Poles and Zeros analyze the performance of a system and check the stability. The values of Poles and Zeros control the working of a system. Usually the numbers of Poles and Zeros are equal in a system and in some cases number of Poles is greater. Poles are the roots of the denominator of a transfer function. Let us take a simple transfer function as an example:.
Generally, the number of Poles is equal or greater than Zeros. When s approached a pole the value of denominator becomes Zero making the value of transfer function reach infinity.
To determine the response, a system the location of Poles is analyze along with the values of real and imaginary parts of each pole. Real part determines the exponential and imaginary part determines sinusoidal values.
Similar to Poles, Zeros are the roots of nominator of a transfer function. The number of Zeros is lesser or equal to the Poles. Zeros mean that the output at those frequencies is zero. Let us have a look at the differences between Poles and Zeros and their effects for a given function:. The frequencies that turn nominator or denominator zero are called zero and poles of a transfer function respectively.
They determine the stability and working of a system. Here, I have summed up the series of tutorials regarding control systems. As s approaches a zero, the numerator of the transfer function and therefore the transfer function itself approaches the value 0. When s approaches a pole, the denominator of the transfer function approaches zero, and the value of the transfer function approaches infinity.
An output value of infinity should raise an alarm bell for people who are familiar with BIBO stability. We will discuss this later. As we have seen above, the locations of the poles, and the values of the real and imaginary parts of the pole determine the response of the system.
Real parts correspond to exponentials, and imaginary parts correspond to sinusoidal values. Addition of poles to the transfer function has the effect of pulling the root locus to the right, making the system less stable. Addition of zeros to the transfer function has the effect of pulling the root locus to the left, making the system more stable. More information on second order systems can be found here. More damping has the effect of less percent overshoot, and slower settling time.
Damping is the inherent ability of the system to oppose the oscillatory nature of the system's transient response. Larger values of damping coefficient or damping factor produces transient responses with lesser oscillatory nature. Control Systems. From Wikibooks, open books for an open world. There is 1 pending change awaiting review. The Wikibook of: Control Systems. The polynomial order of a function is the value of the highest exponent in the polynomial.
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