ECE 4550
Control System Design
Georgia Tech
State-Space Integral Control
1
Introduction
The purpose of a feedback control system is to provide internal stability, a sufficiently fast transient
response, and possibly a command-following behavior. The state
ECE 4550
Fall 2011
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Exam 3
Name:
1. The state-space model of a plant is
0 1
0
x(t)
=
x(t) +
u(t)
1 0
1
y(t) = 1 0 x(t).
Design a reduced-order (i.e. first-order) estimator that generates an estimate x
2
ECE 4550
Fall 2015
Exam 3
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Name:
1. The two parts of this problem are unrelated.
(a) A first-order plant is modeled by
y = y + u
where and are constant coefficients. Experimentally measured input-output da
ECE 4550
Fall 2012
Exam 3
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Name:
1. A permanent-magnet synchronous AC motor drive system is shown below.
DC Source
DC-AC Converter
AC Motor
idc +
+
+
ia
vA
Vdc
va
iA
vB
iB
vC
vc
ib
iC
+
+
vb
ic
N
Assume th
ECE 4550
Summer 2015
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Exam 2
Name:
1. A second-order plant with two inputs and two outputs is modeled by
x 1
0 1 x1
1 0 u1
=
+
x 2
0 0 x2
0 1 u2
y1
1 0 x1
=
.
y2
0 1 x2
(a) If just one actuator i
ECE 4550
Summer 2013
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Exam 2
Name:
1. Consider the second-order system defined by
0 1
1
x =
x+
u
1 0
0
y = 1 1 x.
The transfer function of this system has denominator polynomial
s 1
det(sI A) = det
= s2
ECE 4550
Spring 2014
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Exam 2
Name:
1. The nominal (i.e. best available) model of a given plant is
1 1
0
x(t)
=
x(t) +
u(t).
0 1
1
Using this nominal model, a control engineer has designed the state-feedb
ECE 4550
Spring 2015
Exam 2
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Name:
1. Evaluate the rank of the following matrices; show your work.
Elementary row operations may be used to reduce a matrix to (non-unique) row echelon form; such operations
ECE 4550
Summer 2012
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Exam 2
Name:
1. Consider the following system.
1 0 0
1
x = 1 1 0 x + 1 u
0 1 0
0
y= 0 0 1 x
(a) Determine the location and the controllability/observability properties of each eigen
ECE 4550
Fall 2014
Exam 3
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Name:
1. The schematic diagram of a Y-connected permanent-magnet synchronous AC motor is shown below, along
with the modeling equations that relate the phase currents ia , ib , i
ECE 4550
Spring 2012
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Exam 3
Name:
1. In position control applications, both position and speed are useful feedback signals, but it is common to
install just one sensor which measures only position (not sp
ECE 4550
Spring 2014
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Exam 3
Name:
1. A rotary motion plant is described by the state-space model
0 1
0
x =
x+
(u w)
0 0
1
y= 1 0 x
where y is the position output, u is the control torque input and w is
ECE 4550
Summer 2014
Exam 3
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Name:
1. A permanent-magnet brush-commutated DC motor drive system is shown below.
+
idc
i
+
+
Vdc
vA
iA
v
vB
iB
Apwm
Bpwm
The steady-state modeling equations are as follows:
T
ECE 4550
Summer 2014
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Exam 2
Name:
1. A block diagram depicting the architecture of a control system is shown below, where C(s) is the
controller transfer function and P (s) is the plant transfer function.
ECE 4550
Control System Design
Georgia Tech
Modeling and Analysis of AC Motor Drive Systems
1
System Description
1.1
Magnetic Geometry
Consider the type of permanent-magnet synchronous motor having permanent magnets mounted to the
surface of a cylindrical
ECE 4550
Control System Design
Georgia Tech
Reduced-Order State Estimation
The type of state estimator we have been using up to this point in the course is referred to as a full-order
estimator to emphasize that all n state variables of the plant are bein
ECE 4550
Control System Design
Georgia Tech
Torque-Speed Capability of AC Motor Drive Systems
The DC power supply and three-phase DC-AC power converter used to excite an AC motor will introduce
voltage and current limits, and these will in turn manifest t
ECE 4550
Control System Design
Georgia Tech
Role of Plant Zeros on Integral Control Design
1
Introduction
These notes are intended as a follow-up to the preceding document that comprehensively developed the
theory of state-space integral control. Examples
ECE 4550
Control System Design
Georgia Tech
Integrator Windup and Its Compensation
1
The Idealized System
To understand the phenomenon of integrator windup and to compare potential anti-windup compensation
methods, a simple example will be considered in d
ECE 4550
Control System Design
Georgia Tech
Command-Following Capability
1
Definition of Property
The purpose of a feedback control system is to provide internal stability, a sufficiently fast transient
response, and possibly a command-following behavior.
