Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 3, Problem 10P
MATLAB ML
10. Repeat Problem 9 using MATLAB. [Section: 3.5]
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Homework
For the system shown in figure below, Find the range of K
for stable system.
R
K(s + 2)
C
s(s +5)(s² + 2s + 5)
II
Answer all questions below showing revelent calculations and working with explanation where necessary.
1.Create a mathematical model for the system shown.
2.Develop a transfer function for 0(s)/Qi(s), state the constants that you have used in your transfer function. [Hint: You would also need to derive Q(s)/Qi(s) to predict a theoretical value for the increase in rotational speed ] [Note: Omega, Q=Angular speed]
3. With the use of theoretical values, determine the theoretical increase in rotational speed expected for the water wheel when the inflow is increased by a step. This should be repeated for three different step input values. Show calculations and working throughout.
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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- If a system, * + 10x + 21x = 4f(t) is converted into a state-space model, what would be the state (A), input (B), and output (C) matrices? [where input = f (t) and output = x(t)] %3D A) A = | [-21 l, B = | and C = [0 1] В -10 1 B) A = 21 ol, B = and C = [1 0] %3D C) A = = Al and C = [1 0] В %3D -21 D) None of the abovearrow_forwardPage 8/5 Q4: (M4) LE Velocity: V [km/hr] Wavelength: L [m] M k y(t) Model Height: H [m] The figure above shows a model of a person riding a unicycle that contains a spring under its seat. The spring constant is k = 10,600 N/m. Assume that damping is minimal, the wheel of the unicycle has no mass and is not a spring, the unicyle always stays perfectly upright, and the person is represented by a rigid mass M = kg. a) When the unicycle is being ridden at speed V = 10 km/hr over the sinusoidal bumpy terrain shown above, with bump spacing L=0.6 m and bump height H 0.05 m, what will be the steady-state peak-to-peak amplitude of the motion y(t) [m] of the person riding the unicycle? b) Recalculate the steady-state peak-to-peak amplitude of the motion for 2.5, 5, and 20 km/hr. Will the rider have difficulty reaching speeds above 5 km/hr?arrow_forwardequations: 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_forward
- k₁ 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_forwardSolve this question using MATLAB Language.arrow_forwardMATLAB support with the following:arrow_forward
- a) Suspension system of a car. Finding the transfer function F₁(s) = Y(s)/R(t) and F₂ (s) = Q(s)/R(t), consider the initial conditions equal to zero. car chassis www K₂ M₂ 1 Tire M₁ K₁ B₁ y(t)= output q(t) r(t)= input Where [r, q, y] are positions, [k1, k2] are spring constants. [B₁] coefficient of viscous friction, [M₁, M₂] masses. b) Find the answer in time q(t) of the previous system. With the following Ns values: M₁ = 1 kg, M₂ = 0 kg, k₁ = 4 N/m, k₂ = 0 N/m, B₁. = 1 Ns/m, considered m a unit step input, that is, U(s) = 1/sarrow_forwardFor the mechanical translation system below, find the transfer function 0,/T and O2/T. Use the following values. K = 1+c D1 = 1 Jj = 4+a J2 = 3+b D2 = 5 where a = 3rd digit of your student number %3D = 7 = 5 b = 5th digit of your student number c = 7th digit of your student number For reference, the 1st digit of your student number is the leftmost number in your student number. Indicate your student number when solving problems. T(t) 0(t) 02(1), elel J2 D1 K D2 ON II ||||arrow_forwardFeedback & Control Systems State-Space Representation Write the state-space representation of the system below. Let the output of the mechanical system is x3 (t). 1 N-s/m x₁ (t) M3 = 1kg 1 N/m М1 -0000 1kg > X3 (t) 1 N-s/m 1 N/m oooo x₂ (t) M₂ 1kg 4 1 N-s/m² -1 N-s/m →f(t)arrow_forward
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