SP8 - On 1A, remember that Kp = Delta y/Delta u, so you can calculate the value of y after the step change in u. This helps determine if there was offset or not.
PDC 2.4 - The pressure drop across the valve can be written as a function of Pa, Pg, and rho*g*h.
PDC 2.10 - Although the flows are assumed constant, the concentrations are
not necessarily constant. You will need to write 5 dynamic balance equations:
3 species equations and the energy equation for the reactor;
1 energy equation for the jacket.
In addition write the overall mass balance equations for the jacket and for
the reactor reactor (even thought they do not contain time-dependent terms).
PDC 3.4 - Ramps are fun to use with Laplace transforms, but remember that the function goes on forever. There is no STOP function. If you start a ramp and want it to level off after a certain time, you have to put in a time delay function and then a ramp of opposite sign to make the function level off. Remember that for a time delay in the "time" space, you change all the t's to t-theta, and multiply my the unit step function S(t-theta), where theta is the time delay. In Laplace space, you just multiply the Laplace function by exp(-theta*s).
PDC 3.17 - You do not need to transform this equation into deviation varables. Just take the Laplace of both sides and manipulate it into a form compatible with something in the Laplace table.
PDC 4.10 - Write the energy balance, including the substitution for U that involves the wind velocity. You will have to do the Taylor's expansion to get deviation variables.
PDC 5.15b - Use the equation for the time of the first peak and then using this in an equation to get the peak temperature. I would also like you to plot temperature versus time from 0 to 30 minutes, and see if your calculated peak temperature matches what your graph says.
PDC 6.7b
(1) Get time-domain solution for P_m(t) in terms of K, zeta, and tau.
(2) Use solver in Excel to perform least squares fit using K, zeta, and tau
as variables.
(3) Plot to see goodness of fit.
PDC11.7
Start by solving for U. Follow algebra around the loop until you get U o both
sides. Then manilupate the algebra to get an expression for U.
Next solve for Y, and plug in the expression for U.
PDC 11.10
Use stability criteria on the second line after Equation 11-93. In other words,
all of the coefficients of the characteristic equation (the denominator of the
transfer function) must be ppositive.
PDC 11.14
Use the shortcut method on the inner loop then on the outer loop to get Y/Ysp.
You may get negative coefficients in the denominator, but there is also a negative
coefficient in the numerator which compensates.
PDC 11.18
On part a, you will get two equations and two unknowns (Kc and w). If you put
the sin and cos terms on the left-hand side of the equation, you can divide
the two equations, eliminating Kc and getting tan w. Then solve iteratively
using Mathcad or Excel (guess w= 0.5 to start).
PPC 18.1
I want you to run the jacketed reactor as follows:
(a) without cascade control. You will need to do a doublet test, get tuning
constants for a PI controller, and test response to a dissturbance change.
(b) with cascade control. You will need to tune each controller (like the example
in the book) and test the response to the same disturbance change as in part
(a). Please comment on the improvment (if any).