Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 4, Problem 77P
Given the system shown in Figure P4.22, find the damping, D, to yield a 30% overshoot in output angular displacement for a step input in torque. [Section: 4.6]
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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
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Chapter 4 Solutions
Control Systems Engineering
Ch. 4 - Prob. 1RQCh. 4 - What does the performance specification for a...Ch. 4 - Prob. 3RQCh. 4 - In a system with an input and an output, what...Ch. 4 - Prob. 5RQCh. 4 - Prob. 6RQCh. 4 - 7. What is the difference between the natural...Ch. 4 - Prob. 8RQCh. 4 - Prob. 9RQCh. 4 - Prob. 10RQ
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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- 3. Consider the system shown below. The outputs of the system are the angular displacement of the upper gear (positive about the x-axis) and the Contact force between the upper and lower gear. Assume that the initial conditions for all state variables are zero and that the gears are massless. There are two inputs Ti(t) acting on the top gear and T₂(t) acting on the rightmost disk. If you let • 9₁ denote the state variable for the spring 92 denote the state variable for the rightmost disk. u₁ denote T₁. u₂ denote T₂. You should expect to get the following state space representation and 9= KR + 0₁ 0 LIR -1. 7/2 Ti(t) Jun 0:0⁰ 40² T₂(t) 03 Figure 3: System for problem 3 21 (a) Derive the state-space model (state equation and output equation) in vector form. (b) For the system parameters I = 8 kg m², k = 1 N m,b=2 N s m/rad, R₁ = 1 m, and R₂ = 3 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the ristic equation AS the system? iii. What are the values of the…arrow_forwardP4.7 A robot uses feedback to control the orientation of each joint axis. The load effect varies due to varying load objects and the extended position of the arm. The system will be deflected by the load carried in the gripper. Thus, the system may be represented by Figure P4.7 O, where the load torque is Ta (s) = D/s. Assume R(s) = 0 at the index position. (a) What is the effect of Ta(s) on Y(s)? (b) Determine the sensitivity of the closed loop to k2. (c) What is the steady-state error when R (s) = 1/s and Ta(s) = 0? Load disturbance T (s) R(s) Controller Y(s) Desired k2 Actual k1 joint angle joint angle s(TS + 1) kz + k4s Figure P4.7 Robot control system.arrow_forwardMECHANICAL VIBRATIONS TWO DEGREE OF FREEDOMarrow_forward
- does such a decomposition end up using more bandwidth. (This is an exa Consider the mechanical system shown in the figure below. Suppose the system input u is the velocity d₁, its output y is the velocity d2, and its states ar are the position d2 and velocity d2. Obtain a state-space model of the form i = Ar + Bu and y = Cr + Du describing the system. d₂ d₁ b m k₂arrow_forward1 / 1 Problem No. 1 1A. 100% + 1B. Consider the translational mechanical system shown in Figure P4.17. A 1-pound force, f(t), is applied at t = 0. If fy = 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] 70) 0000 31/1 10000 K FIGURE P4.17 Given the translational mechanical system of Figure P4.17, where K = 1 and f(1) is a unit step. find the values of M and ƒ, to yield a response with 17% overshoot and a settling time of 10 seconds. [Section: 4.6]arrow_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_forward
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