ChE 535 Homework 7
Fall 2016
(Due November 2, 2016)
1)
2)
3)
4)
5)
6)
From Graham and Rawlings Exercise 1.50
From Graham and Rawlings Exercise 2.3
From Graham and Rawlings Exercise 2.5
From Graham and Rawlings Exercise 2.6
From Graham and Rawlings Exercis
Chapter 3:
Review of Linear Algebra
In this chapter we will review a number of the fundamental concepts related to linear
algebra. While many of these concepts are of independent interest, they will serve as a
foundation for our subsequent analysis of lin
Chapter 2:
Modeling of Dynamic Processes
The process model will be the starting point for all of our controller design efforts. This
model should be of sufficient fidelity that the relationship between process inputs and
outputs can be understood. It shou
ChE 535 Homework 2
Fall 2016
(Due September 14, 2016)
Problem 2-10: Consider the Furnace Reactor process of Section 2.6.1.
(i)
Indicate the deviation variable form of the process model.
(ii)
Using a MATLAB ode solver, simulate the following scenario. The
ChE 535 Homework 3
Fall 2016
(Due September 21, 2016)
1) From Chmielewski lecture notes Problem 3-1
Problem 3-1: Consider a set of two differential equations in state-space form: x Ax ,
with the initial conditions x(0) = xo. Prove the following:
If we are
ChE 535 Homework 9
Fall 2016
(Due November 28, 2016)
Problem 1: Consider a time-dependent infinite slab of unit width. The partial differential
equation describing the system is
T
2T
10
t
z 2
T
hTL T (t ,0)
z z 0
T
z
0
z 1
T (0, z ) 303
where h= 1 and
ChE 535 Homework 5
Fall 2016
(Due October 19, 2016)
1) From Chmielewski lecture notes Problem 3-9
2) From Chmielewski lecture notes Problem 3-10
3) From Chmielewski lecture notes Problem 3-12
4) From Chmielewski lecture notes Problem 3-13
Problem 3-9: Con
ChE 535 Homework 8
Fall 2016
(Due November 21, 2016)
Problem 1: Exercise 2.44 from Graham and Rawlings
For part (b) Rather than have you find the eigenvalues and eigenfunctions, Id like you to
verify that those given below are the eigenvalues and eigenfun
ChE 535 Homework 6
Fall 2016
(Due October 26, 2016)
1)
2)
3)
4)
5)
From Chmielewski lecture notes Problem 3-14
From Graham and Rawlings Exercise 1.20
From Graham and Rawlings Exercise 1.21
From Graham and Rawlings Exercise 1.22
Problem 3-14: Consider a se
ChE 535 Homework 6 Solution
Problem 3-14: Consider a set of algebraic equations Mx = b where
0 1
1 1
1
1 1 1
0
0
b=
M =
0
1
1 1 1
1
0
1 0
0
An eigenvector decomposition of A is A = where
0.577 0.5
0.408
0.5
0.707
0
0.707
0
=
0.5
0.577
0.5
Chapter 3:
Review of Linear Algebra
In this chapter we will review a number of the fundamental concepts related to linear
algebra. While many of these concepts are of independent interest, they will serve as a
foundation for our subsequent analysis of lin
ChE 535 Homework 5 Solution
Problem 3-9: Consider a set of algebraic equations Mx = b where
0 1 2 0
1 0 0 0
M =
2 0 0 1
0 0 0 1
The Singular Value Decomposition of M is M = USV * where
1
0
0
0
0.365 0 0.447 0.816
U =
0.913 0
0
0.408
0.408
0.183
ChE 535 Homework 2 Solution
Problem 2-10: Consider the Furnace Reactor process of Section 2.6.1. (i) Indicate the deviation variable form of the
process model. (ii) Using a MATLAB ode solver, simulate the following scenario. The initial condition is s(0)
CHE535 HW#1 Solution
Problem 2-1: Consider the following model of a surge tank for which we plan to implement a liquid level
control system:
A
dh
= vin v out
dt
v out = p v h
where A = 1m2 is the cross-sectional area of the tank, h is the liquid level, vo
ChE 535 Homework 4 Solution
(1) From Graham and Rawlings Exercise 1.14
Solution:
Take any two elements of R(A), y1, y2; they are both expressible as y1=Ax1 and y2=Ax2 for some x1 , x2 R n .
Adding these two elements, we have
y y1 + y2
=
=Ax1 + Ax2
=A( x1
CHE 535 Homework 3 Solution
Problem 3-1: Consider a set of two differential equations in state-space form: x = Ax , with the initial conditions
x(0) = xo. Prove the following:
If we are allowed to choose the initial conditions arbitrarily (i.e., xo can be
Chapter 3:
Review of Linear Algebra
In this chapter we will review a number of the fundamental concepts related to linear
algebra. While many of these concepts are of independent interest, they will serve as a
foundation for our subsequent analysis of lin