Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 3, Problem 7P
Represent the system shown in Figure P3.7 in state space where the output is
![Chapter 3, Problem 7P, Represent the system shown in Figure P3.7 in state space where the output is L t . [Section: 3.41]](https://content.bartleby.com/tbms-images/9781118170519/Chapter-3/images/html_70519-3-7p_image002.jpg)
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3. In this problem, you are going to analyze the dynamics of a rotational mechanical system
shown in Figure below (this is also covered in Lecture Notes #3 of M. Mert Ankarali [1]).
In this system input the external torque t(t), and output is the angular velocity of the load
wL(t).
JR
WR
OR
K
JL
OL WL
T
DL
DR
The state-space representation of this system is provided in the Lecture Notes #3 [1].
Find the transfer function of the dynamical system.
Find another (minimal) state-space representation for the system.
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 system
on
of
nd
25. 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 , n, %OS, Ts, Tp, Tr, and Cfinal for a unit-step
input.
20 N/m
oooo
2 N-s/m
5 kg
x(1)
FIGURE P4.7
f(1)
Chapter 3 Solutions
Control Systems Engineering
Ch. 3 - Prob. 1RQCh. 3 - State an advantage of the transfer function...Ch. 3 - Define state variables.Ch. 3 - Define state.Ch. 3 - Define state vector.Ch. 3 - Define state space.Ch. 3 - What is required to represent a system in state...Ch. 3 - 8. An eighth-order system would be represented in...Ch. 3 - If the state equations are a system of first-order...Ch. 3 - Prob. 10RQ
Ch. 3 - What factors influence the choice of state...Ch. 3 - What is a convenient choice of state variables for...Ch. 3 - If an electrical network has three energy-storage...Ch. 3 - Prob. 14RQCh. 3 - Prob. 1PCh. 3 - Represent the electrical network shown in Figure...Ch. 3 - Prob. 3PCh. 3 - Represent the system shown in Figure P3.4 in state...Ch. 3 - Represent the rotational mechanical system shown...Ch. 3 - Represent the system shown in Figure P3.7 in state...Ch. 3 - 8. Show that the system of Figure 3.7 in the text...Ch. 3 - Find the state-space representation in...Ch. 3 - MATLAB ML 10. Repeat Problem 9 using MATLAB....Ch. 3 - For each system shown in Figure P3.9, write the...Ch. 3 - MATLAB ML
12. Repeat Problem 11 using MATLAB....Ch. 3 - 13. Represent the following transfer function in...Ch. 3 - Find the transfer function G(s) = Y(s)/R(s) for...Ch. 3 - MATLAB ML
15. Use MATLAB to find the transfer...Ch. 3 - 17. A missile in flight, as shown in Figure P3.10,...Ch. 3 - Given the dc servomotor and load shown in Figure...Ch. 3 - Prob. 20PCh. 3 - Prob. 23PCh. 3 - Experiments to identify precision grip dynamics...Ch. 3 - State-space representations are, in general, not...Ch. 3 - Figure P3.16 shows a schematic description of the...Ch. 3 - Prob. 28PCh. 3 - A single-pole oil cylinder valve contains a spool...Ch. 3 - Figure P3.17 shows a free-body diagram of an...Ch. 3 - 33. Parabolic trough collector. A transfer...
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- 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 snp-you tvavearrow_forwardFind: State-space representation Note: Output of mechanical system is X3(t) Given: M1=1 kg, M2=1 kg, M3=1 kg K1=1 N/m, K2=1 N/m Fv1=1 N-s/m, Fv2=1 N-s/m, Fv3=1 N-s/m, Fv4=1 N-s/marrow_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
- Explain the state space functionarrow_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_forwardFor the following state-space representation,define the:– State Vector– System Matrix– Feedforward Matrix– Input Matrix & Input Vector– Output Matrix & Output Vectorarrow_forward
- Q2 In the rotating system shown in Figure Q2. The torque T applied to the rotor and generate the output angular velocity, w. (a) Determine equations of motion system interm of angular displacement, 0. (b) By referring Q2(a), determine the state-space model of the system. Rotor T Figure Q2arrow_forward25. 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_forward3m ä+4cx+2kx = 4cj+3ky For the system given above, obtain the state-space representation.arrow_forward
- Represent the translational mechanical system shown in state space, where x3(t) is the output.arrow_forwardRepresent the system shown in Figure P3.7 in state space where the output is 01 (t). T(1) N1 = 30 2 N-m/rad 3 N-m-s/rad TON-m/rad N2= 300 N3 = 10 N4 = 100 OL(t) -- TTTT 200 N-m-s/rad FIGURE P3.7arrow_forward2. Assume a 2 DOF rigid body with a rigid bar, which is supported by a two-spring damper :3k4, m = supports. Inertia and length of the rigid body are I = 10kg and L= 4m. (a) Derive the mathematical model of the system in variable form (b) Write the state space representation of the above system. (c) k₁= k₂ = 800N.m and c₁ = C₂ = 350N.s/m Develop a simulink model and plot all the system response for input y = sin(wt), where w 1 rad = S (d) k₁ 400v, k₂ 800N.m and c₁ = 175N.s/m, c₂ 350N.s/m Develop a simulink model and plot all the system response for input y = sin(wt), where w = = 1 rad 8 - L/4 k₁,c m, I L/4 k₂,c y = sin wtarrow_forward
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