12-12-2012, 01:14 PM
Transfer Functions and State Space Models
Transfer Functions.PPT (Size: 381.5 KB / Downloads: 76)
Transfer Functions
Provide valuable insight into process dynamics and the dynamics of feedback systems.
Provide a major portion of the terminology of the process control profession.
Defined as G(s) = Y(s)/U(s)
Represents a normalized model of a process, i.e., can be used with any input.
Y(s) and U(s) are both written in deviation variable form.
The form of the transfer function indicates the dynamic behavior of the process.
Unstable Behavior
If the output of a process grows without bound for a bounded input, the process is referred to a unstable.
If the real portion of any pole of a transfer function is positive, the process corresponding to the transfer function is unstable.
If any pole is located in the right half plane, the process is unstable.
Zeros of a Transfer Function
The zeros of a transfer functions are the value of s that render N(s)=0.
If any of the zeros are positive, an inverse response is indicated.
If all the zeros are negative, overshoot can occur in certain situations
Combining Transfer Functions
Consider the CST thermal mixer in which a heater is used to change the inlet temperature of stream 1 and a temperature sensor is used to measure the outlet temperature.
Assume that heater behaves as a first order process with a known time constant.