# Introduction to Digital Control Systems

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15 Νοε 2013 (πριν από 4 χρόνια και 11 μήνες)

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Introduction to
Digital Control Systems
Digital Control Systems (MEE4003)
SogangUniversity
Department of Mechanical Engineering
Control Theory
•Control theory is an interdisciplinary branch of
engineering and mathematics that deals with the
behavior of dynamic systems.
•The desired output of a system is called the
reference.
•When one or more output variables of a system
need to follow a certain reference over time, a
controller adjusts the inputs to a system to
obtain the desired effect on the output of the
system.
Control Theory
•Figure 1.1: The concept of the feedback loop to
control the dynamic behavior of the system: this
is negative feedback, because the sensed value
is subtracted from the desired value to create
the error signal, which is amplified by the
controller.
Controller
System
(Plant)
Sensor
Physical output
Measurement
Control
input
ErrorReference

Cruise control unit
Control System –Example 1
Controller
Vehicle
Tachometer
Vehicle speed
Measured speed
Throttle
angle
Speed
error
Set speed

Control System –Example 2
Controller
Air
conditioner
in a room
Thermocouple
Room
temperature
Measured
temperature
Fan/comp
speed
Temperature
error
Desired
temperature

Control System –Example 3
Controller
Robot arm
with a motor
Encoder
Robot joint
angle
Measured angle
Motor
current
Angle
error
Desired
angle

Control System –Example 4
Spinal Cord
(Central
Nervous
System)
Musculoskeletal Mechanics
Motor
Behavior
Sensory
Neuron
Reflex
Motor
Neuron
V1
M1
C
Spinal
cord
(CNS)
Musculo-
skeletal
system
GTO
Muscular
tension
Measured tension
Motor
neuron
Error
Muscular
tension
order
from
brain

Regulation and Tracking Control
•When the reference is constant, the control process is
called regulation.
•Examples: Cruise control, Air-conditioner control, Process control,
etc.
•When the reference is time-varying, the control process
is called tracking control.
•Examples: Robot arm, X-Y stage control, Hard disk drive control,
Vibration suppression, etc.
System
•System is a set of interacting components
forming an integrated whole.
•Every system has input(s) and output(s).
•Most systems share common characteristics,
including:
–Systems have structure, defined by components and their
composition,
–Systems have behavior, which involves inputs, processing and
outputs of material, energy, information, or data,
–Systems have interconnectivity: the various parts of a system
have functional as well as structural relationships to each other,
–Systems may have some functions or groups of functions
Plant
•A plant in control theory is the combination of
process and actuator. In particular, a plant is the
system to be controlled.
Signal
•A signal is any time-varying or spatial-varying
quantity.
•In the physical world, any quantity measurable
through time or over space can be considered
as a signal.
•More generally, any set of human information or
machine data can also be considered as a
signal.
•Such information or machine data must all be
part of systems existing in the physical world.
Examples of Signal
Electrical signals
(voltage, current,
electromagnetic field…)
Information signals
(number arrays,
functions, series,…)
Motion signals
(position, angle,
velocity,
acceleration,…)
Image signals
(color, video,…)
Sound signals
(frequency, amplitude, tone…)
Discrete-time and Continuous-time Signals
•If the quantities are defined only on a discrete
set of times, we call it a discrete-time signal. The
discrete-time signal can be indexed by an
integer that represents the sequence of each
data point.
•On the other hand, a continuous-time real signal
is any real-valued function that is defined for all
time tin an interval.
Discrete-time and Continuous-time Signals
0
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0.9
1
0
0.1
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0.9
Time (sec.)
Amplitude
0
0.1
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Time (sec.)
Amplitude
Continuous-time signalDiscrete-time signal
Discrete-time and Continuous-time Signals
•Digital control is a branch of control theory that
uses digital computers to act as system
controllers.
•Since a digital computer has finite precision (i.e.,
quantization) extra care is needed to ensure that
the error in coefficients, A/D conversion, D/A
conversion, etc. are not producing undesired or
unplanned effects.
•The benefits of a digital control system include
–Low cost / Flexibility / Scalability / Adaptability / Static
operation
Digital Control System Structure
Analog to digital converter
converts analog voltage signals
into digital information signals
Digital to analog converter
(DAC, D/A, D2A)
converts digital information
signals into analog voltage
signals
Sampling Rate
•The sampling rate, sample rate, or sampling
frequency defines the number of samples per
unit of time (usually seconds) taken from a
continuous signal to make a discrete signal.
•For time-domain signals, the unit for sampling
rate is hertz [Hz] (inverse seconds, 1/s, s−1),
sometimes noted as Sa/s (samples per second).
•The inverse of the sampling frequency is the
sampling period or sampling interval, which is
the time between samples.
Disturbance
•Disturbance is an undesired input that affects
the performance of the overall control system.
•Disturbance includes an environmental change,
an external force, a change in system
parameter, etc.
Control System –Example 1
•Suppose you have a vehicle with a cruise control
function. The cruise control unit (CCU)
calculates the amount of acceleration from the
measured speed error to maintain a set speed.
The vehicle speed is measured by a tachometer.
–What are the signals?
–What is the plant?
–What is the controller?
–What is the sensor?
–How is the block diagram represented?
–What are the expected disturbances?
Control System –Example 2
•An air conditioner is installed in a room. The desired
temperature is 24C, and the current temperature is being
measured by a thermocouple. The fan of the air
conditioner is controlled such that its desired speed is
proportional to the temperature error. The speed of the
fan is controlled by an electric current flowing through
the fan, where the electric current is controlled by a
motor driver.
–What are the signals?
–What is the plant?
–What is the controller?
–What is the sensor?
–How is the block diagram represented?
–What are the expected disturbances?
Control System –Example 3
•A motor installed at a joint of an industrial robot
is to be controlled. The desired angular position
of the motor is a sine wave with an amplitude of
1radian and a frequency of 1Hz. It is known that
the motor follows the equation of motion
, where is the angular position of the motor
and is the torque generated by the motor. The
motor torque is proportional to the electric
current flowing through the motor, where the
electric current is regulated by a motor driver.
•The motor driver is connected to the computer
via a D/A converter, and the torque command is
transferred by an analog voltage signal. A digital
controller generates the torque command to be
proportional to the angular position error. The
angular position is measured by an encoder.
–What are the signals?
–What is the plant?
–What is the controller?
–What is the sensor?
–How is the block diagram represented?
–What are the expected disturbances?Control System –Example 3 (Cont’d)
Goal of Control Systems
•The general goals of a control system are:
–Minimizing the (regulation/tracking) error
–Minimizing the effect induced from a disturbance
–Minimizing the effect of noise in the output