Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 3, Problem 9RQ
If the state equations are a system of first-order differential equations whose solution yields the state variables, then the output equation performs what function?
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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.
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+3
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- +6y=f(t)
Mechanics of machines
QUESTION 4
Consider two degree of freedom of coupled pendulum with horizontal rod vibration system
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4.1- Determine differential equations of motion in matrix form using The equation of
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4.2- Develop state-space model.
Get representation in State Variables
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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- -Get the input-output model -Get the Transfer Function -Get representation in State Variablesarrow_forwardThis question asks for matrix form and NOT state space, but I don't understand what the difference between the two are.arrow_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_forward
- Evaluate the following state-space system provided to find the corresponding transfer function G(s) = Y(s) / U(s)arrow_forward1. 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_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
- Derive the state-space representation of the following system where the input is f(t) and the outputs isthe y1 =X1, y2=X2, y3=X3arrow_forward(b) The response to a unit step input (applied at time t = 0 s) of a system is shown in Figure Q2, determine the transfer function of this system from the step response graph. Amplitude 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 Amplitude 5 Step input of 3 units was applied to a system and the response of this system is shown in Figure Q2.2. Determine the transfer function of this system. 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 o Step Response 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Time (sec) Figure Q2 Step response Step Response 2 Time (seconds) 3arrow_forward2. Consider the state equation x1 1 20 x1 d x2 = 0 10 x2 dt x3 001 x3 where x1, x2 and 23 are state variables. Please answer the following questions. (a) The state matrix (4) 1 20 A = 0 1 0 (5) 0 0 1 has three-fold eigenvalues with \₁ = = A2 A3 1. Find all independent eigenvectors corresponding to this eigenvalue. (b) Find the modal matrix M associated with the state matrix A. Does M-1 AM lead to a Jordan form or not? Hint: The modal matrix M turns out to be a diagonal matrix. For a diagonal matrix, its inverse is given by a 00 0b0 -1 1/a 0 0 = 0 1/b 0 00 с 0 0 1/c 1 (6) (c) Find the state transition matrix (t). (d) Determine the stability of the system. Please justify your answer.arrow_forward
- For the following state-space representation,define the:– State Vector– System Matrix– Feedforward Matrix– Input Matrix & Input Vector– Output Matrix & Output Vectorarrow_forwardExample For the system shown, the equations of motion are given by m₁x₁ + cx₁ + kx₁ Cx₂ = 0 m₂X₂ + CX₂ cx1 = F Use state space method to reduce the equation of motion into a system of 1st order differential equations. www m₁ m₂ farrow_forwardConsider the following mechanical system: k m +f b d²y(t) +b- dy(t) + ky(t) = f (t) m %3D dt? dt Obtain the state space model of the system with input f (t) and output y(t). Calculate the system matrices for m = 1, k = 1 and b = 2. Check the stability by using the second method of Lyapunov. 3.arrow_forward
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