Control Systems

Introduction

Muhammad Farooq Haydar

Flight Dynamics and Control Center

Department of Aeronautics and Astronautics
Institute of Space Technology, Islamabad

June 8, 2018

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 “Men already know how to construct wings or airplanes...

Wilbur Wright, 1901.

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 “Men already know how to construct wings or airplanes...
Men also know how to build engines and screws of sufficient lightness and
power...

Wilbur Wright, 1901.

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 “Men already know how to construct wings or airplanes...
Men also know how to build engines and screws of sufficient lightness and
power...
Inability to balance and steer still confronts students of the flying problem...

Wilbur Wright, 1901.

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 “Men already know how to construct wings or airplanes...
Men also know how to build engines and screws of sufficient lightness and
power...
Inability to balance and steer still confronts students of the flying problem...
When this one feature has been worked out, the age of flying will have
arrived, for all other difficulties are of minor importance.”
Wilbur Wright, 1901.

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From December 17, 1903 to June 18, 1914

Figure: “Gyroscopic Stabilizer Apparatus”

Figure: Wright Flyer on Curtiss C-2

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Two Airplanes with Canards...
but their handling qualities are totally different!

Figure: X-29
Figure: Wright Flyer

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Why Study Feedback Control?

Dynamic systems:
I have memory (or internal dynamics) of past states.
I current state depends on input, but also on the past state.

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Why Study Feedback Control?

Dynamic systems:
I have memory (or internal dynamics) of past states.
I current state depends on input, but also on the past state.
Feedback:

r e u y
Controller System
−

ym

Sensors

Figure: Closed loop system

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Why Study Feedback Control?

Dynamic systems:
I have memory (or internal dynamics) of past states.
I current state depends on input, but also on the past state.
Feedback:
I Interconnection to provide corrective action.

r e u y
Controller System
−

ym

Sensors

Figure: Closed loop system

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Why Study Feedback Control?

Dynamic systems:
I have memory (or internal dynamics) of past states.
I current state depends on input, but also on the past state.
Feedback:
I Interconnection to provide corrective action.
I often counter-intuitive; systematic/formal approaches are required.

r e u y
Controller System
−

ym

Sensors

Figure: Closed loop system

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Examples
Regulates speed

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Examples
Regulates speed
reduces effects of variations in load (disturbance rejection)

Haydar (IST) Figure:Control

Centrifugal
Systems governor. June 8, 2018 6 / 25
Examples

Figure: Balancing a Rocket.

Figure: An inverted pendulum.

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Examples (contd.)

Figure: Attitude of a Satellite.

Figure: Simplified Satellite Attitude
Control.

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Components of a Computer-Controlled System
1.3. WHAT IS CONTROL? 1-5
noise external disturbances noise

Output
Σ Actuators System Sensors Σ

Process

Clock

D/A Computer A/D Filter

Controller

operator input
Figure 1.3: Components of a computer-controlled system. The upper dashed box represents
the process dynamics, which include the sensors and actuators in addition to the dynamical
system being controlled. Noise and external
Haydar (IST)
disturbances can perturb the dynamics
Control Systems June 8, 2018
of the
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Course Objectives

The main objectives of this course are:

understand the basic principle of feedback, and realize the need for feedback.

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Course Objectives

The main objectives of this course are:

understand the basic principle of feedback, and realize the need for feedback.
learn to develop/interpret mathematical models and express them in
appropriate forms.

Haydar (IST) Control Systems June 8, 2018 10 / 25

Course Objectives

The main objectives of this course are:

understand the basic principle of feedback, and realize the need for feedback.
learn to develop/interpret mathematical models and express them in
appropriate forms.
understand the characteristic behavior of a system and analyze its responses.

Haydar (IST) Control Systems June 8, 2018 10 / 25

Course Objectives

The main objectives of this course are:

understand the basic principle of feedback, and realize the need for feedback.
learn to develop/interpret mathematical models and express them in
appropriate forms.
understand the characteristic behavior of a system and analyze its responses.
learn to modify the behavior of system through feedback.

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References

1 Lecture Notes, exercises, case studies.

2 Feedback Systems: An Introduction for Scientists and Engineers, (Second
Edition, v3.0h) 2016, by Karl J. Astrom and R. M. Murray.
3 Control Systems Engineering. sixth edition, 2011 by N. S. Nise.
4 Modern Control Engineering, eleventh/international edition (2008) by R.C.
Dorf and R.H. Bishop

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Outline

1 Feedback and Feedforward Control

2 Feedback Properties

3 Simple Feedback Forms

4 Combining Feedback with Logic

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Outline

1 Feedback and Feedforward Control

2 Feedback Properties

3 Simple Feedback Forms

4 Combining Feedback with Logic

Feedback Control

Negative feedback attenuates the disturbances, and contributes to (static)

stability.

r e u y
Controller System
−

ym

Sensors

Figure: Closed loop system

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Feedback Control

Negative feedback attenuates the disturbances, and contributes to (static)

stability.
I may introduce (dynamic) instability.

