PID PARAMETERS USE OF ONLY TWO FREQUENCIES

Let us begin by rewriting the loss function in Elquation (6.29) in the following 

We now focus our attention on the Y jw) function. Note that from Equation (6.35) the frequency domain error between the desired open-loop frequency response Goiijw) and the actual open-loop frequency response G olijw) = C jw)G jw) is zero for all w if 

Equations (6.41) and (6.42) indicate that the graph of the real part of Y(jw) versus should behave like a straight line with slope -/ 2 and intercept 

Through the next two examples, we examine imaginary parts of the Y jw) function behave as a two different processes. 

We let ar = 1 and therefore t =. Then the desired closed-loop transfer function from setpoint to the control signal is given by 

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