Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 5, Problem 16P
For the system of Figure P5.16, find the values of K1and K2to yield a peak time of 1 second and a settling time of 2 seconds for the closed-loop system’s step response. (Section: 5.3]
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Question 5:
A model for a single joint of a robotic manipulator is shown in Figure below. The usual notation is used.
The gear inertia is neglected and the gear reduction ratio is taken as 1:r (Note: r < 1).
a) Draw a linear graph for the model, assuming that no external (load) torque is present at the robot
arm.
b) Using the linear graph derive a state model for this system. The input is the motor magnetic torque
Tm and the output is the angular speed o, of the robot arm. What is the order of the system?
Jm
m
(viscous)
1:r
Motor
Robot Arm
Gear Box
(Light)
Q5: For the following block diagram find the
(control ratio C(s)/R(s
CLO
Hy
1. 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
0000
Chapter 5 Solutions
Control Systems Engineering
Ch. 5 - Prob. 1RQCh. 5 - Name three basic forms for interconnecting...Ch. 5 - For each of the forms in Question 2, state...Ch. 5 - Besides knowing the basic forms as discussed in...Ch. 5 - For a simple, second-order feedback control system...Ch. 5 - Prob. 6RQCh. 5 - Prob. 7RQCh. 5 - How are summing junctions shown on a signal-flow...Ch. 5 - If a forward path touched all closed loops, what...Ch. 5 - Name five representations of systems in state...
Ch. 5 - Prob. 11RQCh. 5 - Which form of the state-space representation leads...Ch. 5 - When the system matrix is diagonal, what...Ch. 5 - What terms lie along the diagonal for a system...Ch. 5 - Prob. 15RQCh. 5 - Prob. 16RQCh. 5 - For what kind of system would you use the observer...Ch. 5 - Describe state-vector transformations from the...Ch. 5 - Prob. 19RQCh. 5 - Prob. 20RQCh. 5 - Prob. 21RQCh. 5 - Find the closed-loop transfer function, T(s) =...Ch. 5 - Find the equivalent transfer function, T(s) =...Ch. 5 - Reduce the system shown in Figure P5.4 to a single...Ch. 5 - Reduce the block diagram shown in Figure P5.6 to a...Ch. 5 - Find the unity feedback system that is equivalent...Ch. 5 - 8. Given the block diagram of a system shown in...Ch. 5 - 9. Reduce the block diagram shown in Figure P5.9...Ch. 5 - Reduce the block diagram shown in Figure P5.10 to...Ch. 5 - 11. For the system shown in Figure P5.11, find the...Ch. 5 - 12. For the system shown in Figure P5.12, find the...Ch. 5 - Prob. 13PCh. 5 - For the system of Figure P5.14, find the value of...Ch. 5 - 15. For the system shown in Figure P5.15, find K...Ch. 5 - For the system of Figure P5.16, find the values of...Ch. 5 - Find the following for the system shown in Figure...Ch. 5 - 18. For the system shown in Figure P5.18, find ,...Ch. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - Find the transfer function G(s) = Eo(s)/T(s) for...Ch. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - State Space SS
24. Given the system below, draw a...Ch. 5 - Prob. 25PCh. 5 - Using Mason’s rule, find the transfer function,...Ch. 5 - Using Mason’s rule, find the transfer function,...Ch. 5 - Prob. 28PCh. 5 - Use block diagram reduction to find the transfer...Ch. 5 - State Space SS 30. Represent the following systems...Ch. 5 - Prob. 31PCh. 5 - State Space SS 32. Repeat Problem 31 and represent...Ch. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Repeat Problem 34 for the system shown in Figure...Ch. 5 - Prob. 37PCh. 5 - State Space SS 38. Consider the rotational...Ch. 5 - Prob. 40PCh. 5 - Prob. 41PCh. 5 - State Space SS
42. Consider the subsystems shown...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - State Space SS
45. Diagonalize the following...Ch. 5 - Prob. 46PCh. 5 - Prob. 48PCh. 5 - Prob. 51PCh. 5 - Figure P5.33 shows a noninverting operational...Ch. 5 - Figure P5.34 shows the diagram of au inverting...Ch. 5 - Prob. 54PCh. 5 - A car active suspension system adds an active...Ch. 5 - Prob. 58PCh. 5 - Prob. 60PCh. 5 - Some medical procedures require the insertion of a...Ch. 5 - Prob. 62PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - The purpose of an Automatic Voltage Regulator is...Ch. 5 - 68. Integrated circuits are manufactured through a...Ch. 5 - Prob. 69PCh. 5 - Prob. 72PCh. 5 - Prob. 73PCh. 5 - Assume ideal operational amplifiers in the circuit...Ch. 5 - Parabolic trough collector. Effective controller...
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- can i get help for B only.arrow_forwarddoes 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_forwardMechanics of machines QUESTION 4 Consider two degree of freedom of coupled pendulum with horizontal rod vibration system are shown in figure 4. MA KG. oooo MB BAW a Figure 4 k d L 4.1- Determine differential equations of motion in matrix form using The equation of equation with, and ß as generalized coordinates; 4.2- Develop state-space model.arrow_forward
- Given a state space model [1 1 + 0 u -1 -2 y = [1 1 0] with input u and output y. a). Derive the transfer function representation. b). Derive the differential equations representation. c). Compute the response y(t) with step control input u(t) = 1(t) and zero initial condition. d). and initial condition r(0) = [11 0]". Compute the state response r(t) with control input u(t) = 1(t)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 fv, fit), K3 M K2 M2 0000arrow_forwardPlease solve this for me! Thanks!arrow_forward
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