ECE 4550
Control System Design
Georgia Tech
Selection of Actuators and Sensors
1
The Cart-Stick System
Consider the physical system shown in the figure below, the so-called cart-stick system. The motion of
the cart is constrained to move along a straight
ECE 4550
Control System Design
Georgia Tech
Essentials of DC Machine Systems
1
The System
At the highest level of abstraction, a DC machine system is depicted as shown below. The overall system
is an electromechanical system, and the DC machine serves as
ECE 4550
Control System Design
Georgia Tech
State Feedback and State Estimation
1
Controller Design Problem
1.1
Overall System
Consider the block diagram below which illustrates the typical architecture of a feedback control system.
The physical system to
ECE 4550
Control System Design
Georgia Tech
Discrete-Time Equivalent Plant Model
1
Formulation of the Modeling Problem
In this section, we study the response of a continuous-time plant at discrete instants of time in order
to determine the discrete-time e
ECE 4550
Control System Design
Georgia Tech
Summary of Continuous-Time and Discrete-Time Concepts
If a microcontroller is used to implement a control algorithm for a physical system, the overall system
will necessarily be characterized by a combination of
ECE 4550
Control System Design
Georgia Tech
System Analysis
1
Eigenvalues, Modes, Poles and Zeros
1.1
Poles and Zeros in s-Domain
Consider a single-input, single-output, state-space system
x(t)
= Ax(t) + Bu(t)
y(t) = Cx(t) + Du(t)
with scalar transfer fun
ECE 4550
Control System Design
Georgia Tech
System Response
There are essentially two ways to evaluate the response of a linear time-invariant dynamic system; the
Laplace transform method and the numerical integration method. Both have advantages and disa
ECE 4550
Summer 2015
Exam 3
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Name:
1. A permanent-magnet brush-commutated DC motor drive system is shown below.
idc
+
i
+
+
Vdc
vA
iA
v
vB
iB
Apwm
Bpwm
Assume that Vdc = 24 V; that the semiconductor switch
ECE 4550
Control System Design
Georgia Tech
State-Space Modeling
1
State-Space Representation
The state of a system is the information needed at the present time in order to uniquely determine the
future response of the system to some particular input. In
ECE 4550
Fall 2012
Exam 1
Closed-Book, 1 Sheet of Notes Allowed, 4 Problems.
Name:
1. A first-order continuous-time system is modeled according to
x(t)
= x(t) + u(t)
y(t) = x(t) + u(t).
Assuming x(0) = 0, determine the input u(t) required to generate the
GEORGIA INSTITUTE OF TECHNOLOGY
SCHOOL of ELECTRICAL and COMPUTER ENGINEERING
ECE 4550 Control System Design Fall 2014
Problem Set #5: Pulse-Width Modulation and DC Motor Drives
The objective of this problem set is to understand the use of pulse-width mod
GEORGIA INSTITUTE OF TECHNOLOGY
SCHOOL of ELECTRICAL and COMPUTER ENGINEERING
ECE 4550 Control System Design Fall 2014
Problem Set #3: Dynamic System Analysis
The objective of this problem set is to reinforce lecture material on physical system analysis i
GEORGIA INSTITUTE OF TECHNOLOGY
SCHOOL of ELECTRICAL and COMPUTER ENGINEERING
ECE 4550 Control System Design Fall 2014
Problem Set #4: Controllability and Observability
The objective of this problem set is to reinforce lecture material relating to control
GEORGIA INSTITUTE OF TECHNOLOGY
SCHOOL of ELECTRICAL and COMPUTER ENGINEERING
ECE 4550 Control System Design Fall 2014
Problem Set #8: AC Motor Drive System Operating Principles
The objective of this problem set is to explore some elementary concepts rela
GEORGIA INSTITUTE OF TECHNOLOGY
SCHOOL of ELECTRICAL and COMPUTER ENGINEERING
ECE 4550 Control System Design Fall 2014
Problem Set #9: Torque-Speed Capability of AC Motors
The objective of this problem set is to study steady-state operation of AC motor dr