Addition of zeros in a transfer function causesa)lag compensatorb)lead...
Pole-zero plot for lead and lag compensators are shown below.
Since zero is close to origin in a lead compensator, therefore addition of zero in a transfer function will cause lead compensator.
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Addition of zeros in a transfer function causesa)lag compensatorb)lead...
Introduction:
In control systems, compensators are used to improve the performance and stability of the system. They are added to the control system to modify the transfer function of the system. The transfer function represents the relationship between the input and output of the system.
Explanation:
When we add zeros to a transfer function, it affects the phase and magnitude of the transfer function. Depending on the location of the zeros, it can either increase or decrease the phase and magnitude of the transfer function. In this case, when zeros are added to the transfer function, it causes a lead compensator.
Lead Compensator:
A lead compensator is a type of compensator that improves the transient response of the system. It increases the system's stability and reduces the settling time. A lead compensator adds a pole and zero to the transfer function. The zero is added at a higher frequency than the pole, which introduces phase lead. This phase lead helps in reducing the phase lag and improves the overall system response.
Effect of Adding Zeros:
When zeros are added to the transfer function, they contribute to the phase lead. This phase lead helps in improving the system response by reducing the phase lag. The phase lag affects the stability of the system and can lead to oscillations or instability. By adding zeros, the phase lag is reduced, resulting in a more stable and responsive system.
Adding zeros also affects the magnitude of the transfer function. Depending on the location and number of zeros added, it can increase or decrease the magnitude. In the case of a lead compensator, the zeros are added at a higher frequency, which increases the magnitude of the transfer function.
Conclusion:
In summary, the addition of zeros to a transfer function causes a lead compensator. This lead compensator improves the system response by reducing the phase lag and increasing the stability. Adding zeros at a higher frequency introduces phase lead, which helps in reducing the phase lag and improving the overall system performance.
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