3. Negative Feedback Control Heat Exchanger Transfer Function

4. Given the following Characteristic Equation

5. Stable  Unstable Process Transition Criteria Solve for the root(s) of the characteristic equation when the real component of the root(s) is equal to zero. real imaginary r>0r<0

6. Substitute into the characteristic equation K cu is the ultimate gain, and,  u is the ultimate frequency

7. Split the equation into the real part and the imaginary part to solve for K cu and  u. From the imaginary equation we know that: {

8. From the real equation we know that: {