APR_L1.txt

Adaptive and Predictive Control
L1: Introduction

Dr.-Ing. Stefan Sosnowski
Institute for Information-Oriented Control
Technische Universit¨t M¨nchen
a
u
APR Lecture, summer semester 2014

www.itr.ei.tum.de

Organizational Info
Hours:

2 SWS lecture, 1 SWS exercises,
1 SWS tutorials

Exercises:

Denis Cehajic, M.H. Mamduhi

Time :

Monday 13:15 to 14:45, room N0507
Thursday 13:15 to 14:45, room N0507

Consultation hours:

Please make an appointment via eMail:
sosnowski@tum.de, denis.cehajic@tum.de,
mh.mamduhi@tum.de

Introduction

2

Location

Address:
Barerstr. 21, 4. OG
80333 M¨nchen
u

Building: 0305 S5 (old LRZ)
Area: South-East-Area

Introduction

3

Organizational Info
Exams:

Midterm:
- Participation is optional
- One grade step bonus for final exam grade
- written exam
Final exam:
- 90 min written exam

Materials:

Moodle / Elearning
http://www.moodle.tum.de/
- Lecture slides
- Exercises
- Solutions to exercises
- Complementary material
- Notifications

Introduction

4

Recommended Literature
Adaptive Control: Second Edition, K. J. Astrom and D. B.
Wittenmark, [Astrom and Wittenmark 2008]
Model Predictive Control, E. F. Camacho and C. B. Alba,
[Camacho and Alba 2007]

Further Reading:
Adaptive Control Design and Analysis, G. Tao, [Tao 2003]
Constrained Control and Estimation, G. C. Goodwin, J. A. De
Don´, and M. M. Seron, [Goodwin, Don´, and Seron 2005]
a
a
Adaptive Control Tutorial, P. Ioannou and B. Fidan, [Ioannou and
Fidan 2006]

Introduction

5

Motivation

to adapt (latin: ”adaptare”): Make (something) suitable for a new
use or purpose; modify1
In control ⇒ modify the controller according to changes in the
plant

1

definition: Oxford dictionary
Introduction

6

Changes in System-behavior: Example 1

Figure: X15 experimental aircraft

Introduction

7

Flight Control

Table: Parameter changes
Mach
Altitude [ft]
a11
a12
a13
a21
a22
a23
b1
λ1
λ2

0.5
5000

1.5
35000

-0.9896
17.41
96.15
0.2648
-0.8512
-11.39
-97.78
-3.07
1.23

-0.51262
26.96
178.9
-0.6896
-1.225
-30.38
-175.6
− 0.87 ± 4.3i
− 0.87 ± 4.3i

Pitch angle Θ
˙
Pitch rate q = Θ
Normal acceleration Nz
Elevon angle δe
Input to elevon servo u


 
a11 a12 a13
b1
x = a21 a22 a23  x +  0  u
˙
0
0 −a
a

where xT = (Nz

˙
Θ δe )

Introduction

8

Flight Control

Table: Parameter changes
Mach
Altitude [ft]
a11
a12
a13
a21
a22
a23
b1
λ1
λ2

0.5
5000

1.5
35000

-0.9896
17.41
96.15
0.2648
-0.8512
-11.39
-97.78
-3.07
1.23

-0.51262
26.96
178.9
-0.6896
-1.225
-30.38
-175.6
− 0.87 ± 4.3i
− 0.87 ± 4.3i

unstable

poorly
damped

Pitch angle Θ
˙
Pitch rate q = Θ
Normal acceleration Nz
Elevon angle δe
Input to elevon servo u


 
a11 a12 a13
b1
x = a21 a22 a23  x +  0  u
˙
0
0 −a
a

where xT = (Nz

˙
Θ δe )

Introduction

8

Changes in System-behavior: Example 2
Hard disk drives (HDD)
Data is written in concentric
tracks
Track-following: disturbance
rejection problem
Disturbance consists of
RRO (repeatable runout) –
imperfections on the tracks,
etc.
NRRO (non-repeatable
runout) – vibrations,
ball-bearing imperfections,
etc.
Introduction

9

Changes in System-behavior: Example 3
Effects of waves on ship steering by an autopilot

wind speed: 2-4
m/s

wind speed: 18-20
m/s

waves have a dominating effect on the ship heading and speed
autopilot has to cope with large changes of wave frequencies
(factor 3)
Introduction

