System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 5, Problem 5.17P
Put the following model in standard state-variable form and obtain the expressions for the matrices A, B, C, and D. The output ¡s x.
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Given the following state-variable models, obtain the expressions for the matrices A, B, C, and D for the
given inputs and outputs.
The output is x₁; the inputs are 4₁ and 42.
X₁ = -9x1 +5x2 + 3u1
2-9x2 +2u2
Consider the system shown in the figure below. Assume that when z is zero, that the spring is at its unstretched length. That is, the restoring force in the
spring only develops when z, (the figure is a little misleading here). Note that z, is defined as positive to the left and zg is defined as positive downwards.
Syntax notes: when entering your responses, use x[1] for z1and x2] for z2. m[1] for m1. m[2] for mg, and g for gravity. Use T for the tension in the rope.
You can use the loupimagnifying glass to check that what you entered is what you intended.
Kinematics
The change in z is related to the change in zgsince they are part of the same string. What is the kinematic relationship between the two of them?
21- -2x(2]
Kinetic Energy
Write the total system kinetic energy. (ie write it in terms of both z1and zgand their velocities). Use diffio(1]t).) for ż and diffx(2]t).1) for ż
KE = (12)m[1]*(difix[1]{t),f)^2+(1/2}*m[2]*(diff(x{2]{t),f)^2
Now use your kinematic relationship to write…
2. In the following electrical circuit system, where R is the resistance, L is the
inductance, and C is the capacitance. The input variable is the applied voltage
the output variable is the voltage Find the transfer function of the
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İR
OR
10
Chapter 5 Solutions
System Dynamics
Ch. 5 - Prob. 5.1PCh. 5 - Obtain the transfer function Xs/Fs from the block...Ch. 5 - Obtain the transfer function Xs/Fs from the block...Ch. 5 - Draw a block diagram for the following equation....Ch. 5 - Draw a block diagram for the following model. The...Ch. 5 - Referring to Figure P5.6, derive the expressions...Ch. 5 - Prob. 5.7PCh. 5 - Prob. 5.10PCh. 5 - Obtain the state model for the reduced-form model...Ch. 5 - Obtain the state model for the reduced-form model...
Ch. 5 - Prob. 5.13PCh. 5 - Obtain the state model for the transfer-function...Ch. 5 - Obtain the state model for the two-mass system...Ch. 5 - Prob. 5.16PCh. 5 - Put the following model in standard state-variable...Ch. 5 - Given the state-variable model...Ch. 5 - Given the following state-variable models, obtain...Ch. 5 - Prob. 5.20PCh. 5 - The transfer function of a certain system is...Ch. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Use MATLAB to obtain a state model for the...Ch. 5 - Use MATLAB to obtain a state-variable model for...
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- The figure shows a function generator linkage in which the motion of rocker 2 corresponds to x and the motion of rocker 4 to the function y=f(x). Use three precision points and chebychev spacing and synthesize the linkage to generate the following function. y = 4cos (-x) 0arrow_forwardDetermine if the system is consistent or inconsistent. Justify your answer and find all solutions to the system of linear equations. Justification should be written on your solution paper. Transform the matrix into ROW ECHELON FORM (REF) using row operations. 2x +8y+ 6z = 20 4x+2y-2z =-2 3x-y+z = 11 Enter final answer: (x, y, z) =(arrow_forwardThe following EOMs describe the behavior of a dynamic system ( à = -K₁a + din b = K₁a - K₂b K₂b - K3c = ċ Assume K₁, K2, K3 are constant, and din is the input. A. How many states does this system of equations have, and why? B. Write the state space form of the system as x = Ax + Bu. You will have to define your state vector and input vector. Clearly identify the matrices. C. Assume the desired output of the system is the vector y that consists of a and K₂b as individual elements. Write the output equation in the form of y = Cx + Du. Clearly identify the matrices.arrow_forward2.9. The following mechanical system may be used to measure acceleration. Construct the block diagram model and find the transfer functions and . FF K, K2 X2 FIGURE 2-9arrow_forwardThe values of p and h which renders (makes) the following set of equations dynamically and statically decoupled are, respectively. k,+k2 5 p+4 x1 = 0, X2 7 h+1 + [7h+1 J+e 5 p+4 J+e h= -0.214 and p = -1.76 h = -0.143 and p= -0.8 h = -0.281 and p= -1.2 h = -0.081 and p = -0.536arrow_forwardپشم را 2 Pk k Düngür 3 F4 Lo S Find the face FL that develops in the system. Show derivation (using matrix analysis) in a step-by-step fashion.arrow_forward1. write the transfer function of the differential equation. d'y 2dy2 3dy 3dx3 + dt4 X dt3 a.- + + 4y = dt² dt + 4xarrow_forward200 OOOD O Subject Date: Q1/Find the domain P the function 2. Y3DIn(2x+X-6-6)arrow_forwardFind the transformation matrix for the following transformations: 1) Rotate 45° about Xo-axis. (Xo, Yo, Zo) → (X₁, Y₁, Z₁); 2) Followed by a rotation of 90° about Xo-axis. (X₁, Y₁, Z₁)→ (X₂, Y₂, Z₂); 3) Followed by a rotation of 60° about Y₂-axis. (X₂, X2, Z2)→ (X3, Y, Z3); 4) Followed by a rotation of 60° about Z₂-axis. (X3, Y3, Z3) → (X, Y4, Z4). Note: give final answer in matrix multiplication form, no need to write out the elements of the matrices or multiply the matrices out. URALLY AND AFICIALLY LGarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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