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Stability in Z Plane: Example

The document provides two examples of analyzing stability in the z-plane of digital control systems. The first example finds the value of a digital compensator gain K that makes the system just unstable. It is determined that the system is marginally stable when K = 105.23 and 9.58. The second example determines that a system is stable when the closed loop gain K = 1, as the roots of the characteristic equation satisfy |Z1| = |Z2| < 1.

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Mustfa Ahmed
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206 views6 pages

Stability in Z Plane: Example

The document provides two examples of analyzing stability in the z-plane of digital control systems. The first example finds the value of a digital compensator gain K that makes the system just unstable. It is determined that the system is marginally stable when K = 105.23 and 9.58. The second example determines that a system is stable when the closed loop gain K = 1, as the roots of the characteristic equation satisfy |Z1| = |Z2| < 1.

Uploaded by

Mustfa Ahmed
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Lecture 8

Stability in Z plane
Example
Dr. Sadeq Al-Majidi

Dept. Of Electrical Engineering/ College


of Engineering/ Misan University
Control Engineering
Fourth Year
• Example 1 : Figure below shows the digital control system. Find the value of
the digital compensator gain K to make the system just unstable.

• Solution: K?

G(Z) =

• The characteristic equation of the system:

2
• Simplify:

• Now, the first row of jury's array:

• Condition 1 Q(1) ˃ 0

• The condition 1 is satisfied if K ˃ 1 (stable)


• Condition 2

3
• Hance, the system is marginally stable when the K =105.23 and 9.58

4
Example 2: Determine the closed loop stability of the system shown in
Figure below when K = 1?

Solution:

Since H(S)= 1

5
We know that the characteristics equation is 1 + G(z) = 0

Since |Z1| = |Z2| < 1, the system is stable.

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