Test Stability using Routh Stability Method

In summary, for a control system with G(s)H(s) = \frac{1}{s^{2}*(s+\alpha)}, the equation 1 + G(s)H(s) = 0 indicates that the system is unstable and has at least one root in the RHP. To find the value of \alpha for which the system can be classified as critically stable, the Routh algorithm does not need to be used.
  • #1
mym786
11
0

Homework Statement



For a control system that has G(s)H(s) = [itex]\frac{1}{s^{2}*(s+\alpha)}[/itex]

Homework Equations



1 + G(s)H(s) = 0

The Attempt at a Solution



Exam question i messed up . I really need to know the answer.
 
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  • #2
mym786 said:

Homework Statement



For a control system that has G(s)H(s) = [itex]\frac{1}{s^{2}*(s+\alpha)}[/itex]


Homework Equations



1 + G(s)H(s) = 0

The Attempt at a Solution



Exam question i messed up . I really need to know the answer.

i + G(s)H(s) = 0 means:
[tex]s^3+\alpha s^2 + 1 = 0[/tex]
Since the polynomial is incomplete (there is no term in [tex]s^1[/tex]) there is at least one root in the RHP and the system is unstable. No need to use Routh algorithm.
 
  • #3
I forgot one more thing. It also says find the value of [itex]\alpha[/itex] for which the system can be classified in the critically stable state.
 

What is the Routh Stability Method?

The Routh Stability Method is a mathematical technique used to analyze the stability of a control system. It is based on the location of the roots of a characteristic equation, which can determine whether a system is stable, marginally stable, or unstable.

How does the Routh Stability Method work?

The Routh Stability Method involves constructing a table using the coefficients of the characteristic equation. The table is then used to determine the number of roots in the right half-plane, which indicates instability, and the number of roots on the imaginary axis, which indicates marginal stability. A system is considered stable if all of the roots are in the left half-plane.

What are the advantages of using the Routh Stability Method?

The Routh Stability Method is a quick and efficient way to determine the stability of a control system. It does not require the actual roots of the characteristic equation to be calculated, which can be time-consuming for complex systems. It also provides a clear visual representation of the stability of a system through the use of the Routh array.

What are the limitations of the Routh Stability Method?

The Routh Stability Method is limited to systems with polynomial transfer functions. It also cannot determine the stability of systems with repeated roots or roots on the imaginary axis. In addition, the method can only determine the number of roots in the right half-plane, but not their exact values.

How is the Routh Stability Method used in practice?

The Routh Stability Method is often used in control system design to ensure the stability of a system. It is also used in the analysis of complex systems to identify potential stability issues. In addition, the Routh Stability Method is commonly used in the aerospace and automotive industries to design stable control systems for vehicles and aircraft.

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