California State Polytechnic University Pomona
Department of Electrical and Computer Engineering
ECE 309 Control Systems Engineering Spring 2016
Homework 4
Root locus, compensator design
Due date: Thu, June 2, 2016
Problem 1
For the following unity feedba
Experiment 6
Closed Loop Analysis
ECE 309L
November 20, 2011
Professor Boskovich
1
Objectives
To become familiar and understand forward gain in a feedback system and the effect on
the transient response and the relationship to the Root Locus
Equipment and
Experiment 7 & 8
PI and PID Controller using
A Microcontroller
ECE 309L
Professor Boskovich
12/5/2011
Objectives:
To become familiar and understand Controller techniques using an embedded
micro-controller
Equipment and Materials:
Prototype Embedded Proces
Experiment #5
Steady State Errors
ECE 309L
November 21, 2011
Prof. Boskovich
1
Objectives
To become familiar with the effects of system type on the steady state errors of a system
for step and ramp inputs.
Equipment and Materials
Material from Lab 5A,
Sim
Experiment #4
Closed Loop Response to Induced
Disturbance (an unwanted signal)
ECE 309L
Professor Boskovich
October 21, 2011
1
Objectives:
1.
Derive a real circuit from block diagram.
2.
Investigate a Systems output error caused from an unwanted noise sou
Experiment #2
Time Domain Response of First and Second
Order Systems
ECE 309L
Professor Boskovich
October 16, 2011
Part 1 1st Order Systems Pre-Lab
A. Using the schematic in figure 2.3, find the transfer function that describes the circuit.
B. Use Matlab
Experiment #3
Frequency Response of First and
Second Order Systems
ECE 309L
Professor Boskovich
October 21, 2011
Objectives:
To become familiar with the response of first and second order systems. The response
considered here is in frequency domain, and i
Experiment #1
Basic Control Components
ECE 309L
Professor Boskovich
October 7, 2011
Prelab
1. Show that for an attenuator
2. Design an attenuator using a 1M potentiometer such that the input signal is attenuated by
a factor of 4.
Rt = 1M
3. Show that for
ECE309
Dr. Chandra
Class Project
(Due: 08/24/2017)
For the unity feedback system shown in Below Figure:
1) Do the following by hand:
a. Sketch the root locus.
b. Find the value of K that will yield a 10% overshoot.
c. Locate all nondominant poles. What ca
ECE309
Dr. Chandra
Homework 2
(Due: 07/10/2017)
1) Write, the mesh and nodal equations for the network of the figure below:
Use MATLAB to solve for the transfer function,
.
Show your work for both, mesh and Nodal Analysis.
2) Find the transfer function,
s
ECE309
Dr. Chandra
Homework 4 Solution
1) Find the equivalent transfer function, ()
Figure below:
=
()
()
for the system shown in the
ECE309
Dr. Chandra
2) Using Masons rule, find the transfer function, ()
=
()
()
for the system
represented by the Figure
ECE309
Dr. Chandra
Homework 1
1) Derive the Laplace transforms for the following time functions:
a) sin()()
b) cos()()
c) 3 ()
2) A system is described by the following differential equation:
()
Find the expression for the transfer function of the system,
ECE 309 Control Systems Engineering
Root Locus Example #1
Instructor: Dr. Chandra
TA: Imed Abdellaoui
August 13, 2017
Given the following transfer function
GH(s) =
K(s + 1.5)
s(s + 1)(s + 10)
Design the value of K to yield 1.52% overshoot. Also, at this v
ECE309
Dr. Chandra
Homework 4
(Due: 08/07/2017)
1) Find the equivalent transfer function, ()
=
()
()
for the system shown in the
Figure below:
2) Using Masons rule, find the transfer function, ()
represented by the Figure below:
=
()
()
for the system
ECE
ECE309
Dr. Chandra
Homework 2 solution
1) Write, the mesh and nodal equations for the network of the figure below:
Use MATLAB to solve for the transfer function, () =
Show your work for both, mesh and Nodal Analysis.
()
()
.
ECE309
Matlab code:
syms s V %
Summer 2014 ECE 309 Midterm 7/23/14
R. Chandra
Last name: First name: 't
YOU MUST SHOW ALL YOUR WORK.
1. Consider the RC ladder network shown in Figure 1. 03\
. ,/
W I! ' "2 ' x '/
Figure 1.
(a) Write the mesh equations and present them the matrix form
California State Polytechnic University Pomona
Department of Electrical and Computer Engineering
ECE 309 Control Systems Engineering Spring 2016
Homework 3
Block reduction, Stability, Steady-state error
Due date: Tue, May 10, 2016
Problem 1
Find the close
ECE 309
Control Systems Engineering
Part 7: Root Locus Techniques
Instructor: Dr. Ha Le
Department of Electrical and Computer Engineering
California State Polytechnic University, Pomona
Winter 2017
What will be presented?
1) Definition and properties of a
ECE 309
Control Systems Engineering
Part 5: Stability
Instructor: Dr. Ha Le
Department of Electrical and Computer Engineering
California State Polytechnic University, Pomona
Winter 2017
What will be presented?
1) Stability of linear time invariant systems
ECE 309
Control Systems Engineering
Part 2: Modeling in frequency domain
(s-domain)
Instructor: Dr. Ha Le
Department of Electrical and Computer Engineering
California State Polytechnic University, Pomona
Winter 2017
What will be presented?
1)
Finding tran
ECE 309
Control Systems Engineering
Part 1: Introduction to control engineering
and review of Laplace transform
Instructor: Dr. Ha Le
Department of Electrical and Computer Engineering
California State Polytechnic University, Pomona
Winter 2017
What will b
ECE 309
Control Systems Engineering
Part 4: Reduction of multiple subsystems
and closed-loop systems
Instructor: Dr. Ha Le
Department of Electrical and Computer Engineering
California State Polytechnic University, Pomona
Winter 2017
What will be presented
ECE 309
Control Systems Engineering
Part 8: Compensator Design via Root Locus
Instructor: Dr. Ha Le
Department of Electrical and Computer Engineering
California State Polytechnic University, Pomona
Winter 2017
What will be presented?
1) Design of cascade
ECE 309
Control Systems Engineering
Part 6: Steady-state error
Instructor: Dr. Ha Le
Department of Electrical and Computer Engineering
California State Polytechnic University, Pomona
Winter 2017
What will be presented?
1) Calculating steady-state error fo
ECE 309
Control Systems Engineering
Part 3: Evaluating time response of controlled systems
Instructor: Dr. Ha Le
Department of Electrical and Computer Engineering
California State Polytechnic University, Pomona
Winter 2017
What will be presented?
1) Deter
ECE309
Dr. Chandra
Homework 2 solution
1) Write, the mesh and nodal equations for the network of the figure below:
Use MATLAB to solve for the transfer function, () =
Show your work for both, mesh and Nodal Analysis.
()
()
.
ECE309
Matlab code:
syms s V %
Summer 2017
Prof. Rajan Chandra , Ph.D.
ECE 309 Control Systems
Department of Electrical and Computer Engineering
California State Polytechnic University, Pomona
SYLLABUS
Class Information and Description
ECE 309 Control Systems
Modeling, Time Response, R
ECE309
Dr. Chandra
Homework 3
(Due: 07/24/2017)
1) For each of the second-order systems that follow, find
; n; Ts; Tp; Tr , and %OS.
a)
b)
c)
2) Find the transfer function of a second-order system that yields a 15% overshoot and
a settling time of 0.7 sec