the origin to the uncompensated poles 


Term
7. Why is there more improvement in steadystate error if a PI controller is used instead of a lag network?
(9) 

Definition
The PI controller places a pole right at the origin, thus increasing the system type and driving the error to zero. A lag network places the pole only close to the origin yielding improvement but no zero error. 

