Simulating the Controlled Process

The differentiating term ensures that the controller anticipates changes. This term has a stabilizing effect and makes it possible to increase the controller gain. In practice, the derivative term is not often used because it causes easily oscillations in the controller output, especially in the presence of measurement noise. However, for higher-order processes with one relatively small time constant and one relatively large time constant, differentiating action may be beneficial and enhance control loop performance. 

In steady state, when e(t) = 0, the control action of a proportional integral controller becomes  

In this section an example will be given of a simulated control loop. Let us assume that the process can be described by the following continuous transfer function  

All time constants are given in minutes. The controller is a PID controller, which executes every minute. To simulate a discrete PID controller, Eqn. (31.6) should be differentiated and the derivatives be replaced by a backward difference, which yields  

It is further assumed that the correcting element has linear characteristics and that the control valve equation can be given by  

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