CONTROL SYSTEMS ENGINEERING
7th Edition
ISBN: 2819770197050
Author: NISE
Publisher: WILEY
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Textbook Question
Chapter 4, Problem 25P
For the system shown in Figure P4.7, do the following: [Section: 4.6]
a. Find the transfer function G(s) = X(s)/F(s).
b. Find ,
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3. You are working at a medical device company, and are helping to design a new needle system that pricks the skin of
a patient so that a drop of blood becomes available for a glucose test. The needle tip position a can be modeled as a
system with the transfer function:
Position x, mm
Here, f(t) is an input force. It is constrained to be a step function with amplitude 1 (e.g. f(t) = u(t). Given all the
current design parameters, the response that the team is getting is shown below:
1.4
1.2
1
0.8
0.6
0.4
0.2
0
H(s) = X(s)/F(s) =
0
Kw2/20
s² + 25wns + w²/12
0.02 0.04
Step Response
0.06 0.08
Time (seconds)
0.1
0.12 0.14
Unfortunately, the problem is that the needle needs to reach a maximum position of 1.5 mm, but then after the over-
shoot, retract to a position of 0.5 mm. The peak time should be exactly 0.2 seconds. Given that you can control the
damping ratio , the natural frequency wn, and the gain K, write in a few sentences a proposed strategy for modifying
the design to meet the…
equations:
QB: Obtain the transfer function of system defined by the following state space
Hi
0 4 8 [x₁
0 8 5
X2 +
-10-30-20x330/u
[123]
[x1
Y=[1 2 0] X₂
X3
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26. For the system shown in Figure P4.8, a step torque is
applied at 01 (t). Find
a. The transfer function, G(s) = 02(s)/T(s).
b. The percent overshoot, settling time, and peak
time for 02(t). [Section: 4.6]
T(t) 01(1)
02(1)
ff
1.07 kg-m2
1.53 N-m-s/rad
1.92 N-m/rad
FIGURE P4.8
Chapter 4 Solutions
CONTROL SYSTEMS ENGINEERING
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Ch. 4 - List five specifications for a second-order...Ch. 4 - Prob. 12RQCh. 4 - What pole locations characterize (1) the...Ch. 4 - Prob. 14RQCh. 4 - How can you justify pole-zero cancellation?Ch. 4 - Prob. 16RQCh. 4 - 17. What is the relationship between , which...Ch. 4 - Name a major advantage of using time-domain...Ch. 4 - Prob. 19RQCh. 4 - What three pieces of information must be given in...Ch. 4 - 21. How can the poles of a system be found from...Ch. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - MATIAB ML 3. Plot the step responses for Problem 2...Ch. 4 - Find the capacitor voltage in the network shown in...Ch. 4 - For the system shown in Figure P4.3, (a) find an...Ch. 4 - Prob. 8PCh. 4 - MATLAB ML 9. Use MATLAB to find the poles of...Ch. 4 - Find the transfer function and poles of the system...Ch. 4 - MATLAB ML 11. Repeat Problem 10 using MATLAB....Ch. 4 - Write the general form of the capacitor voltage...Ch. 4 - Solve for x(t) in the system shown in Figure P4.5...Ch. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Calculate the exact response of each system of...Ch. 4 - Prob. 18PCh. 4 - Prob. 19PCh. 4 - For each of the second-order systems that follow,...Ch. 4 - MATLAB ML 21. Repeat Problem 20 using MATLAB. Have...Ch. 4 - GUI Tool GUIT
