Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Textbook Question
Chapter 3, Problem 7RQ
What is required to represent a system in state space?
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Summarize five key steps involved in defining a
system using state-space approach.
1) a) Derive the mathematical model for the system shown below.
b) Find a state variable model (matrix form) for the system.
b) Determine state matrix, input matrix, and output matrix, when f (t) is defined as
the input and X2 is defined as output for the system.
(Here, both of the X1 and x2 , are time-dependent functions)
» f(t)
X1
X2
3,000 N
1,000 N
4,000
30 kg
20 kg
200 유
N.s
Find: 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/m
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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- Answer the following (words, not equations): a) State space analysis - what/why/how we do it b) Short period, Phugoid, Dutch roll, Roll, and Spiral - what do these collectively represent?arrow_forwardFind a state space representation of the network shown below when the output is the displacement on m Let my = 2 kg, m₁ = 4kg, F = 10 N, b₁ = 1 Ns/m, b2 = 2 Ns/m, k₁ = 2 N/m, and k2 = 4 N/m, Force of material placed in truck bed M Truck vehicle mass Shock absorber www www A Tirearrow_forwardMechanical Control Engg.arrow_forward
- Describe the concept of a transfer function in the context of system modeling. How is it used to represent a system's behavior?arrow_forwardk₁ B₁ Fs(t) ww k2 12 m B2 Figure 4: A translational system 2. Consider a translational system shown in Fig. 4. Answer the following questions. (a) Draw a linear graph and write down all the elemental equations. (Don't draw the normal tree yet.) (b) From the elemental equation you write down, identify three variables that can potentially serve as state variables and explain why. (c) Are these potential state variables independent of each other? If not, use either conti- nuity or compatibility equation to prove it. How would you choose your state variables? (d) Draw a normal tree to see if there is any dependent energy storage element. What are the state variables according to your normal tree? Are they consistent with the explanation in the Part (c)?arrow_forwardwhat is the solution?arrow_forward
- 1. Reduce the following differential equation to the state space equation form. a. y" (t) + 3y' (t) + 2y (t) = u(t) b. y" (t) = u(t) — b₁y' (t) — boy (t) c. 4y" (t) cos (t) y' (t) + sin (t) y (t) = u(t)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_forwardFind a state space representation for the network shown below when the output is the displacement at M3.arrow_forward
- Represent the translational mechanical system shown below in state space, where x3(t) is the output. State variables ニュ=X 3 = X2 Let -4 = X2 Es = X3 E6 = X3 x1(t) x2(t) x3(t) 1 N-sim 1 N-sim 1 Nim 1 Nim 1kg 1kg 1 kg J1 J2 J3 Fit)arrow_forwardRepresent the translational mechanical system shown in Figure P3.5 in state space, where x1(t) is the output. [Section: 3.4] x2(1) x3(1) M3 = 1 kg fv, = 1 N-s/m fv,= 1 N-s/m K1 = 1 N/m 000 M: = 2 kg + x1(1) f() -- K2 = 1 N/m M1 = 1 kg fv,= 1 N-s/m FIGURE P3.5arrow_forwardPlease solve the following question. Note that the second picture is the solution of the question from the book, I just want to know the steps to reach it.arrow_forward
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