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# lec13_print - Dynamics of Commercial Controllers Srinivas...

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Dynamics of Commercial Controllers Srinivas Palanki University of South Alabama Srinivas Palanki (USA) Dynamics of Commercial Controllers 1 / 18

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Commercial Controllers Controller A controller is an electronic device that helps to: 1 regulate a process at its desired set-point despite disturbances to the process. 2 take the system to a new set-point safely, with desired dynamic characteristics. The vast majority of controllers used in the process industry (over 80%) are P, PI or PID controllers. In this lecture, we develop the dynamic models for these commercial controllers. Srinivas Palanki (USA) Dynamics of Commercial Controllers 2 / 18
Commercial Controllers Definitions Set-Point, Ysp Controller Signal from sensor, Y Error, E + - Signal to actuator, U Y sp : Desired set-point Y : Signal from sensor E : Error(input to controller) E = Y sp - Y U : Signal to actuator (output of controller) Controller Types P = Proportional PI = Proportional-Integral PID = Proportional-Integral-Derivative Srinivas Palanki (USA) Dynamics of Commercial Controllers 3 / 18

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Commercial Controllers P Controller Set-Point, Ysp Controller Signal from sensor, Y Error, E + - Signal to actuator, U U = k c E (1) The variable k c is called the controller gain and is a tunable parameter, which is set by the user. Srinivas Palanki (USA) Dynamics of Commercial Controllers 4 / 18
Commercial Controllers PI Controller Set-Point, Ysp Controller Signal from sensor, Y Error, E + - Signal to actuator, U de I dt = E U = k c E + k c τ I e I (2) The variable τ I is called the integral time constant . The PI controller has two tunable parameters: k c and τ I . Srinivas Palanki (USA) Dynamics of Commercial Controllers 5 / 18

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Commercial Controllers PID Controller Set-Point, Ysp Controller Signal from sensor, Y Error, E + - Signal to actuator, U de I dt = E de F dt = - 1 λ e F + 1 λ E U = k c E + k c τ I e I + k c τ D - 1 λ e F + 1 λ E (3) The variable τ D is called the
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