By P.Jackel.

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This is expressed by the derivative-action time (rate time). Derivative-action time The derivative-action time Td is a measure for how much faster a PD controller compensates a change in the controlled variable than a pure P controller. A jump in the manipulated variable compensates a large part of the system deviation before a pure P controller would have reached this value. The P component therefore appears to respond earlier by a period equal to the rate time (see Fig. B1-14). xd y t System deviation xd t Td Td = derivative-action time Controller Manipulated variable y Two disadvantages result in the PD controller seldom being used.

Time response of a controller . 5 Mode of operation of various controller The proportional controller . . . . The integral-action controller . . . The PI controller . . . . . . The PD controller . . . . . . The PID controller . . . . . . 8 . . . . . . . . . . . . . . B1-12 B1-14 . . . . . . . . . . . B1-16 . B1-17 . B1-18 . B1-20 types . . . . . . . . . . . . . . . . . . . . . . . . . B1-21 B1-21 B1-23 B1-24 B1-25 B1-26 Summary .

The time response of the P controller in the ideal state is exactly the same as the input variable (see Fig. B1-11). xd y y0 x0 t System deviation xd t Manipulated variable y Controller The relationship of the manipulated variable to the system deviation is the proportional coefficient or the proportional gain. These are designated by xp, Kp or similar. These values can be set on a P controller. It determines how the manipulated variable is calculated from the system deviation. The proportional gain is calculated as: Kp = y0 / x0 Festo Didactic • Process Control System Fig.

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Monte Carlo Methods in Finance by P.Jackel.


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