[MECH387]
Automatic Control
Lecture 1 – Introduction
(Chap. 1 of the textbook)
Professor Joonbum Bae
School of Mechanical Engineering
Korea University
Definition of a Control System
• A control system consists of subsystems and processes (or plants)
assembled for the purpose of controlling the outputs of the processes.
(obtaining a desired output with desired performance).
Input
Desired response
Control
System
Output
Actual response
• Control systems can be found everywhere.
Examples of Control Systems
• Pancreas (췌장): regulating adrenaline (a.k.a. epinephrine), which plays an
important role in the fight-or-flight response by increasing blood flow to
muscles, output of the heart, pupil dilation response, and blood sugar
level.
➢ How can the pancreas regulate adrenaline?
➢ What happens in the pancreas?
➢ What is the input and output?
Examples of Control Systems
• Furnace
➢What happens at the furnace to melt the metals?
➢Many subsystems (e.g. valves, actuators)
Examples of Control Systems
• MECH387 class
Desired
performance
(knowledge, skill, etc.)
−
Prof. Bae
(controller)
Measured
performance
Every
possible
teaching
methods
Students
(plant)
Exam
Homework
▲ Block diagram
Performance
Objective of Control Systems
1. The automatic regulation (or tracking) of certain variables in the
controlled plant to desired values (or trajectories) in the presence
of unpredictable disturbances, noises, etc.
2. The stabilization or improved stability of the controlled plant.
In this course, we will learn how to analyze, simulate and design
automatic control strategies for various engineering systems.
A History of Control Systems
Please read Chapter 1.2 of the textbook.
Block Diagram
• Abstract expression of (sub)systems and signals.
• Not a just simple blocks and arrows, but a well-defined mathematical
relationship.
Block: (sub)systems (controller, plant, sensor, etc.)
Signal: general input/output, or with specific units
a
or
Junction: sum or subtraction of signals
c
-
b
a-b=c
a
c
+
b
a+b=c
(+ can be omitted.)
Block Diagram: Blocks
𝑃
Plant
A system to be controlled (= control target)
(The term ‘plant’ has its origins in chemical engineering where the control
of chemical plants or factories is of concern.)
𝐶
Controller
A device that processes the measured signals from the sensors and the
reference signals, and generates the control signals to affect the behavior
of the plant.
𝑆
Sensor
A device that measures a physical quantity like pressure, acceleration,
humidity, or chemical concentration. Very often, in modern engineering
systems, sensors produce an electrical signal whose voltage is proportional
to the physical quantity being measured.
Block Diagram: Arrows
𝑢
𝑦 (or 𝑐)
𝑟
Control input
Input signal to the plant to make the plant outputs respond in a desirable
manner. Output of a controller.
Output (Plant output)
The plant’s behavior quantified by the value of several quantities.
Reference (Command)
A signal that represents what we would like the controlled variable to
behave like.
𝑟
𝐶
𝑢
𝑃
𝑦
Block Diagram: Arrows
𝑑
𝑛
Disturbance
Any signal that affects the behavior of the plant being controlled.
Disturbances are often induced by the environments, and often cannot be
predicted in advance or measured directly.
Noise
An unwanted disturbance in an electrical signal. Measurement noise (which
captures inaccuracies of sensor readings), process noise (due to quantization
errors in a digital implementation of the control algorithm), etc.
https://www.predig.com/
Open-loop Systems
• A block diagram without a feedback loop.
• The values of the control input can be decided ahead of time.
• The design of the open-loop controller is based on inversion and/or
calibration.
𝑟
𝐶
𝑢
𝑃
𝑦
• The ideal controller of the open-loop system is inverse of the plant.
➢ If 𝐶 ∙ = 𝑃−1 ∙ , then 𝑢 = 𝑃−1 𝑟 and 𝑦 = 𝑃 𝑃−1 𝑟 = 𝑟.
