Question

a. How does increasing Kp reduce the steady state error of a proportional controller? b. What are some benefits and challenges associated with using an integral controller? C. Derivative controllers can be impacted by small amounts of noise on the signal more than either proportional or integral controllers. Why? d. There is an alternative used in implementing a derivative controller in PID controllers which is less susceptible to high frequency noise. Describe it.

Answer 1

a.)Sol. On increasing Kp the rise time of the system reduces making the system less oscillatory and more stable thereby also reducing the steady state error.Therefore, this is the reason that by increasing Kp the steady state error of a proportional controller reduces.

b.)Sol. The most important benefit of using an integral controller is the elimination of offset error which can't be reduced in case of using a proportional controller and one of the major drawback or challange of Integral Controller is that the integral controller tends to increase the oscillatory nature of the output response thereby making it somewhat unstable.

c.)Sol. The derivative controller is affected much more by noise compared to the proportional and integral controller because the derivative action futher extrapolates the noise or we can say that icreases the noise in a much larger scale compared to the other proportional and integral controllers.Therefore, this is the reason why derivative controller is impacted much by a small amount of noise also.

d.)Sol. When the time constant of the system is less than 1/5 times of the derivative time constant then the derivative controller can be implemented in PID controllers which is less susceptible to the high frequency noise.