22. Use MATLAB’s LTI Viewer and...Ch. 4 - Prob. 23PCh. 4 - Find the transfer function of a second-order...Ch. 4 - For the system shown in Figure P4.7, do the...Ch. 4 - For the system shown in Figure P4.8, a step torque...Ch. 4 - Prob. 28PCh. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - State Space SS 38. A system is represented by the...Ch. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - State Space SS 41. Given the following system...Ch. 4 - State Space SS 42. Solve the following state...Ch. 4 - Prob. 43PCh. 4 - Prob. 44PCh. 4 - Prob. 46PCh. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 53PCh. 4 - Prob. 54PCh. 4 - A MOEMS (optical MEMS) is a MEMS (Micro...Ch. 4 - Prob. 56PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Prob. 63PCh. 4 - Prob. 67PCh. 4 - Figure P4.l6 shows the step response of an...Ch. 4 - Figure P4. I 7 shows the free-body diagrams for...Ch. 4 - Find an equation that relates 2% settling time to...Ch. 4 - Prob. 74PCh. 4 - Prob. 75PCh. 4 - 76. Find J and K in the rotational system shown in...Ch. 4 - Given the system shown in Figure P4.22, find the...Ch. 4 - Prob. 78PCh. 4 - Find M and K, shown in the system of Figure P4.24,...Ch. 4 - If vi(t) is a step voltage in the network shown in...Ch. 4 - Prob. 81PCh. 4 - Prob. 82PCh. 4 - For the circuit shown in Figure P4.26, find the...Ch. 4 - Prob. 84PCh. 4 - Prob. 86P
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- 2. For the system below, find the transfer function fromfi to x (driving point receptance) and from f. to ä, (driving point accelerance). What is the acceleration response of mass m, if m; = 2 kg, m; = 4 kg, k, = 40 N/m, k =100 N/m, and k; = 200 N/m, fi(t) = 20 cos(3t) N and f:(r) = 0? WW m, WW m Warrow_forward2) Assume F(t) is a step force input and the displacement is x(t) obtain the transfer function for the system shown below. Assume all initial conditions are zero. F(t) = 5 N, m = 0.2 kg, c = 0.3 N-s/m, kl = 5 N/m and k2=4 N/m. C 1 k1 k2 m www //// Warrow_forwardConsider the following mechanical system: k m +f b d²y(t) +b- dy(t) + ky(t) = f (t) m %3D dt? dt Obtain the state space model of the system with input f (t) and output y(t). Calculate the system matrices for m = 1, k = 1 and b = 2. Check the stability by using the second method of Lyapunov. 3.arrow_forward
- 25. For the system shown in Figure P4.7, do the follow- ing: [Section: 4.6] a. Find the transfer function G(s) = X(s)/F(s). b. Find $, om, %OS, T;, Тр, and T,. 28 N/m x(t) 3 kg f(t) 5 N-s/m FIGURE P4.7arrow_forward32. For the rotational mechanical system with gears shown in Figure P2.18, find the transfer function, G(s) = 03(s)/T(s). The gears have inertia and bear- ing friction as shown. [Section: 2.7] T(t) to |N1 小D N2 N3 2, D2 Jz, D3 03(1) N4 J4. D4 J5. D5 FIGURE P2.18 sairarrow_forwardAssume F(t) is a step force input and the displacement is x(t) obtain the transfer function for the system shown below. Assume all initial conditions are zero. F(t) = 5 N-s N, m = 0.2 kg, c = 0.3 N k1 = 5 and k2 = 4 S k2 Inarrow_forward
- 3m ä+4cx+2kx = 4cj+3ky For the system given above, obtain the state-space representation.arrow_forwardFind the transfer function,G(s)=Z1(s)/H(s) Find the state space model.arrow_forward38. Given the rotational system shown in Figure P2.24, find the transfer function, G(s) = 06(s)/01(s). [Section: 2.7]arrow_forward
- Consider the following state space system 1 B = 1 C =[1 0] D=[0] -5 -6 1- Check the controllability of the system. 2- Check the observability of the systemarrow_forwardQ5: Given the rotational system shown in below, find the transfer function G(s)= 01(s)/T(s) D K2 Please help ASAP. Pls show all steps and calculations. Make sure to find theta1(s)/T(s)arrow_forwarda) Determine the state space representation for the translational mechanical system shown in Figure Q4(a), where force, f(t) and displacement, x(t) are the input and output of the system respectively. Use these state variables in your answer. oooo K M -x(1) -ƒ(1)arrow_forward
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