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We know that a system must be stable if all of the closed loop poles are located exclusively in the LHP (of the s-plane). As a means of determining this numerically on paper, one way this can be achieved is through the use of a Routh array. For the system below with transfer function $Y(s)/X(s)$, complete the following questions: $frac{Y(s)}{X(s)} = frac{s + 1.39}{10s^4 + 4s^3 + 2s^2 + 4s - 8}$ a) Using a Routh Array, confirm if the system is either stable, critically stable, or unstable. b) State the locations (LHP, IA, or RHP) of all system poles ($s_1, s_2, s_3, and s_4$). c) Using MATLAB, verify your answer to part (b) by using the function exttt{pzplot(sys)}. Note: for MATLAB questions, you must complete the work on a computer and have the tutor check your results and sign your group of two off, once all MATLAB questions for the tutorial are completed. No written answers for submission are required for any MATLAB questions in this course.

          We know that a system must be stable if all of the closed loop poles are located exclusively in the LHP (of the s-plane). As a means of determining this numerically on paper, one way this can be achieved is through the use of a Routh array. For the system below with transfer function $Y(s)/X(s)$, complete the following questions:

$frac{Y(s)}{X(s)} = frac{s + 1.39}{10s^4 + 4s^3 + 2s^2 + 4s - 8}$

a) Using a Routh Array, confirm if the system is either stable, critically stable, or unstable.
b) State the locations (LHP, IA, or RHP) of all system poles ($s_1, s_2, s_3, and s_4$).
c) Using MATLAB, verify your answer to part (b) by using the function 	exttt{pzplot(sys)}.

Note: for MATLAB questions, you must complete the work on a computer and have the tutor check your results and sign your group of two off, once all MATLAB questions for the tutorial are completed. No written answers for submission are required for any MATLAB questions in this course.
        
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We know that a system must be stable if all of the closed loop poles are located exclusively in the LHP (of the s-plane). As a means of determining this numerically on paper, one way this can be achieved is through the use of a Routh array. For the system below with transfer function Y(s)/X(s), complete the following questions:

fracY(s)X(s) = fracs + 1.3910s^4 + 4s^3 + 2s^2 + 4s - 8

a) Using a Routh Array, confirm if the system is either stable, critically stable, or unstable.
b) State the locations (LHP, IA, or RHP) of all system poles (s1, s2, s3, and s4).
c) Using MATLAB, verify your answer to part (b) by using the function 	extttpzplot(sys).

Note: for MATLAB questions, you must complete the work on a computer and have the tutor check your results and sign your group of two off, once all MATLAB questions for the tutorial are completed. No written answers for submission are required for any MATLAB questions in this course.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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We know that a system must be stable if all of the closed loop poles are located exclusively in the LHP (of the s-plane). As a means of determining this numerically on paper, one way this can be achieved is through the use of a Routh array. For the system below with transfer function Y(s)/X(s), complete the following questions: Y(s)/X(s) = (s + 1.39) / (10s^4 + 4s^3 + 2s^2 + 4s - 8) a) Using a Routh Array, confirm if the system is either stable, critically stable, or unstable. b) State the locations (LHP, IA, or RHP) of all system poles (s1, s2, s3, and s4). c) Using MATLAB, verify your answer to part (b) by using the function pzplot(sys). Note: for MATLAB questions, you must complete the work on a computer and have the tutor check your results and sign your group of two off, once all MATLAB questions for the tutorial are completed. No written answers for submission are required for any MATLAB questions in this course.
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Transcript

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00:03 So here the transfer function given in the question will be in terms of r of s divided by x of s is equal to 5 plus 1 .39 divided by 10 s power 4 plus 4 s cube plus 2 s square plus 4 s minus 8.
00:31 So root array for stability analysis will be, that is, the characteristic polynomials in terms of the denominator, 10 s power 4 plus 4 s cube plus 2 s square plus 4s minus 8.
00:51 We will be having it in terms of s4, s3, s2, s1 and s, it will be in terms of s4, s3, s2, s1 and s, it will be in terms of 10, 4, 4, 4, minus 8, 0 and epsilon which is very small.
01:11 So the concern polynomial will be in terms of 2, 4, minus 8.
01:20 The balance concept will be nil values...
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