s + Kce(t) The basic time equation for a proportional only controller is: p(t) w

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s + Kce(t) The basic time equation for a proportional only controller is: p(t) where p(t) is the process signal output and e(t) is the error. a) Determine the transfer function for this system. Now consider a simplified block diagram with only Gc and Gp Y'spls) shown at right. E(s) P(s) Y(s) b) What is the transfer function for this loop Goueall = Y'(s)Xsg(s) Express your result in terms of Gc and Gp c Assume the process is first order with gain and time constant. Assuming the controller is appropriately characterized by the transfer function from (a), what is the overall transfer function in the standard form? d) For a unit step change in the setpoint, what is the new steady-state value ofy'()?

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