r e u y
Controller System
−

ym

Sensors

Figure: Closed loop system

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Feedback Control

Negative feedback attenuates the disturbances, and contributes to (static)

stability.
I may introduce (dynamic) instability.
Positive feedback amplifies the disturbances and thus results in (static)
instability.

r e u y
Controller System
−

ym

Sensors

Figure: Closed loop system

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Feedforward Control

Feedback is reactive.

r u y
Controller System

Figure: Open loop control system

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Feedforward Control

Feedback is reactive.
Feedforward can used as an anticipative/pre-emptive action.

r u y
Controller System

Figure: Open loop control system

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Feedforward Control

Feedback is reactive.
Feedforward can used as an anticipative/pre-emptive action.
Requires the precise knowledge of the system and does not change its
dynamics.

r u y
Controller System

Figure: Open loop control system

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Feedback vs Feedforward Control

Feedback Feedforward
Closed loop Open loop
Acts on deviations Acts on plans
Robust to model uncertainty Sensitive to model uncertainty
Able to reject disturbances Unable to reject disturbances
Risk for (dynamic) instability No risk for instability
Sensitive to measurement noise Insensitive to measurement noise
e.g., a market based economy e.g., a planned economy
Its possible to combine both approaches in a two degree of freedom controller.

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Applications of Control

Aerospace (Flight Control/Aerospace Subsystems)

Automotive
Power Generation and Transmission
Robotics
Telecommunications
Networks
Economics
Nature and Biological Systems

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Outline

1 Feedback and Feedforward Control

2 Feedback Properties

3 Simple Feedback Forms

4 Combining Feedback with Logic

 Robustness
Feedback provides a corrective action by comparing measured value with
4 desired value. CHAPTER 1. INTRODUCTION
1-14 CHAPTER 1. INTRODUCTION

Actuate Sense
Actuate Sense

Speed [m/s]
hrottle Speed 30

Speed [m/s]
Throttle Speed 30

m m
25 25
Compute
Compute 0 0 5 5 10 10
Time Time
[s] [s]
Figure 1.10: A feedback system for controlling the speed of a vehicle. In the block diagram
Figure on1.10:
Figure: A the
Speed
the left, feedback
Control system
Diagram for(Compute
speed of the vehicle iscontrolling
measured and the speed of
compared a vehicle.
to the In thewithin
desired speed blockthediagram
on block contains
the “Compute”
left, the speed proportional-integral (PI)in theandFigure: Effect
to of variations in car within
mass the
block.ofBased
the vehicle is measured
on the difference compared
actual and desired the desired
speeds, speed
the throttle (or
terms) (1000kg, 2000kg and 3000kg) on the
“Compute”
brake) block.
is used toBased
modifyonthethe difference
force applied to in
thethe actual
vehicle and
by the desired
engine, speeds,
drivetrain andthe throttle (or
wheels.
step-response (reference/command changes
brake)The figure
is used toon the right
modify theshows
forcethe response
applied to of
thethe control
vehicle system
by to a commanded
the engine, drivetrain change
and wheels.
in speed from 25 m/s to 30 m/s. The three from
different 25 correspond
curves m/s to 30m/s).to differing masses
The figure on the right shows the response of the control system to a commanded change
of the vehicle, between 1000 and 3000 kg, demonstrating the robustness of the closed loop
in speed from 25 m/s to 30 m/s. The three different curves correspond to differing masses
system to a very large change in the vehicle characteristics.
of the vehicle, between 1000 and 3000 kg, demonstrating the robustness of the closed loop
system to a very large change in the vehicle characteristics.
and the Haydar
desired speed and the integralControl
(IST) of that error. The plot on the right
Systems shows
June 8, 2018 17 / 25
Changing Natural Frequency/Stiffness using
Position-Feedback

(a) A mass-spring system.

xeq ex F x
− K Mass

xm

Position Encoder

(b) Feedback loop to create an artificial spring.

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Changing Damping using Rate-Feedback

(c) A mass-damper system.

veq ev F v
− C Mass

vm

Tachometer

(d) Feedback loop to create an artificial damper.

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Design of Dynamics (Summary)

Feedback can modify the dynamics!

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Design of Dynamics (Summary)

Feedback can modify the dynamics!

I position-feedback changes stiffness.

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Design of Dynamics (Summary)

Feedback can modify the dynamics!

I position-feedback changes stiffness.
I rate-feedback changes damping.

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Design of Dynamics (Summary)

Feedback can modify the dynamics!

I position-feedback changes stiffness.
I rate-feedback changes damping.
The Wright Flyer was unstable but maneuverable.

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Design of Dynamics (Summary)

Feedback can modify the dynamics!

I position-feedback changes stiffness.
I rate-feedback changes damping.
The Wright Flyer was unstable but maneuverable.
Modern fighters are also designed to be unstable/maneuverable,

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Design of Dynamics (Summary)

Feedback can modify the dynamics!

