CONTROL SYSTEMS ENGINEERING
7th Edition
ISBN: 9781119185666
Author: NISE
Publisher: WILEY
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Textbook Question
Chapter 6, Problem 35P
For the system shown in Figure P6.8, find the value of gain, K, that will make the system oscillate. Also, find the frequency of oscillation. [Section: 6.4]
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3m ä+4cx+2kx = 4cj+3ky
For the system given above, obtain the
state-space representation.
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
Consider
in Figure
1 = 0. Iff,
the translational mechanical system shown
P4.17. A 1-pound force, f(t), is applied at
1, find K and M such that the response
is characterized by a 4-second settling time and a
1-second peak time. Also, what is the resulting
percent overshoot? [Section: 4.6]
1+
270
K
Chapter 6 Solutions
CONTROL SYSTEMS ENGINEERING
Ch. 6 - Prob. 1RQCh. 6 - Prob. 2RQCh. 6 - What would happen to a physical system chat...Ch. 6 - Why are marginally stable systems considered...Ch. 6 - Prob. 5RQCh. 6 - Prob. 6RQCh. 6 - Prob. 7RQCh. 6 - Prob. 8RQCh. 6 - Prob. 9RQCh. 6 - Why do we sometimes multiply a row of a Routh...
Ch. 6 - Prob. 11RQCh. 6 - Prob. 12RQCh. 6 - 13. Does the presence of an entire row of zeros...Ch. 6 - Prob. 14RQCh. 6 - Prob. 15RQCh. 6 - Prob. 16RQCh. 6 - Tell how many roots of the following polynomial...Ch. 6 - Tell how many roots of the following polynomial...Ch. 6 - Using the Routh table, tell how many poles of the...Ch. 6 - Prob. 4PCh. 6 - Determine how many closed-loop poles lie in the...Ch. 6 - Determine how many closed-loop poles lie in the...Ch. 6 - MATLAB ML 7. Use MATLAB to find the pole location...Ch. 6 - Symbolic Math SM 8. Use MATLAB and the Symbolic...Ch. 6 - Determine whether the unity feedback system of...Ch. 6 - Use MATLAB to find the pole locations for the...Ch. 6 - Consider the unity feedback system of Figure P6.3...Ch. 6 - In the system of Figure P6.3, let Gs=Ks+1ss2s+3...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Using the Routh-Hurwitz criterion and the unity...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Repeat Problem 15 using MATLAB.Ch. 6 - Prob. 17PCh. 6 - For the system of Figure P6.4, tell how many...Ch. 6 - Using the Routh-Hurwitz criterion, tell how many...Ch. 6 - Determine if the unity feedback system of Figure...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - In the system of Figure P6.3, let Gs=Ksassb Find...Ch. 6 - For the unity feedback system of Figure P63 with...Ch. 6 - Find the range of K for stability for the unity...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - find the range of K for stability. [Section: 6.41]...Ch. 6 - Find the range of gain, K, to ensure stability in...Ch. 6 - Using the Routh-Hurwitz criterion, find the value...Ch. 6 - Use the Routh-Hurwitz criterion to find the range...Ch. 6 - Prob. 32PCh. 6 - Given the unity feedback system of Figure P63 with...Ch. 6 - Repeat Problem 33 for [Section: 6.4]...Ch. 6 - For the system shown in Figure P6.8, find the...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Using the Routh-Hurwitz criterion and the unity...Ch. 6 - Find the range of K to keep the system shown in...Ch. 6 - Prob. 43PCh. 6 - The closed-loop transfer function of a system is...Ch. 6 - Prob. 45PCh. 6 - Prob. 46PCh. 6 - An interval polynomial is of the form...Ch. 6 - A linearized model of a torque-controlled crane...Ch. 6 - The read/write head assembly arm of a computer...Ch. 6 - A system is represented in state space as...Ch. 6 - State Space SS 52. The following system in state...Ch. 6 - Prob. 54PCh. 6 - A model for an airplane’s pitch loop is shown in...Ch. 6 - Prob. 57PCh. 6 - Prob. 58PCh. 6 - Prob. 59PCh. 6 - Prob. 60PCh. 6 - Prob. 61PCh. 6 - Look-ahead information can be used to...Ch. 6 - Prob. 63PCh. 6 - It has been shown (Pounds, 2011) that an unloaded...Ch. 6 - Prob. 65PCh. 6 - The system shown in Figure P6.16 has G1s=1/ss+2s+4...Ch. 6 - Prob. 67PCh. 6 - Prob. 68PCh. 6 - Hybrid vehicle. Figure P6.l8 shows the HEV system...Ch. 6 - Prob. 70P
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- a. For the translational mechanical system shown in Figure (3). 1. Write the mathematical model in a format of matrices. 2. Find the transfer function G(s) = a₁ (s)/T (s) where a is the acceleration. t 45²² +16,5 245+628²-2-05+96 M₁ = 8 kg 6 N-s/m f(t) 1 N/m 0000 4 N-s/m -x₂(1) M₂-3kg Frictionless 0000 15 N/m Frictionless Figure (3) Translational mechanical systemarrow_forwardFor the mechanical translation system below, find the force-voltage analogy and force-current analogy. Use the following values. K1 = 2 fv, = 1/2 M1 = 1+a %3D K2 = 2 fv2 = 4+b M2 = 5 K3 = 3+c fv3 = 3 a = 0 where a = 3rd digit of your student number %3D b = 5th digit of your student number b =7 C = 7th digit of your student number C = 5 For reference, the 1st digit of your student number is the leftmost number in your student number. Indicate your student number when solving problems.arrow_forward1. For the following mechanical translational system a. Write two differential equations of Order in s domain b. Change to time domain, and choose state variables c. Write the state equations, and the state matrix equation d. Write the output equation if x2 is the output Hint: the state variables will be x1, V1, X2, V2 X(1) fv, At) KI oll K3 M K2 0000 0000arrow_forward
- For the system shown in the figure. the system parameters, the length of the rod, l is 2 m, mass of the rigid rod, m is 7, and the stiffness of the springs, k, is the last two digits of 57. Derive the equation of motion, b) Find the transfer function between force input (F) and angular displacement (θ) of the system c) Find the step response of the system, and show time-domain characteristics of the system d) Find the frequency response function, and draw frequency response graphs, and draw bode diagrams, show frequency-domain characteristics.arrow_forwardA certain mass is driven by base excitation through a spring (Figure P4.13). Its parameter values are m = 100 kg, c = 1000 N * s/m, and k = 10,000 N/m. Determine its peak frequency w_p, it’s peak M_p, and its bandwidth.arrow_forward4. The pitch (angular motion) and bounce (up-down linear motion) of a motor vehicle is shown in Figure Q4. Write down the two equations of motion of the vehicle and hence find its frequency equation. (a) (b) Assume that the mass of the vehicle is 1,000 kg, radius of gyration is 0.9 m, spring stiffnesses kr = 18 kN/m and kr = 22 kN/m, distances Iı = 1.0 m and l2 = 1.5 m, determine the two natural frequencies and mode shapes of the system. Bounce Pitch C.G.I Figure Q4arrow_forward
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