CONTROL SYSTEMS ENGINEERING - WILEYPLUS
7th Edition
ISBN: 9781119143277
Author: NISE
Publisher: WILEY
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Chapter 5, Problem 14P
For the system of Figure P5.14, find the value of K that yields 10% overshoot for a step input. [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)
Use MATLAB to obtain a state model for the following equations; obtain the expressions for
the matrices A, B, C, and D. In both cases, the input is f(t); the output: is y.
a. 5d³yd²y
+7.
b.
dy
+3
dt³ dt² dt
Y(s)
5
=
F(s) s² +7s+4
- +6y=f(t)
For the given close-loop system transfer function, determine its stability using Routh-Hurwitz Test for Stability.1. What is the stability of the system? (Stable, Unstable, Marginally Stable)
Chapter 5 Solutions
CONTROL SYSTEMS ENGINEERING - WILEYPLUS
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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- Problem 3. Find the transfer function C(s)/R(s) for the following block diagram using block diagram reduction: R(S) Gso G200 G G3()arrow_forwardReduce the block diagram to a single transfer function.arrow_forwardThis question asks for matrix form and NOT state space, but I don't understand what the difference between the two are.arrow_forward
- For the following state-space representation,define the:– State Vector– System Matrix– Feedforward Matrix– Input Matrix & Input Vector– Output Matrix & Output Vectorarrow_forwardUse the block diagram reduction method, find the transfer function, C(s)/R(s), of the system shown below. R(s) G1 G2 C(s) H2arrow_forwardFind the transfer function C(s)/R(s) by block-reduction technique.arrow_forward
- Get the input-output model Get the Transfer Function Get representation in State Variablesarrow_forwardReduce the block diagram shown in Figure below to a single transfer function, T(s) = C(s)/R(s) Use the block diagram reduction method.arrow_forwardDevelop a state space model for the transfer function s2 + 5s + 4 G1 (s) = s2 +7s + 12 What is the dimension of the minimal state space realization?arrow_forward
- Part A: Find the steady-state solution of the mechanical system shown below: k mu E m G(s) F(t) F(t) = F sin wt Part B: Sketch the root locus for the transfer function: Ks (s+ 4) (s + 3)(s + 1)arrow_forwardFind a state space representation for the network shown below when the output is the displacement at M3.arrow_forwardGiven 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_forward
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