Solved Problems

Category: Stability

Solved problems on stability of control systems using Routh stability criterion

Stability Analysis of a First-Order System with Proportional Control – Bode Plot

Let’s analyze the stability of a first-order system with a proportional controller using Bode Plot method. The process has a time constant of 10 seconds, and the proportional controller gain is $K_p$ .

The transfer function of the process under control is:

$P(s) = \frac{1}{10s + 1}$

The transfer function of the open-loop system is:
(more…)

January 1, 2025
Stability using Routh Stability Criterion

Determine the stability of the system whose characteristics equation is:

$a(s) = 2s^5 + 3s^4 + 2s^3 + s^2 + 2s + 2$ .

Solution

All coefficients are positive and non-zero; therefore, the necessary condition for stability is satisfied. Let’s write the Routh array:

$\begin{array}{l | c c c} s^5 & 2 & 2 & 2 \\ s^4 & 3 & 1 & 2 \\ s^3 & & & \\ s^2 & & & \\ s^1 & & & \\ s^0 & & &\end{array}$
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September 30, 2014