Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Textbook Question
Chapter 3, Problem 10P
MATLAB ML
10. Repeat Problem 9 using MATLAB. [Section: 3.5]
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I am trying to convert orbital elements to the state vector in MATLAB. My orbital elements are as follows
a = 6731;
ecc = 0.01;
inc = 142.461;
raan = 155.9325;
argp = 321.0439;
f = 145.8291;
After transforming them I get :
x = 3898.6;
y = 3898.6;
z = 3957;
vx = 5.9771;
vy = -4.5575;
vz = -1.3245;
I am wondering if the transformation is done correctly. Because x, y, and z are defined from earth's radius to the spacecraft, right? If that is the case then x, y, and z should have values greater than the earth's radius. Is my assumption correct?
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.
O 1::09
O [Template] Ho...
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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
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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- The state transmission matrix of the system whose state-space [3²₁] = [0²2 J]+[]u a. b. C. O 0 cosh at c. Ø(t) = [ a sinh at/a cosh a. ¢(t) = [sinhat cosh at a. Ø(t) = [a cosh at sinh at b. Ø(t) = [a [a cosh at a sinh at sinhat cosh at] sinhat/a] cosh at [/a] sinh at/a] a cosh at sinh at att cosh atarrow_forward3. 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.arrow_forwardIf 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_forward
- I need help with my MATLAB code. I am trying to propagte 10 different initial state vectors. In the end, I get 1 state matrix. I need to get 10 different state matrices for the 10 different initial state vectors. How do I store each state matrices seperately in MATLAB? R = 6378.0; %km mu = 398600.4415; %km^3/s^2 r = [7000, 0, 0, 0, 7.5, 0; 7100, 0, 0, 0, 7.6, 0; 7200, 0, 0, 0, 7.4, 0; 7300, 0, 0, 0, 7.3, 0; 7400, 0, 0, 0, 7.2, 0; 7500, 0, 0, 0, 7.1, 0; 7600, 0, 0, 0, 7.0, 0; 7700, 0, 0, 0, 6.9, 0; 7800, 0, 0, 0, 6.8, 0; 7900, 0, 0, 0, 6.7, 0]; % Initialize cell array to store results for each initial state results = cell(size(r, 1), 1); for i = 1:length(r) % Finding Period T_orbit = 2 * pi * sqrt((norm(r(i, :))^3) / mu); time_span = [0, T_orbit]; state_init = r(i, :); % Numerical integration using ODE solver options = odeset('RelTol', 1e-12, 'AbsTol', 1e-12); [t, state] = ode45(@(t, state) orbital_dynamics(t, state, mu), time_span, state_init, options); end %%…arrow_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_forward1arrow_forward
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