10

Changes in System-behavior: Example 3
Adaptive autopilot

PID autopilot

Introduction

11

Changes in System-behavior: Example 4
Underwater Robotics
6D motion
Dynamics dependent on center of mass and motion direction
Equations of motion: highly coupled and non-linear in every
degree of freedom
Online estimation through recursive least-squares optimization
with forgetting factor

Introduction

12

Changes in System-behavior: Example 5
Cooperative manipulation with robots
Uncertainty in kinematic parameters
Least-squares estimation of rigid transformations
Minimization of actuator torques

Introduction

13

Changes in System-behavior: Example 5
Cooperative manipulation with robots
Joint manipulation with haptic coupling
Partial knowledge of grasp geometries
Control design for closed kinematic chains
Limited availability of information on each robot

Introduction

14

Other changes in System-behavior

Friction
Temperature
Load
etc. . .

Introduction

15

Parameter Variation: Example 1
Influence of parameter variations on the system behavior
G(s) =
open loop

1
,
(s + 1)(s + a)

a ∈ [−0.01, 0.01]

closed loop

Introduction

16

Parameter Variation: Example 1
Influence of parameter variations on the system behavior
G(s) =
open loop

1
,
(s + 1)(s + a)

a ∈ [−0.01, 0.01]

closed loop

Introduction

16

Parameter Variation: Example 2
Influence of parameter variations on the system behavior
G(s) =
open loop

400(1 − T s)
,
(s + 1)(s + 20)(1 + T s)

T ∈ [0, 0.03]

closed loop

Introduction

17

Parameter Variation: Example 2
Influence of parameter variations on the system behavior
G(s) =
open loop

400(1 − T s)
,
(s + 1)(s + 20)(1 + T s)

T ∈ [0, 0.03]

closed loop

Introduction

17

History of Adaptive Control

Figure: Development of adaptive control methods [IoannouSlides]
Introduction

18

Adaptive Control Loop

Figure: Basic concept of an adaptive control loop

Introduction

19

Self-tuning Regulator

Figure: Self-tuning regulator loop

Introduction

20

Model-Reference Adaptive Systems

Figure: MRAS block diagram

Introduction

21

Gain Scheduling

Figure: Gain scheduling control loop

Introduction

22

Predictive Control

Model based computation of future system behavior based on
future reference values
For each timestep: Calculate optimal control input (cost
function)
Use of a moving prediction horizon
Use of constraints on inputs and state variables
Introduction

23

MPC Analogy

Figure: Analogy of the model predictive control idea

Introduction

24

MPC structure

Figure: Basic structure of an MPC loop
Introduction

25

Adaptation and Prediction
Adaptation:

Prediction:

adjust parameters of the
current controller to current
(and past) process states

adapt model to current (and
past) process states to predict
future behavior and compute
optimal control strategy

⇒ Adaptive control

⇒ Predictive control

Introduction

26

Content
1. Introduction to Adaptive and Predictive Control
2. Parameter Estimation
3. Self tuning regulators, pole placement
4. Model Reference Adaptive systems
5. Autotuning, Gain Scheduling
6. Practical Issues and Implementation, Applications

Introduction

27

Content

7. Stochastic Adaptive Controllers, Predictive Self-tuning
controllers
8. Fixed horizon optimal control, Receding horizon optimal control
(RHC)
9. Constrained Linear Quadratic Optimal Control
10. Model predictive control, Generalized predictive control

Introduction

28

References

Karl J Astrom and Dr. Bjorn Wittenmark.
Adaptive Control: Second Edition (Dover Books on Electrical Engineering). Second Edi.
Dover Publications, 2008. isbn: 9780486462783.
Eduardo F Camacho and Carlos Bordons Alba.
Model Predictive Control (Advanced Textbooks in Control and Signal Processing). 2nd. Springer, 2007.
isbn: 9781852336943.
Graham C. Goodwin, Jos´ A. De Don´, and Mar´ M. Seron.
e
a
ıa
Constrained Control and Estimation: an optimisation approach. Communications and Control Engineering.
London: Springer-Verlag, 2005. isbn: 1-85233-548-3. doi: 10.1007/b138145.
Petros Ioannou and Bar´p Fidan. Adaptive Control Tutorial (Advances in Design and Control).
y
SIAM, Society for Industrial and Applied Mathematics, 2006. isbn: 9780898716153.
Gang Tao. Adaptive Control Design and Analysis (Adaptive and Learning Systems for Signal Processing,
Communications and Control Series). 1st. Wiley-IEEE Press, 2003, p. 640. isbn: 9780471274520.

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