Chapter 2. Mathematical Models of Systems
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Modeling is an essential step in the control system design process.
Why do we need system modeling?
We need quantitative mathematic models to understand and predict
the effects of control actions (in dynamical
MECH 3610 Control Principles
Lilong Cai
Department of Mechanical Engineering
HKUST
melcai@ust.hk
1
Outline
Introduction
-What is a control?
- Concept of feedback control
- Brief history of automatic control
- Control applications
-Syllabus
-Terms and conc
MECH 3610
Control Principle
Tutorial #3
Content
Feedback of homework 1 -Laplace
Transform
Review
Transfer function
Why Block Diagram
Block Diagram
Block Diagram Reduction
Example 1 and 2
Why Signal-Flow Graph
SFG to Transfer function
Example 3
Signal-Flow
Chapter 8 Frequency Response Methods
The frequency response
Nyquist diagram polar plots
Bode diagram magnitude and phase
Frequency domain specifications
Frequency Response Methods
In preceding chapters the response and performance of
a system have be
MECH 3610
Control Principle
Tutorial #2
Content
Last discussion question
Example 1
Laplace Transform
Transfer function
Final Value Theorem
Example 2
Review some physical laws
Force-Current analogous system
2
Discussion
(b) Solution
Description:
I
Chapter 6 The Stability of Linear
Feedback Systems
The concept of stability
Routh-Hurwitz criterion
Relative stability
Stability of state-space systems
1
The Concept of Stability
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o
2
Why Stability Is Important
https:/www.youtube.com/watch?v=XggxeuFD
The Laplace Transform
The method of Laplace Transforms converts a calculus
problem (the linear differential equation) into an algebra
problem (the algebra equation).
The solution of the algebra problem is then fed backwards
through what is called an Inve
Chapter 4: Feedback Control System
Characteristics
Open vs. Closed-loop control
Sensitivity of feedback
Propagation of disturbances in the
feedback loop
Robustness and Sensitivity
Steady-State Error
1
Open-Loop Control
An open-loop (direct) system op
Chapter 7: The Root Locus Method
The relative stability and the transient performance of a closedloop system are directly related to the location of the closed-loop
roots of the characteristic equation in the s-plane.
It is frequently necessary to adjus
Chapter 5 The Performance of
Feedback Control Systems
The ability to adjust the transient and steady-state performance
is a distinct advantage of feedback control system.
The performance of the control system is specified in terms
of both the transient r
Block Diagrams
( s )
=?
G( s) =
V f ( s)
1
Block Diagram Transformations
1. Combining blocks in cascade
X 3 = G2 X 2 = G2 (G1 X 1 ) = G2G1 X 1
2
Block Diagram Transformations
2 Moving a summing point behind a block
X 3 = G ( X 1 X 2 ) = GX 1 GX 2
3
Block
MECH 3610
Control Principle
Tutorial #7
Content
Chapter 2: Mathematical model of system
Physical system Transfer function
Chapter 3: State variable models
Physical system State-space representation
Chapter 4: Feedback control system
characteristics
MECH 3610
Control Principles
Tutorial #9
Content
System Stability
All Poles with negative real parts
How to determine?
1. Solve the roots of characteristic equation
2. Use Routh-Hurwitz Criterion
Number of roots with positive real parts
Number of cha
Chapter 3 State-Variable Models
State-Variable Models
State equations
State Variables of a Dynamic System
The concept of State
Form of the State Equations
The State Differential Equation
Transfer Function of a State Space Model
The State Transitio
MECH 3610
Control Principles
Tutorial #11
Contents
Frequency Response Methods
R(s )
r (t ) A sin(t )
G (s )
Y (s )
y (t ) A | G ( j ) | sin(t G ( jw)
Three Diagram-representation Methods
Polar plot - Real & Imaginary Re[G ( j )], Im[G ( j )]
Logarithm
MECH 3610
Control Principles
Tutorial #10
Content
The Root Locus
Referred to following concepts
Transfer function
Roots of Characteristic Equation
Stability
How to draw Root Locus?
Two conditions
Magnitude Condition
Angle Condition
Example
2
Rev
MECH 3610
Control Principle
Tutorial #1
Introduction
TAs-ourselves
- LEE, Hau Him
hhleeaa@ust.hk , Rm 1213, lift 21
Tel: 2358-8808
- CHAI Yuting
ychai@ust.hk , Rm 4226, lift 24
Tel: 2358-8815
No office hour. If any questions, please appoint
a time with
MECH 3610
Control Principle
Tutorial #12
Contents
Questions format in Exam : Question and answer, like your homework
3 or 4 problems
Chapter 2 - 5 : Concept
Chapter 6: Stability of linear feedback system
Concept of stability
Application of Routh-Hurw
Chapter 9 The Nyquist Stability
Criterion
Harry Nyquist
Born in 1889 in Sweden
Died in 1976, USA
Yale PhD, 1917
Career at Bell Labs
138 patents
Nyquist diagram, criterion,
sampling theorem
Laid the foundation for
information theory, data
transmission and
MECH 3610
Control Principle
Tutorial #4
Content
State-Space Representation
State differential equation
Output differential equation
Eigenvalues
Controllability & Observability
Example 1, 2
2
Example 1
(1) Write the state-space representation of the
MECH 3610
Control Principle
Tutorial #5
Content
Sensitivity
Steady state - Final-value theorem
4 examples
2
Example 1
A closed-loop system is used to track the sun to obtain
maximum power. The tracking system is a negative
feedback system with
G ( s )
MECH 3610
Control Principle
Tutorial #6
Content
Performance of a Second-Order System
Peak time
P.O. (percent overshoot)
Settling time
2 examples
2
Standard performance measures - step signals as input
3
Example 1
A system is shown as following.
(1) H
What is Control?
The word control is usually taken to mean
- regulate,
- direct,
- command.
Control is a sequence of decisions and actions aimed at the
attainment of specified objectives in an environment of
uncertainty and presence of disturbances.
What