I position-feedback changes stiffness.
I rate-feedback changes damping.
The Wright Flyer was unstable but maneuverable.
Modern fighters are also designed to be unstable/maneuverable,
I but Stability Augmentation Systems (SAS) completely hide the instabilities
from the pilot!

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 to the current the dynamics relating velocity to the input of the current controller is
Creating Modularity
approximately an integrator, because force is proportional to current and angular
acceleration is proportional to force. This simplified model can be used to design
the velocity loop so that effects of friction and other disturbances are reduced.
With a well-designed
Components velocity
can be loop, the
individually designinofathe
replaced positionsystem.
modular loop is also simple.
The loops can also be tuned sequentially starting with the inner loop. The architec-
ture illustrates how feedback can be used to simplify modeling and create modular

vr
yr Ir F
PC Σ y
VC Σ I v 1
CC Amplifier Motor
s

Current loop

Velocity loop

Position loop

Figure 1.12: Block diagram of a system for position control. The system has three cascaded
Figure: Cascaded Control
loops for control of current, velocity and position.

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 to the current the dynamics relating velocity to the input of the current controller is
Creating Modularity
approximately an integrator, because force is proportional to current and angular
acceleration is proportional to force. This simplified model can be used to design
the velocity loop so that effects of friction and other disturbances are reduced.
With a well-designed
Components velocity
can be loop, the
individually designinofathe
replaced positionsystem.
modular loop is also simple.
The loops can also be tuned sequentially starting with the inner loop. The architec-
Feedback maintains their input/output behaviour.
ture illustrates how feedback can be used to simplify modeling and create modular

vr
yr Ir F
PC Σ y
VC Σ I v 1
CC Amplifier Motor
s

Current loop

Velocity loop

Position loop

Figure 1.12: Block diagram of a system for position control. The system has three cascaded
Figure: Cascaded Control
loops for control of current, velocity and position.

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Challenges of Feedback

Feedback can introduce instability.

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Challenges of Feedback

Feedback can introduce instability.

I Too much corrective action can lead to instability.

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Challenges of Feedback

Feedback can introduce instability.

I Too much corrective action can lead to instability.
I We are all familiar with the effects of positive-feedback on a microphone!

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Challenges of Feedback

Feedback can introduce instability.

I Too much corrective action can lead to instability.
I We are all familiar with the effects of positive-feedback on a microphone!
Sensor/measurement noise.

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Challenges of Feedback

Feedback can introduce instability.

I Too much corrective action can lead to instability.
I We are all familiar with the effects of positive-feedback on a microphone!
Sensor/measurement noise.
Costs and Complexity.

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Outline

1 Feedback and Feedforward Control

2 Feedback Properties

3 Simple Feedback Forms

4 Combining Feedback with Logic

 On-Off (Bang-Bang) Control
(
umax if e > 0
u=
umin if e < 0
where e = r − y, and u is the actuation command.
1-18 Simple on-off control usually overreacts. CHAPTER CHAPTER 1. IN
1. INTRODUCTION
CHAPTER 1. INTRODUCT

u u
u u u
u u u
u

e e e e e e e e

On-off
(a)control
(a) on-off
On-off
(a) On-off
control control (b) Dead(b)
(bang-bang) zone
(b)Dead (b) Dead zone (c)
zone
dead-zone (c)Hysteresis (c) Hyste
(c) Hysteresis
hysteresis

13: Input/output
FigureFigure 1.13:characteristics
1.13: Input/output of on-offofcontrollers.
characteristics
Input/output Eachcontrollers.
plot
on-offofcontrollers.
characteristics on-off shows
Each the
plot Eachinput
shows theon
plot input on
shows
ontal axis and
he horizontal the corresponding output on the vertical axis. Ideal on-off control
the horizontal axis and the corresponding output on the vertical axis. Ideal on-oi
axis and the corresponding output on the vertical axis. Ideal on-off is
control
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 PID Control
Z t
de(t)
u(t) = kp e(t) + kI e(τ )dτ + kd
0 dt
CHAPTER 1. INTRODUC

Error Present
Past Future

Time
t t + Td
gure 1.14: Action of a PID controller.
Figure: At time
The rationale fort,PID
thecontrol
proportional term depends on t
stantaneous value of the error. The integral portion of the feedback is based on the integr
the error up to time t (shaded portion). The derivative term provides an estimate of t
owth or decay
Haydar of the error over time Control
(IST) by looking
Systems at the rate of change of2018
June 8, the error.
24 / 25
Outline

1 Feedback and Feedforward Control

2 Feedback Properties

3 Simple Feedback Forms

4 Combining Feedback with Logic

 Cruise Control
WITH LOGIC

off

set Cruise
on cancel
Off Standby brake resume

off
Hold
off
machine for cruise control
Figure: system.
Finite state The control.
machine for cruise figure on the left sh
o control the system. The controller can be in one of four mo
s in the diagram on the right. Transition between the mod
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