Open-loop Systems
• Pros and Cons
➢ Simple
➢ Cannot effectively deal with exogenous disturbances, changes in
the plant’s behavior (e.g. aging).
➢ Cannot deal with uncertainty.
➢ Cannot stabilize an unstable system (e.g. balancing a rocket in
the early stages of liftoff, inverted pendulum, etc.).
Closed-loop Systems
• A block diagram with feedback loops.
• Continuously sense (measure) the output of the plant, and adjust the
control input by control algorithms, which are usually based on how
the current (and past) values of the plant output deviate from its
desired value.
• Based on the model (i.e. a mathematical description of the plant)
Error (tracking error): 𝑒 = 𝑟 – 𝑦𝑚
Measured output: 𝑦𝑚 = 𝑦𝑠 + 𝑛
Sensor output: 𝑦𝑠
𝑑
𝑟
𝑒
𝐶
−
𝑦𝑚
𝑛
𝑦𝑠
𝑢
𝑃
𝑆
𝑦
Closed-loop Systems
• Pros and Cons
➢ More robust to uncertainties an disturbances.
➢ Can stabilize an unstable system.
➢ Complicated.
➢ Can destabilize a stable system.
Details of Real Control Systems
• Plant (control target): Motor
Motor
Encoder
(sensor)
Gear
• Controller: Computer (e.g. LabVIEW, Matlab) or Microprocessor with
motor driver
Details of Real Control Systems
𝑟
(desired movement
(position))
−
Controller
𝑒
Motor
driver
Computer
𝑦𝑚
(measured movement 𝑛
(position))
𝑑
𝑦𝑠
𝑢
Encoder
(Sensor)
Geared Motor
(Plant)
𝑦
Details of Real Control Systems
Continuous controller
r (t )
e(t )
-
Controller
u (t )
Plant
Sensors
y (t )
Details of Real Control Systems
Digital controller
Sampler
r (t )
T
Quantization
r (kT ) e(kT )
-
Digital
Controller
u (kT )
D/A and
hold
u (t )
Plant
A/D converter
Clock
Sampler
y (kT )
Quantization
A/D converter
Sensors
T
y (t )
Details of Real Control Systems
• Analog-to-Digital (A/D) Converter
➢ To convert a voltage level to the correct bit pattern usable by the
computer. (sampler + quantization)
➢ Bit resolution (ex. ±10 V to 16 bit, 20/216=0.0003)
Signal (V)
T: sampling time
Time (sec)
▲ Sampler
Details of Real Control Systems
▲ Quantization
Details of Real Control Systems
• Digital-to-Analog (D/A) Converter
➢ To convert the digital words from the computer to a voltage level
➢ Zero order holder (ZOH), First order holder (FOH), etc.
Signal (V)
Time (sec)
▲ ZOH D/A converter
Analysis and Design Objectives
• Transient Response & Steady-state Response
➢ Example: an elevator
➢ Limitation of structures and actuators should be considered.
Output
2nd floor
Desired output (reference)
1st floor
Steady-state
error (SSE)
Time
(sec)
Transient response
Steady-state response
Analysis and Design Objectives
• Stability
Total response = Natural response + Forced response
(Homogeneous solution)
𝑥ሷ + 2𝑥ሶ = sin 𝑡
𝑥ሷ + 2𝑥ሶ = 0
𝑥 = 𝑒 𝜆𝑡
(Particular solution)
𝜆2 + 2𝜆 = 0
𝜆 = 0 𝑜𝑟 − 2
𝑥 = 𝐴𝑒 0𝑡 + 𝐵𝑒 −2𝑡 (Homogeneous solution)
𝑥 = 𝐴 sin 𝑡 + 𝐵 cos 𝑡 (Particular solution)
Analysis and Design Objectives
• Stability
Total response = Natural response + Forced response
(Homogeneous solution)
(Particular solution)
Output
Desired output (reference)
Time
(sec)
Analysis and Design Objectives
• Others
➢ Robustness
➢ System identification
➢ Operating conditions