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Control Systems
Control Systems Engineering
178 SOLVED PROBLEMS
Question: 10.18
Find the transfer function of the subsystem whose Bode plots are shown in Figure 10.57. ...
Verified Answer:
Let us first extract the underdamped poles that we...
Question: 10.CS.1
Antenna Control: Stability Design and Transient Performance Our ongoing antenna position control system serves now as an example that summarizes the major objectives of the chapter. The case study demonstrates the use of frequency response methods to find the range of gain for stability and to ...
Verified Answer:
Using the block diagram (Configuration 1) shown in...
Question: 13.4
Given a zero-order hold in cascade with G_1(s) = (s + 2)/(s + 1) or G (s) = 1 − e^−Ts / s (s + 2) / (s + 1) find the sampled-data transfer function, G(z), if the sampling time, T, is 0.5 second. ...
Verified Answer:
Equation (13.38) represents a common occurrence in...
Question: 13.5
Find the z-transform of the system shown in Figure 13.10(a). ...
Verified Answer:
The objective of the problem is to proceed in an o...
Question: 13.6
The missile shown in Figure 13.14(a) can be aerodynamically controlled by torques created by the deflection of control surfaces on the missile’s body. The commands to deflect these control surfaces come from a computer that uses tracking data along with programmed guidance equations to determine ...
Verified Answer:
The input to the control system is an acceleration...
Question: 13.7
Determine the range of sampling interval, T, that will make the system shown in Figure 13.15 stable, and the range that will make it unstable. ...
Verified Answer:
Since H(s) = 1, the z-transform of the closed-loop...
Question: 13.8
Given T(z) = N(z)/D(z), where D(z) = z³ − z² − 0.2 z + 0.1, use the Routh–Hurwitz criterion to find the number of z-plane poles of T(z) inside, outside, and on the unit circle. Is the system stable? ...
Verified Answer:
Substitute Eq. (13.60) into D(z) = 0 and obtain³ [...
Question: 13.9
For step, ramp, and parabolic inputs, find the steady-state error for the feedback control system shown in Figure 13.17(a) if G_1 (s) = 10 / s (s + 1) ...
Verified Answer:
First find G(s), the product of the z.o.h. and the...
Question: 13.10
Sketch the root locus for the system shown in Figure 13.21. Also, determine the range of gain, K, for stability from the root locus plot. ...
Verified Answer:
Treat the system as if z were s, and sketch the ro...
Question: 13.11
For the system of Figure 13.21, find the value of gain, K, to yield a damping ratio of 0.7. ...
Verified Answer:
Figure 13.23 shows the constant damping ratio curv...
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